Showing papers on "Statistical hypothesis testing published in 2001"

A new method for non-parametric multivariate analysis of variance

Abstract: Hypothesis-testing methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps more intuitive formulation for ANOVA (based on sums of squared distances) to complement the description pro- vided by McArdle and Anderson (in press) for the analysis of any linear model. It is an improvement on previous non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack of formal assumptions of other non-parametric methods. The test- statistic is a multivariate analogue to Fisher's F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.

Fitting multivariate models to community data: a comment on distance‐based redundancy analysis

Abstract: Nonparametric multivariate analysis of ecological data using permutation tests has two main challenges: (1) to partition the variability in the data according to a complex design or model, as is often required in ecological experiments, and (2) to base the analysis on a multivariate distance measure (such as the semimetric Bray-Curtis measure) that is reasonable for ecological data sets. Previous nonparametric methods have succeeded in one or other of these areas, but not in both. A recent contribution to Ecological Monographs by Legendre and Anderson, called distance-based redundancy analysis (db-RDA), does achieve both. It does this by calculating principal coordinates and subsequently correcting for negative eigenvalues, if they are present, by adding a constant to squared distances. We show here that such a correction is not necessary. Partitioning can be achieved directly from the distance matrix itself, with no corrections and no eigenanalysis, even if the distance measure used is semimetric. An ecological example is given to show the differences in these statistical methods. Empirical simulations, based on parameters estimated from real ecological species abundance data, showed that db-RDA done on multifactorial designs (using the correction) does not have type 1 error consistent with the significance level chosen for the analysis (i.e., does not provide an exact test), whereas the direct method described and advocated here does.

The psychometric function: I. Fitting, sampling, and goodness of fit

Abstract: The psychometric function relates an observer’s performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function’s parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (orlapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function’s parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditionalX2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.

The local power of some unit root tests for panel data

Abstract: To test the hypothesis of a difference stationary time series against a trend stationary alternative, Levin & Lin (1993) and Im, Pesaran & Shin (1997) suggest bias adjusted t-statistics. Such corrections are necessary to account for the nonzero mean of the t-statistic in the case of an OLS detrending method. In this chapter the local power of panel unit root statistics against a sequence of local alternatives is studied. It is shown that the local power of the test statistics is affected by two different terms. The first term represents the asymptotic effect on the bias due to the detrending method and the second term is the usual location parameter of the limiting distribution under the sequence of local alternatives. It is argued that both terms can offset each other so that the test has no power against the sequence of local alternatives. These results suggest to construct test statistics based on alternative detrending methods. We consider a class of t-statistics that do not require a bias correction. The results of a Monte Carlo experiment suggest that avoiding the bias can improve the power of the test substantially.

The Abuse of Power: The Pervasive Fallacy of Power Calculations for Data Analysis

Abstract: It is well known that statistical power calculations can be valuable in planning an experiment. There is also a large literature advocating that power calculations be made whenever one performs a statistical test of a hypothesis and one obtains a statistically nonsignificant result. Advocates of such post-experiment power calculations claim the calculations should be used to aid in the interpretation of the experimental results. This approach, which appears in various forms, is fundamentally flawed. We document that the problem is extensive and present arguments to demonstrate the flaw in the logic.

Modelling and quantitative methods in fisheries

Abstract: Fisheries and Modelling Fish Population Dynamics The Objectives of Stock Assessment Characteristics of Mathematical Models Types of Model Structure Simple Population Models Introduction Assumptions-Explicit and Implicit Density-Independent Growth Density-Dependent Models Responses to Fishing Pressure The Logistic Model in Fisheries Age-Structured Models Simple Yield-per-Recruit Model Parameter Estimation Models and Data Least Squared Residuals Nonlinear Estimation Likelihood Bayes' Theorem Concluding Remarks Computer-Intensive Methods Introduction Resampling Randomization Tests Jackknife Methods Bootstrapping Methods Monte Carlo Methods Bayesian Methods Relationships between Methods Computer Programming Randomization Tests Introduction Hypothesis Testing Randomization of Structured Data Statistical Bootstrap Methods The Jackknife and Pseudo Values The Bootstrap Bootstrap Statistics Bootstrap Confidence Intervals Concluding Remarks Monte Carlo Modelling Monte Carlo Models Practical Requirements A Simple Population Model A Non-Equilibrium Catch Curve Concluding Remarks Characterization of Uncertainty Introduction Asymptotic Standard Errors Percentile Confidence Intervals Using Likelihoods Likelihood Profile Confidence Intervals Percentile Likelihood Profiles for Model Outputs Markov Chain Monte Carlo (MCMC) Conclusion Growth of Individuals Growth in Size von Bertalanffy Growth Model Alternatives to von Bertalanffy Comparing Growth Curves Concluding Remarks Stock Recruitment Relationships Recruitment and Fisheries Stock Recruitment Biology Beverton-Holt Recruitment Model Ricker Model Deriso's Generalized Model Residual Error Structure The Impact of Measurement Errors Environmental Influences Recruitment in Age-Structured Models Concluding Remarks Surplus Production Models Introduction Equilibrium Methods Surplus Production Models Observation Error Estimates Beyond Simple Models Uncertainty of Parameter Estimates Risk Assessment Projections Practical Considerations Conclusions Age-Structured Models Types of Models Cohort Analysis Statistical Catch-at-Age Concluding Remarks Size-Based Models Introduction The Model Structure Conclusion Appendix: The Use of Excel in Fisheries Bibliography Index

On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals

Abstract: To judge whether the difference between two point estimates is statistically significant, data analysts often examine the overlap between the two associated confidence intervals. We compare this technique to the standard method of testing significance under the common assumptions of consistency, asymptotic normality, and asymptotic independence of the estimates. Rejection of the null hypothesis by the method of examining overlap implies rejection by the standard method, whereas failure to reject by the method of examining overlap does not imply failure to reject by the standard method. As a consequence, the method of examining overlap is more conservative (i.e., rejects the null hypothesis less often) than the standard method when the null hypothesis is true, and it mistakenly fails to reject the null hypothesis more frequently than does the standard method when the null hypothesis is false. Although the method of examining overlap is simple and especially convenient when lists or graphs of confidence int...

How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test.

Abstract: The Mantel test provides a means to test the association between distance matrices and has been widely used in ecological and evolutionary studies. Recently, another permutation test based on a Procrustes statistic (PROTEST) was developed to compare multivariate data sets. Our study contrasts the effectiveness, in terms of power and type I error rates, of the Mantel test and PROTEST. We illustrate the application of Procrustes superimposition to visually examine the concordance of observations for each dimension separately and how to conduct hypothesis testing in which the association between two data sets is tested while controlling for the variation related to other sources of data. Our simulation results show that PROTEST is as powerful or more powerful than the Mantel test for detecting matrix association under a variety of possible scenarios. As a result of the increased power of PROTEST and the ability to assess the match for individual observations (not available with the Mantel test), biologists now have an additional and powerful analytical tool to study ecological and evolutionary relationships.

Statistical methods for geography

Abstract: Introduction to Statistical Analysis in Geography Probability and Probability Models Hypothesis Testing and Sampling Analysis of Variance Correlation Introduction to Regression Analysis More on Regression Spatial Patterns Some Spatial Aspects of Regression Analysis Data Reduction Factor Analysis and Cluster Analysis

Calibration of p Values for Testing Precise Null Hypotheses

Abstract: P values are the most commonly used tool to measure evidence against a hypothesis or hypothesized model. Unfortunately, they are often incorrectly viewed as an error probability for rejection of the hypothesis or, even worse, as the posterior probability that the hypothesis is true. The fact that these interpretations can be completely misleading when testing precise hypotheses is first reviewed, through consideration of two revealing simulations. Then two calibrations of a ρ value are developed, the first being interpretable as odds and the second as either a (conditional) frequentist error probability or as the posterior probability of the hypothesis.

Defending against statistical steganalysis

Abstract: The main purpose of steganography is to hide the occurrence of communication. While most methods in use today are invisible to an observer's senses, mathematical analysis may reveal statistical anomalies in the stego medium. These discrepancies expose the fact that hidden communication is happening. This paper presents improved methods for information hiding. One method uses probabilistic embedding to minimize modifications to the cover medium. Another method employs error-correcting codes, which allow the embedding process to choose which bits to modify in a way that decreases the likelihood of being detected. In addition, we can hide multiple data sets in the same cover medium to provide plausible deniability. To prevent detection by statistical tests, we preserve the statistical properties of the cover medium. After applying a correcting transform to an image, statistical steganalysis is no longer able to detect the presence of steganography. We present an a priori estimate to determine the amount of data that can be hidden in the image while still being able to maintain frequency count based statistics. This way, we can quickly choose an image in which a message of a given size can be hidden safely. To evaluate the effectiveness of our approach, we present statistical tests for the JPEG image format and explain how our new method defeats them.

The power of statistical tests in meta-analysis.

Abstract: Calculations of the power of statistical tests are important in planning research studies (including meta-analyses) and in interpreting situations in which a result has not proven to be statistically significant. The authors describe procedures to compute statistical power of fixed- and random-effects tests of the mean effect size, tests for heterogeneity (or variation) of effect size parameters across studies, and tests for contrasts among effect sizes of different studies. Examples are given using 2 published meta-analyses. The examples illustrate that statistical power is not always high in meta-analysis.

Statistical methods in spatial epidemiology

Abstract: Preface and Acknowledgements to Second Edition Preface and Acknowledgements I: The Nature of Spatial Epidemiology 1 Definitions, Terminolgy and Data Sets 11 Map Hypotheses and Modelling Approaches 12 Definitions and Data Examples 13 Further definitions 14 Some Data Examples 2Scales of Measurement and Data Availability 21 Small Scale 22 Large Scale 23 Rate Dependence 24 DataQuality and the Ecological Fallacy 25 Edge Eects 3Geographical Representation and Mapping 31 Introduction and Definitions 32 Maps and Mapping 33 Statistical Accuracy 34 Aggregation 35 Mapping Issues related toAggregated Data 36 Conclusions 4Basic Models 41 Sampling Considerations 42 Likelihood-based and Bayesian Approaches 43 Point EventModels 44 CountModels 5Exploratory Approaches, Parametric Estimation and Inference 51 ExploratoryMethods 52 Parameter Estimation 53 Residual Diagnostics 54 Hypothesis Testing 55 Edge Eects II:Important Problems in Spatial Epidemiology 6Small Scale: Disease Clustering 61 Definition of Clusters and Clustering 62 Modelling Issues 63 Hypothesis Tests for Clustering 64 Space-Time Clustering 65 Clustering Examples 66 OtherMethods related to clustering 7Small Scale: Putative Sources of Hazard 71 Introduction 72 StudyDesign 73 Problems of Inference 74 Modelling the Hazard Exposure Risk 75 Models for Case Event Data 76 ACase Event Example 77 Models for CountData 78 ACountData Example 79 OtherDirections 8 Large Scale: Disease Mapping 81 Introduction 82 Simple Statistical Representation 83 BasicModels 84 AdvancedMethods 85 Model Variants and Extensions 86 ApproximateMethods 87 MultivariateMethods 88 Evaluation ofModel Performance 89 Hypothesis Testing in DiseaseMapping 810 Space-Time DiseaseMapping 811 Spatial Survival and longitudinal data 812 DiseaseMapping: Case Studies 9Ecological Analysis and Scale Change 91 Ecological Analysis: Introduction 92 Small-ScaleModelling Issues 93 Changes of Scale andMAUP 94 A Simple Example: Sudden Infant Death in North Carolina 95 ACase Study: Malaria and IDDM 10Infectious Disease Modelling 101 Introduction 102 GeneralModelDevelopment 103 SpatialModelDevelopment 104 Modelling Special Cases for Individual Level Data 105 Survival Analysis with spatial dependence 106 Individual level data example 107 Underascertainment and Censoring 108 Conclusions 11Large Scale: Surveillance 111 Process ControlMethodology 112 Spatio-Temporal Modelling 113 Spatio-TemporalMonitoring 114 Syndromic Surveillance 115 Multivariate-Mulitfocus Surveillance 116 Bayesian Approaches 117 Computational Considerations 118 Infectious Diseases 119 Conclusions Appendix A:Monte Carlo Testing, Parametric Bootstrap and Simulation Envelopes Appendix B:Markov ChainMonte Carlo Methods Appendix C:Algorithms and Software Appendix D: Glossary of Estimators Appendix E:Software Bibliography Index

Invited Paper: SUGGESTIONS FOR PRESENTING THE RESULTS OF DATA ANALYSES

Abstract: We give suggestions for the presentation of research results from frequentist, information-theoretic, and Bayesian analysis paradigms, followed by several general suggestions. The information-theoretic and Bayesian methods offer alternative approaches to data analysis and inference compared to traditionally used methods. Guidance is lacking on the presentation of results under these alternative procedures and on nontesting aspects of classical frequentist methods of statistical analysis. Null hypothesis testing has come under intense criticism. We recommend less reporting of the results of statistical tests of null hypotheses in cases where the null is surely false anyway, or where the null hypothesis is of little interest to science or management. JOURNAL OF WILDLIFE MANAGEMENT 65(3):373-378

Suggestions for presenting the results of data analyses

Abstract: We give suggestions for the presentation of research results from frequentist, information-theoretic, and Bayesian analysis paradigms, followed by several general suggestions. The information-theoretic and Bayesian methods offer alternative approaches to data analysis and inference compared to traditionally used methods. Guidance is lacking on the presentation of results under these alternative procedures and on nontesting aspects of classical frequentist methods of statistical analysis. Null hypothesis testing has come under intense criticism. We recommend less reporting of the results of statistical tests of null hypotheses in cases where the null is surely false anyway, or where the null hypothesis is of little interest to science or management.

Testing When a Parameter is on the Boundary of the Maintained Hypothesis

Abstract: This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi-likelihood ratio, rescaled quasi-likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models. Examples treated in the paper are: (i) tests of the null hypothesis of no conditional heteroskedasticity in a GARCH(1, 1) regression model and (ii) tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with (possibly) correlated random coefficients.

Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials

Abstract: The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This article begins with a review of these quantities, their interpretation, and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented that builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low-variance gaussian process. It is found that in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus. Although the material discussed is of general applicability to point processes, attention will be confined to sequences of neuronal action potentials (spike trains), the motivation for this work.

An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative

Abstract: We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n -1/2 . Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n -1/2 . There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.

Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: an integrated alternative method of conducting null hypothesis statistical tests

Abstract: Null hypothesis statistical testing (NHST) has been debated extensively but always successfully defended. The technical merits of NHST are not disputed in this article. The widespread misuse of NHST has created a human factors problem that this article intends to ameliorate. This article describes an integrated, alternative inferential confidence interval approach to testing for statistical difference, equivalence, and indeterminacy that is algebraically equivalent to standard NHST procedures and therefore exacts the same evidential standard. The combined numeric and graphic tests of statistical difference, equivalence, and indeterminacy are designed to avoid common interpretive problems associated with NHST procedures. Multiple comparisons, power, sample size, test reliability, effect size, and cause-effect ratio are discussed. A section on the proper interpretation of confidence intervals is followed by a decision rule summary and caveats.

Robust Inference for Generalized Linear Models

Abstract: By starting from a natural class of robust estimators for generalized linear models based on the notion of quasi-likelihood, we define robust deviances that can be used for stepwise model selection as in the classical framework. We derive the asymptotic distribution of tests based on robust deviances, and we investigate the stability of their asymptotic level under contamination. The binomial and Poisson models are treated in detail. Two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures.

Constrained Statistical Inference: Inequality, Order, and Shape Restrictions

Abstract: Dedication. Preface. 1. Introduction. 1.1 Preamble. 1.2 Examples. 1.3 Coverage and Organization of the Book. 2. Comparison of Population Means and Isotonic Regression. 2.1 Ordered Hypothesis Involving Population Means. 2.2 Test of Inequality Constraints. 2.3 Isotonic Regression. 2.4 Isotonic Regression: Results Related to Computational Formulas. 3. Two Inequality Constrained Tests on Normal Means. 3.1 Introduction. 3.2 Statement of Two General Testing Problems. 3.3 Theory: The Basics in 2 Dimensions. 3.4 Chi-bar-square Distribution. 3.5 Computing the Tail Probabilities of chi-bar-square Distributions. 3.6 Detailed Results relating to chi-bar-square Distributions. 3.7 LRT for Type A Problems: V is known. 3.8 LRT for Type B Problems: V is known. 3.9 Inequality Constrained Tests in the Linear Model. 3.10 Tests When V is known. 3.11 Optimality Properties. 3.12 Appendix 1: Convex Cones. 3.13 Appendix B. Proofs. 4. Tests in General Parametric Models. 4.1 Introduction. 2.2 Preliminaries. 4.3 Tests of Rtheta = 0 against Rtheta 0. 4.4 Tests of h(theta) = 0. 4.5 An Overview of Score Tests with no Inequality Constraints. 4.6 Local Score-type Tests of Ho : psi = 0 vs H1 : psi &epsis PSI. 4.7 Approximating Cones and Tangent Cones. 4.8 General Testing Problems. 4.9 Properties of the mle When the True Value is on the Boundary. 5. Likelihood and Alternatives. 5.1 Introduction. 5.2 The Union-Intersection principle. 5.3 Intersection Union Tests (IUT). 5.4 Nanparametrics. 5.5 Restricted Alternatives and Simes-type Procedures. 5.6 Concluding Remarks. 6. Analysis of Categorical Data. 6.1 Motivating Examples. 6.2 Independent Binomial Samples. 6.3 Odds Ratios and Monotone Dependence. 6.4 Analysis of 2 x c Contingency Tables. 6.5 Test to Establish that Treatment is Better than Control. 6.6 Analysis of r x c Tables. 6.7 Square Tables and Marginal Homogeneity. 6.8 Exact Conditional Tests. 6.9 Discussion. 7. Beyond Parametrics. 7.1 Introduction. 7.2 Inference on Monotone Density Function. 7.3 Inference on Unimodal Density Function. 7.4 Inference on Shape Constrained Hazard Functionals. 7.5 Inference on DMRL Functions. 7.6 Isotonic Nonparametric Regression: Estimation. 7.7 Shape Constraints: Hypothesis Testing. 8. Bayesian Perspectives. 8.1 Introduction. 8.2 Statistical Decision Theory Motivations. 8.3 Stein's Paradox and Shrinkage Estimation. 8.4 Constrained Shrinkage Estimation. 8.5 PC and Shrinkage Estimation in CSI. 8.6 Bayes Tests in CSI. 8.7 Some Decision Theoretic Aspects: Hypothesis Testing. 9. Miscellaneous Topics. 9.1 Two-sample Problem with Multivariate Responses. 9.2 Testing that an Identified Treatment is the Best: The mini-test. 9.3 Cross-over Interaction. 9.4 Directed Tests. Bibliography. Index.

Research frontiers in null model analysis

Abstract: Null models are pattern-generating models that deliberately exclude a mechanism of interest, and allow for randomization tests of ecological and biogeographic data. Although they have had a controversial history, null models are widely used as statistical tools by ecologists and biogeographers. Three active research fronts in null model analysis include biodiversity measures, species co-occurrence patterns, and macroecology. In the analysis of biodiversity, ecologists have used random sampling procedures such as rarefaction to adjust for differences in abundance and sampling effort. In the analysis of species co-occurrence and assembly rules, null models have been used to detect the signature of species interactions. However, controversy persists over the details of computer algorithms used for randomizing presence-absence matrices. Finally, in the newly emerging discipline of macroecology, null models can be used to identify constraining boundaries in bivariate scatterplots of variables such as body size, range size, and population density. Null models provide specificity and flexibility in data analysis that is often not possible with conventional statistical tests.

On tests of the overall treatment effect in meta-analysis with normally distributed responses.

Abstract: For the meta-analysis of controlled clinical trials or epidemiological studies, in which the responses are at least approximately normally distributed, a refined test for the hypothesis of no overall treatment effect is proposed. The test statistic is based on a direct estimation function for the variance of the overall treatment effect estimator. As outcome measures, the absolute and the standardized difference between means are considered. In simulation studies it is shown that the proposed test keeps the prescribed significance level very well in contrast to the commonly used tests in the fixed effects and random effects model, respectively, which can become very liberal. Furthermore, just for using the proposed test it is not necessary to choose between the fixed effects and the random effects approach in advance.

Chapter 52 The Bootstrap

Abstract: The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that are more accurate than the approximations of first-order asymptotic distribution theory. The reductions in the differences between true and nominal coverage or rejection probabilities can be very large. The bootstrap is a practical technique that is ready for use in applications. This chapter explains and illustrates the usefulness and limitations of the bootstrap in contexts of interest in econometrics. The chapter outlines the theory of the bootstrap, provides numerical illustrations of its performance, and gives simple instructions on how to implement the bootstrap in applications. The presentation is informal and expository. Its aim is to provide an intuitive understanding of how the bootstrap works and a feeling for its practical value in econometrics.

Effect size, power, and sample size determination for structured means modeling and MIMIC approaches to between-groups hypothesis testing of means on a single latent construct.

Abstract: While effect size estimates, post hoc power estimates, and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables (e.g., ANOVA), such measures and methods have not been articulated for analyses involving latent means. The current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and MIMIC approaches to hypothesis testing about differences among means on a single latent construct. These measures are then related to post hoc power analysis, a priori sample size determination, and a relevant measure of construct reliability.

Detecting graph-based spatial outliers: algorithms and applications (a summary of results)

Abstract: Identification of outliers can lead to the discovery of unexpected, interesting, and useful knowledge. Existing methods are designed for detecting spatial outliers in multidimensional geometric data sets, where a distance metric is available. In this paper, we focus on detecting spatial outliers in graph structured data sets. We define statistical tests, analyze the statistical foundation underlying our approach, design several fast algorithms to detect spatial outliers, and provide a cost model for outlier detection procedures. In addition, we provide experimental results from the application of our algorithms on a Minneapolis-St.Paul(Twin Cities) traffic dataset to show their effectiveness and usefulness.

Promoting Good Statistical Practices: Some Suggestions

Abstract: Researchers want to answer three basic questions: (a) Is an observed effect real or should it be attributed to chance? (b) If the effect is real, how large is it? and (c) Is the effect large enough to be useful? The first question concerning whether chance is a viable explanation for an observed effect is usually addressed with a null hypothesis significance test. A null hypothesis significance test tells us the probability of obtaining the effect or a more extreme effect if the null hypothesis is true. A significance test does not tell us how large the effect is or whether the effect is important or useful. Unfortunately, all too often the primary focus of research is on rejecting a null hypothesis and obtaining a small p value. The focus should be on what the data tell us about the phenomenon under investigation. This is not a new idea. Critics of significance testing have been saying it for years. For example, Frank Yates (1951), a contemporary of Ronald Fisher, observed that the use of the null hypothesis significance test

A Parametric Approach to Flexible Nonlinear Inference

Abstract: This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt = µ(xt) + et where the functional form of µ(.) is unknown. We propose viewing µ(.) itself as the outcome of a random process. The paper introduces a new stationary random random field m(.) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for µ(.). We view the parameters that characterize the relation between a given realization of m(.) and the particular value of µ(.) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions µ(.). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment tradeoff may explain the previously reported uneven empirical success of the Phillips Curve.