Showing papers on "Statistical hypothesis testing published in 1991"

Practical Statistics for Field Biology

Abstract: Measurement and Sampling Concepts. Processing Data. Presenting Data. Measuring the Average. Measuring Variability. Probability. Probability Distributions as Models of Dispersion. The Normal Distribution. Data Transformation. How Good are Our Estimates? The Basis of Statistical Testing. Analysing Frequencies. Measuring Correlations. Regression Analysis. Comparing Averages. Analysis of Variance - ANOVA. Multivariate Analysis. Appendices. Bibliography and Further Reading. Index.

Statistical Data Analysis in the Computer Age

Abstract: Most of our familiar statistical methods, such as hypothesis testing, linear regression, analysis of variance, and maximum likelihood estimation, were designed to be implemented on mechanical calculators. Modern electronic computation has encouraged a host of new statistical methods that require fewer distributional assumptions than their predecessors and can be applied to more complicated statistical estimators. These methods allow the scientist to explore and describe data and draw valid statistical inferences without the usual concerns for mathematical tractability. This is possible because traditional methods of mathematical analysis are replaced by specially constructed computer algorithms. Mathematics has not disappeared from statistical theory. It is the main method for deciding which algorithms are correct and efficient tools for automating statistical inference.

Optimal Inference in Cointegrated Systems

Abstract: Properties of maximum likelihood estimates of cointegrated systems are studied. Alternative formulations are considered, including a new triangular system error correction mechanism. We demonstrate that full system maximum likelihood brings the problem of inference within the family covered by the locally asymptotically mixed normal asymptotic theory, provided all unit roots have been eliminated by specification and data transformation. Methodological issues provide a major focus of the paper. Our results favor use of full system estimation in error correction mechanisms or subsystem methods that are asymptotically equivalent. They also point to disadvantages in the use of unrestricted VAR's formulated in levels and of certain single equation approaches to estimation of error correction mechanisms. Copyright 1991 by The Econometric Society.

Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?

Abstract: The standard conclusion that is drawn from this empirical evidence is that many or most aggregate economic time series contain a unit root. However, it is important to note that in this empirical work the unit root is set up as the null hypothesis testing is carried out ensures that the null hypothesis is accepted unless there is strong evidence against it. Therefore, an alternative explanation for the common failure to reject a unit root is simply that most economic time series are not very informative about whether or not there is a unit root; or, equivalently, that standard unit root tests are not very powerful against relevant alternatives.

Two guidelines for bootstrap hypothesis testing

Abstract: Two guidelines for nonparametric bootstrap hypothesis testing are highlighted. The first recommends that resampling be done in a way that reflects the null hypothesis, even when the true hypothesis is distant from the null. The second guideline argues that bootstrap hypothesis tests should employ methods that are already recognized as having good features in the closely related problem of confidence interval construction. Violation of the first guideline can seriously reduce the power of a test. Sometimes this reduction is spectacular, since it is most serious when the null hypothesis is grossly in error. The second guideline is of some importance when the conclusion of a test is equivocal. It has no direct bearing on power, but improves the level accuracy of a test.

Statistical Power and Design Requirements for Environmental Monitoring

Abstract: This paper discusses, from a philosophical perspective, the reasons for considering the power of any statistical test used in environmental biomonitoring. Power is inversely related to the probability of making a Type II error (i.e. low power indicates a high probability of Type II error). In the context of environmental monitoring, a Type II error is made when it is concluded that no environmental impact has occurred even though one has. Type II errors have been ignored relative to Type I errors (the mistake of concluding that there is an impact when one has not occurred), the rates of which are stipulated by the a values of the test. In contrast, power depends on the value of α, the sample size used in the test, the effect size to be detected, and the variability inherent in the data. Although power ideas have been known for years, only recently have these issues attracted the attention of ecologists and have methods been available for calculating power easily. Understanding statistical power gives three ways to improve environmental monitoring and to inform decisions about actions arising from monitoring. First, it allows the most sensitive tests to be chosen from among those applicable to the data. Second, preliminary power analysis can be used to indicate the sample sizes necessary to detect an environmental change. Third, power analysis should be used after any nonsignificant result is obtained in order to judge whether that result can be interpreted with confidence or the test was too weak to examine the null hypothesis properly. Power procedures are concerned with the statistical significance of tests of the null hypothesis, and they lend little insight, on their own, into the workings of nature. Power analyses are, however, essential to designing sensitive tests and correctly interpreting their results. The biological or environmental significance of any result, including whether the impact is beneficial or harmful, is a separate issue. The most compelling reason for considering power is that Type II errors can be more costly than Type I errors for environmental management. This is because the commitment of time, energy and people to fighting a false alarm (a Type I error) may continue only in the short term until the mistake is discovered. In contrast, the cost of not doing something when in fact it should be done (a Type II error) will have both short- and long-term costs (e.g. ensuing environmental degradation and the eventual cost of its rectification). Low power can be disastrous for environmental monitoring programmes.

The SRI IDES statistical anomaly detector

Abstract: SRI International's real-time intrusion-detection expert system (IDES) contains a statistical subsystem that observes behavior on a monitored computer system and adaptively learns what is normal for individual users and groups of users. The statistical subsystem also monitors observed behavior and identifies behavior as a potential intrusion (or misuse by authorized users) if it deviates significantly from expected behavior. The multivariate methods used to profile normal behavior and identify deviations from expected behavior are explained in detail. The statistical test for abnormality contains a number of parameters that must be initialized and the substantive issues relating to setting those parameter values are discussed. >

A Bayesian method for constructing Bayesian belief networks from databases

Abstract: This paper presents a Bayesian method for constructing Bayesian belief networks from a database of cases. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. We relate the methods in this paper to previous work, and we discuss open problems.

Detecting small, moving objects in image sequences using sequential hypothesis testing

Abstract: An algorithm is proposed for the solution of the class of multidimensional detection problems concerning the detection of small, barely discernible, moving objects of unknown position and velocity in a sequence of digital images. A large number of candidate trajectories, organized into a tree structure, are hypothesized at each pixel in the sequence and tested sequentially for a shift in mean intensity. The practicality of the algorithm is facilitated by the use of multistage hypothesis testing (MHT) for simultaneous inference, as well as the existence of exact, closed-form expressions for MHT test performance in Gaussian white noise (GWN). These expressions predict the algorithm's computation and memory requirements, where it is shown theoretically that several orders of magnitude of processing are saved over a brute-force approach based on fixed sample-size tests. The algorithm is applied to real data by using a robust preprocessing procedure to eliminate background structure and transform the image sequence into a residual representation, modeled as GWN. Results are verified experimentally on a variety of video image sequences. >

Procedures for two-sample comparisons with multiple endpoints controlling the experimentwise error rate.

Abstract: Clinical trials are often concerned with the comparison of two treatment groups with multiple endpoints. As alternatives to the commonly used methods, the T2 test and the Bonferroni method, O'Brien (1984, Biometrics 40, 1079-1087) proposes tests based on statistics that are simple or weighted sums of the single endpoints. This approach turns out to be powerful if all treatment differences are in the same direction [compare Pocock, Geller, and Tsiatis (1987, Biometrics 43, 487-498)]. The disadvantage of these multivariate methods is that they are suitable only for demonstrating a global difference, whereas the clinician is further interested in which specific endpoints or sets of endpoints actually caused this difference. It is shown here that all tests are suitable for the construction of a closed multiple test procedure where, after the rejection of the global hypothesis, all lower-dimensional marginal hypotheses and finally the single hypotheses are tested step by step. This procedure controls the experimentwise error rate. It is just as powerful as the multivariate test and, in addition, it is possible to detect significant differences between the endpoints or sets of endpoints.

Measures of Discrimination Skill in Probabilistic Judgment

Abstract: People's ability to assess probabilities of various events has been the topic of much interest in the areas of judgment, prediction, decision making, and memory. The evaluation of probabilistic judgments, however, raises interesting logical questions as to what it means to be a"good" judge. In this article, we focus on a normative concept of probabilistic accuracy that we call discrimination and present a measure of a judge's discrimination skill. This measure builds on an earlier index (Murphy, 1973) and has the advantages that (a) it can be interpreted as the percentage of variance accounted for by the judge and (b) it is unbiased. By way of deriving this new discrimination measure, we also show that it is related to Pearson's chi-square statistic, a result which may be useful in the future development of hypothesis testing and estimation procedures.

The local nature of hypothesis tests involving inequality constraints in nonlinear models

Abstract: This paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis. The paper is organized around a lemma which characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test. We then present two examples which illustrate several implications of this lemma. We also discuss the impact of these properties on the empirical implementation and interpretation of these test procedures.

Unequally spaced longitudinal data with AR(1) serial correlation.

Abstract: This paper discusses longitudinal data analysis when each subject is observed at different unequally spaced time points. Observations within subjects are assumed to be either uncorrelated or to have a continuous-time first-order autoregressive structure, possibly with observation error. The random coefficients are assumed to have an arbitrary between-subject covariance matrix. Covariates can be included in the fixed effects part of the model. Exact maximum likelihood estimates of the unknown parameters are computed using the Kalman filter to evaluate the likelihood, which is then maximized with a nonlinear optimization program. An example is presented where a large number of subjects are each observed at a small number of observation times. Hypothesis tests for selecting the best model are carried out using Wald's test on contrasts or likelihood ratio tests based on fitting full and restricted models.

The comparison of quantitative genetic parameters between populations

Abstract: A statistical method for comparing matrices of genetic variation and covariation between groups (e.g., species, populations, a single population grown in distinct environments) is proposed. This maximum-likelihood method provides a test of the overall null hypothesis that two covariance component matrices are identical. Moreover, when the overall null hypothesis is rejected, the method provides a framework for isolating the particular components that differ significantly between the groups. Simulation studies reveal that discouragingly large experiments are necessary to obtain acceptable power for comparing genetic covariance component matrices. For example, even in cases of a single trait measured on 900 individuals in a nested design of 100 sires and three dams per sire in each population, the power was only about 0.5 when additive genetic variance differed by a factor of 2.5. Nevertheless, this flexible method makes valid comparison of covariance component matrices possible.

Clinical Epidemiology and Biostatistics : A Primer for Clinical Investigators and Decision-Makers

Abstract: I Epidemiologic Research Design.- 1: Introduction.- 1.1 The Compatibility of the Clinical and Epidemiologic Approaches.- 1.2 Clinical Epidemiology: Main Areas of Interest.- 1.3 Historical Roots.- 1.4 Current and Future Relevance: Controversial Questions and Unproven Hypotheses.- 2: Measurement.- 2.1 Types of Variables and Measurement Scales.- 2.2 Sources of Variation in a Measurement.- 2.3 Properties of Measurement.- 2.4 "Hard" vs "Soft" Data.- 2.5 Consequences of Erroneous Measurement.- 2.6 Sources of Data.- 3: Rates.- 3.1 What is a Rate?.- 3.2 Prevalence and Incidence Rates.- 3.3 Stratification and Adjustment of Rates.- 3.4 Concluding Remarks.- 4: Epidemiologic Research Design: an Overview.- 4.1 The Research Objective: Descriptive vs Analytic Studies.- 4.2 Exposure and Outcome.- 4.3 The Three Axes of Epidemiologic Research Design.- 4.4 Concluding Remarks.- 5: Analytic Bias.- 5.1 Validity and Reproducibility of Exposure-Outcome Associations.- 5.2 Internal and External Validity.- 5.3 Sample Distortion Bias.- 5.4 Information Bias.- 5.5 Confounding Bias.- 5.6 Reverse Causality ("Cart-vs-Horse") Bias.- 5.7 Concluding Remarks.- 6: Observational Cohort Studies.- 6.1 Research Design Components.- 6.2 Analysis of Results.- 6.3 Bias Assessment and Control.- 6.4 Effect Modification and Synergism.- 6.5 Advantages and Disadvantages of Cohort Studies.- 7: Clinical Trials.- 7.1 Research Design Components.- 7.2 Assignment of Exposure (Treatment).- 7.3 Blinding in Clinical Trials.- 7.4 Analysis of Results.- 7.5 Interpretation of Results.- 7.6 Ethical Considerations.- 7.7 Advantages and Disadvantages of Clinical Trials.- 8: Case-Control Studies.- 8.1 Introduction.- 8.2 Research Design Components.- 8.3 Analysis of Results.- 8.4 Bias Assessment and Control.- 8.5 Advantages and Disadvantages of Case-Control Studies.- 9: Cross-Sectional Studies.- 9.1 Introduction.- 9.2 Research Design Components.- 9.3 Analysis of Results.- 9.4 Bias Assessment and Control.- 9.5 "Pseudo-Cohort" Cross-Sectional Studies.- 9.6 Advantages, Disadvantages, and Uses of Cross-Sectional Studies.- II Biostatistics.- 10: Introduction to Statistics.- 10.1 Variables.- 10.2 Populations, Samples, and Sampling Variation.- 10.3 Description vs Statistical Inference.- 10.4 Statistical vs Analytic Inference.- 11: Descriptive Statistics and Data Display.- 11.1 Continuous Variables.- 11.2 Categorical Variables.- 11.3 Concluding Remarks.- 12: Hypothesis Testing and P Values.- 12.1 Formulating and Testing a Research Hypothesis.- 12.2 The Testing of Ho.- 12.3 Type II Error and Statistical Power.- 12.4 Bayesian vs Frequentist Inference.- 13: Statistical Inference for Continuous Variables.- 13.1 Repetitive Sampling and the Central Limit Theorem.- 13.2 Statistical Inferences Using the t-Distribution.- 13.3 Calculation of Sample Sizes.- 13.4 Nonparametric Tests of Two Means.- 13.5 Comparing Three or More Means: Analysis of Variance.- 13.6 Control for Confounding Factors.- 14: Statistical Inference for Categorical Variables.- 14.1 Introduction to Categorical Data Analysis.- 14.2 Comparing Two Proportions.- 14.3 Statistical Inferences for a Single Proportion.- 14.4 Comparison of Three or More Proportions.- 14.5 Analysis of Larger (r x c) Contingency Tables.- 15: Linear Correlation and Regression.- 15.1 Linear Correlation.- 15.2 Linear Regression.- 15.3 Correlation vs Regression.- 15.4 Statistical Inference.- 15.5 Control for Confounding Factors.- 15.6 Rank (Nonparametric) Correlation.- III Special Topics.- 16: Diagnostic Tests.- 16.1 Introduction.- 16.2 Defining "Normal" and "Abnormal" Test Results.- 16.3 The Reproducibility and Validity of Diagnostic Tests.- 16.4 The Predictive Value of Diagnostic Tests.- 16.5 Bayes'I Epidemiologic Research Design.- 1: Introduction.- 1.1 The Compatibility of the Clinical and Epidemiologic Approaches.- 1.2 Clinical Epidemiology: Main Areas of Interest.- 1.3 Historical Roots.- 1.4 Current and Future Relevance: Controversial Questions and Unproven Hypotheses.- 2: Measurement.- 2.1 Types of Variables and Measurement Scales.- 2.2 Sources of Variation in a Measurement.- 2.3 Properties of Measurement.- 2.4 "Hard" vs "Soft" Data.- 2.5 Consequences of Erroneous Measurement.- 2.6 Sources of Data.- 3: Rates.- 3.1 What is a Rate?.- 3.2 Prevalence and Incidence Rates.- 3.3 Stratification and Adjustment of Rates.- 3.4 Concluding Remarks.- 4: Epidemiologic Research Design: an Overview.- 4.1 The Research Objective: Descriptive vs Analytic Studies.- 4.2 Exposure and Outcome.- 4.3 The Three Axes of Epidemiologic Research Design.- 4.4 Concluding Remarks.- 5: Analytic Bias.- 5.1 Validity and Reproducibility of Exposure-Outcome Associations.- 5.2 Internal and External Validity.- 5.3 Sample Distortion Bias.- 5.4 Information Bias.- 5.5 Confounding Bias.- 5.6 Reverse Causality ("Cart-vs-Horse") Bias.- 5.7 Concluding Remarks.- 6: Observational Cohort Studies.- 6.1 Research Design Components.- 6.2 Analysis of Results.- 6.3 Bias Assessment and Control.- 6.4 Effect Modification and Synergism.- 6.5 Advantages and Disadvantages of Cohort Studies.- 7: Clinical Trials.- 7.1 Research Design Components.- 7.2 Assignment of Exposure (Treatment).- 7.3 Blinding in Clinical Trials.- 7.4 Analysis of Results.- 7.5 Interpretation of Results.- 7.6 Ethical Considerations.- 7.7 Advantages and Disadvantages of Clinical Trials.- 8: Case-Control Studies.- 8.1 Introduction.- 8.2 Research Design Components.- 8.3 Analysis of Results.- 8.4 Bias Assessment and Control.- 8.5 Advantages and Disadvantages of Case-Control Studies.- 9: Cross-Sectional Studies.- 9.1 Introduction.- 9.2 Research Design Components.- 9.3 Analysis of Results.- 9.4 Bias Assessment and Control.- 9.5 "Pseudo-Cohort" Cross-Sectional Studies.- 9.6 Advantages, Disadvantages, and Uses of Cross-Sectional Studies.- II Biostatistics.- 10: Introduction to Statistics.- 10.1 Variables.- 10.2 Populations, Samples, and Sampling Variation.- 10.3 Description vs Statistical Inference.- 10.4 Statistical vs Analytic Inference.- 11: Descriptive Statistics and Data Display.- 11.1 Continuous Variables.- 11.2 Categorical Variables.- 11.3 Concluding Remarks.- 12: Hypothesis Testing and P Values.- 12.1 Formulating and Testing a Research Hypothesis.- 12.2 The Testing of Ho.- 12.3 Type II Error and Statistical Power.- 12.4 Bayesian vs Frequentist Inference.- 13: Statistical Inference for Continuous Variables.- 13.1 Repetitive Sampling and the Central Limit Theorem.- 13.2 Statistical Inferences Using the t-Distribution.- 13.3 Calculation of Sample Sizes.- 13.4 Nonparametric Tests of Two Means.- 13.5 Comparing Three or More Means: Analysis of Variance.- 13.6 Control for Confounding Factors.- 14: Statistical Inference for Categorical Variables.- 14.1 Introduction to Categorical Data Analysis.- 14.2 Comparing Two Proportions.- 14.3 Statistical Inferences for a Single Proportion.- 14.4 Comparison of Three or More Proportions.- 14.5 Analysis of Larger (r x c) Contingency Tables.- 15: Linear Correlation and Regression.- 15.1 Linear Correlation.- 15.2 Linear Regression.- 15.3 Correlation vs Regression.- 15.4 Statistical Inference.- 15.5 Control for Confounding Factors.- 15.6 Rank (Nonparametric) Correlation.- III Special Topics.- 16: Diagnostic Tests.- 16.1 Introduction.- 16.2 Defining "Normal" and "Abnormal" Test Results.- 16.3 The Reproducibility and Validity of Diagnostic Tests.- 16.4 The Predictive Value of Diagnostic Tests.- 16.5 Bayes' Theorem.- 16.6 The Uses of Diagnostic Tests.- 17: Decision Analysis.- 17.1 Strategies for Decision-Making.- 17.2 Constructing a Decision Tree.- 17.3 Probabilities and Utilities.- 17.4 Completing the Analysis.- 17.5 Cost-Benefit Analysis.- 17.6 Cost-Effectiveness Analysis.- 18: Life-Table (Survival) Analysis.- 18.1 Introduction.- 18.2 Alternative Methods of Analysis: an Example.- 18.3 The Actuarial Method.- 18.4 The Kaplan-Meier (Product-Limit) Method.- 18.5 Statistical Inference.- 19: Causality.- 19.1 What is a "Cause"?.- 19.2 Necessary, Sufficient, and Multiple Causes.- 19.3 Patterns of Cause.- 19.4 Probability and Uncertainty.- 19.5 Can Exposure Cause Outcome?.- 19.6 Is Exposure an Important Cause of Outcome?.- 19.7 Did Exposure Cause Outcome in a Specific Case?.- Appendix Tables.

Evaluating measurement models in clinical research: covariance structure analysis of latent variable models of self-conception.

Abstract: Indirect measures of psychological constructs are vital to clinical research. On occasion, however, the meaning of indirect measures of psychological constructs is obfuscated by statistical procedures that do not account for the complex relations between items and latent variables and among latent variables. Covariance structure analysis (CSA) is a statistical procedure for testing hypotheses about the relations among items that indirectly measure a psychological construct and relations among psychological constructs. This article introduces clinical researchers to the strengths and limitations of CSA as a statistical procedure for conceiving and testing structural hypotheses that are not tested adequately with other statistical procedures. The article is organized around two empirical examples that illustrate the use of CSA for evaluating measurement models with correlated error terms, higher-order factors, and measured and latent variables.

Statistics in spectroscopy

Abstract: INTRODUCTION: WHY THIS BOOK? IMPORTANT CONCEPTS FROM PROBABILITY THEORY POPULATIONS AND SAMPLES: THE MEANING OF "STATISTICS" DEGREES OF FREEDOM INTRODUCTION TO DISTRIBUTIONS AND PROBABILITY SAMPLING THE NORMAL DISTRIBUTION ALTERNATIVE WAYS TO CALCULATE STANDARD DEVIATION THE CENTRAL LIMIT THEOREM SYNTHESIS OF VARIANCE WHERE ARE WE AND WHERE ARE WE GOING? MORE AND DIFFERENT STATISTICS THE T-STATISTIC DISTRIBUTION OF MEANS ONE-AND TWO-TAILED TESTS PHILOSOPHICAL INTERLUDE BIASED AND UNBIASED ESTIMATORS THE VARIANCE OF VARIANCE HYPOTHESIS TESTING OF CHI-SQUARE MORE HYPOTHESIS TESTING STATISTICAL INFERENCES HOW TO COUNT AND STILL COUNTING CONTINGENCY TABLES WHAT DO YOU MEAN, RANDOM? THE F-STATISTIC PRECISION AND ACCURACY: INTRODUCTION TO ANALYSIS OF VARIANCE ANALYSIS OF VARIANCE AND STATISTICAL DESIGN OF EXPERIMENTS CROSSED AND NESTED EXPERIMENTS MISCELLANEOUS CONSIDERATIONS REGARDING ANALYSIS OF VARIANCE PITFALLS OF STATISTICS PITFALLS OF STATISTICS CONTINUED CALIBRATION IN SPECTROSCOPY CALIBRATION: LINEAR REGRESSION AS A STATISTICAL TECHNIQUE CALIBRATION: ERROR SOURCES IN CALIBRATION CALIBRATION: SELECTING THE CALIBRATION SAMPLES CALIBRATION: DEVELOPING THE CALIBRATION MODEL CALIBRATION: AUXILIARY STATISTICS FOR THE CALlBRATION MODEL THE BEGINNING

Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography

Abstract: An image reconstruction method motivated by positron emission tomography (PET) is discussed. The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. The authors set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. An iterative approach which requires the solution of simple quadratic equations is proposed. The authors also present a methodology which allows them to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. The new MAP algorithm is compared to a method which maximizes likelihood and with two variants of the filtered backprojection method. >

Heterogeneity and spatial hierarchies

Abstract: To apply the traditional scientific method, ecologists ordinarily focus on the mean or central tendency of a data set. For example, a typical hypothesis test would involve demonstrating that the mean is significantly different from a control measurement. However, ecological systems are heterogeneous, and much information may be lost if the variance of a data set is ignored. This chapter shows that a specific prediction of hierarchy theory can be tested by examining how variance changes as measurements are taken across a range of scales.

Test Consistency with Varying Sampling Frequency

Abstract: This paper considers the consistency property of some test statistics based on a time series of data. While the usual consistency criterion is based on keeping the sampling interval fixed, we let the sampling interval take any equispaced path as the sample size increases to infinity. We consider tests of the null hypotheses of the random walk and randomness against positive autocorrelation (stationary or explosive). We show that tests of the unit root hypothesis based on the first-order correlation coefficient of the original data are consistent as long as the span of the data is increasing. Tests of the same hypothesis based on the first-order correlation coefficient of the first-differenced data are consistent against stationary alternatives only if the span is increasing at a rate greater than T ½ , where T is the sample size. On the other hand, tests of the randomness hypothesis based on the first-order correlation coefficient applied to the original data are consistent as long as the span is not increasing too fast. We provide Monte Carlo evidence on the power, in finite samples, of the tests Studied allowing various combinations of span and sampling frequencies. It is found that the consistency properties summarize well the behavior of the power in finite samples. The power of tests for a unit root is more influenced by the span than the number of observations while tests of randomness are more powerful when a small sampling frequency is available.

Invariance, nonlinear models, and asymptotic tests

Abstract: The invariance properties of some well known asymptotic tests are studied. Three types of invariance are considered: invariance to the representation of the null hypothesis, invariance to one-to-one transformations of the parameter space (reparameterizations), and invariance to one-to-one transformations of the model variables such as changes in measurement units. Tests that are not invariant include the Wald test and generalized versions of it, a widely used variant of the Lagrange multiplier test, Neyman's C(a) test, and a generalized version of the latter. For all these tests, we show that simply changing measurement units can lead to vastly different answers even when equivalent null hypotheses are tested. This problem is illustrated by considering regression models with Box-Cox transformations on the variables. We observe, in particular, that various consistent estimators of the information matrix lead to test procedures with different invariance properties. General sufficient conditions are then established, under which the generalized C(a) test becomes invariant to reformulations of the null hypothesis and/or to one-to-one transformations of the parameter space as well as to transformations of the variables. In many practical cases where Wald-type tests lack invariance, we find that special formulations of the generalized C(a) test are invariant and hardly more costly to compute than Wald tests. This computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test. We conclude that noninvariant asymptotic tests should be avoided or used with great care. Further, in many situations, the suggested implementation of the generalized C(a) test often yields an attractive substitute to the Wald test (which is not invariant) and to other invariant tests (which are more costly to perform).

Nonparametric Comparison of Cumulative Periodograms

Abstract: Motivated by a problem in the analysis of hormonal time series data, this paper proposes a simple graphical method for comparing two periodograms and describes a new nonparametric approach to testing the hypothesis that the two underlying spectra are the same. Simulation studies show that the new test has power characteristics that are competitive with existing procedures. The relative merits of nonparametric and semiparametric tests are discussed.

Stock Market Forecastability and Volatility: A Statistical Appraisal

Abstract: This paper presents and implements statistical tests of stock market forecastability and volatility that are immune from the severe statistical problems of earlier tests. It finds that although the null hypothesis of market efficiency is rejected, the rejections are only marginal. The paper also shows how volatility tests and recent regression tests are closely related, and demonstrates that when finite sample biases are taken into account, regression tests also fail to provide strong evidence of violations of the conventional valuation model.