Showing papers on "Nonparametric statistics published in 1990"
Book•
01 Jan 1990
TL;DR: In this article, applied nonparametric statistics are applied to the problem of applied non-parametric statistical data collection in the context of the application of applied NN statistics, including:
Abstract: Applied nonparametric statistics , Applied nonparametric statistics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
4,097 citations
TL;DR: In this article, the authors study the study of randomness sampling distributions of data and their relationship with data-relationships, and propose a two-way analysis of variance in Logistic Regression and Nonparametric Tests.
Abstract: PART I: LOOKING AT DATA Looking at Data-Distributions Looking at Data-Relationships Producing Data PART II: PROBABILITY AND INFERENCE Probability: The Study of Randomness Sampling Distributions Introduction to Inference Inference for Distributions Inference for Proportions PART III: TOPICS ON INFERENCE Analysis of Two-Way Tables Inference for Regression Multiple Regression One-Way Analysis of Variance Two-Way Analysis of Variance Additional chapters available on the CD-ROM and the website: Logistic Regression Nonparametric Tests Bootstrap Methods and Permutation Tests Statistics for Quality: Control and Capability
2,778 citations
IBM1
TL;DR: The authors define L-moments as the expectations of certain linear combinations of order statistics, which can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions.
Abstract: L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis and new methods of parameter estimation
2,668 citations
Book•
01 Jan 1990TL;DR: This chapter discusses smoothing in high Dimensions, Investigating multiple regression by additive models, and incorporating parametric components and alternatives.
Abstract: Preface Part I. Regression Smoothing: 1. Introduction 2. Basic idea of smoothing 3. Smoothing techniques Part II. The Kernel Method: 4. How close is the smooth to the true curve? 5. Choosing the smoothing parameter 6. Data sets with outliers 7. Smoothing with correlated data 8. Looking for special features (qualitative smoothing) 9. Incorporating parametric components and alternatives Part III. Smoothing in High Dimensions: 10. Investigating multiple regression by additive models Appendices References List of symbols and notation.
2,664 citations
TL;DR: In this paper, a flexible parametric proportional hazards model is proposed and the model specification is flexibly parametric in the sense that the baseline hazard is non-parametric while the effect of the covariates takes a particular functional form.
Abstract: In this paper we specify and estimate a flexible parametric proportional hazards model. The model specification is flexibly parametric in the sense that the baseline hazard is non parametric while the effect of the covariates takes a particular functional form. We also add parametric heterogeneity to the underlying hazard model specification. We specify a flexible parametric proportional competing risks model which permits unrestricted correlation among the risks. Unemployment duration data are then analysed using the flexible parametric duration and competing risks specifications. We find an important effect arising from the exhaustion of unemployment insurance and significantly different hazards for the two types of risks, new jobs and recalls.
696 citations
TL;DR: The authors found that conditional heteroskedasticity is a characteristic of the true data-generating process, or whether it indicates misspecification associated with linear conditional-mean representations, which bode poorly for recent conjectures that exchange rates contain nonlinearities exploitable for enhanced point prediction.
550 citations
Book•
01 Jan 1990
TL;DR: In this paper, the authors present a list of some Stata commands Monte Carlo and Bootstrap Methods, as well as some other Stata data graphs, including frequency distributions and univariate statistics T tests, anova and nonparametric comparisons.
Abstract: Introduction to STATA data graphs frequency distributions and univariate statistics T tests, anova, and nonparametric comparisons bivariate regression multiple regression regression diagnostics fitting curves robust regression logistics regression principal components and factor analysis list of some Stata commands Monte Carlo and Bootstrap Methods.
532 citations
TL;DR: In this article, the problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments was studied.
Abstract: Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments. A particular class of prior processes, termed beta processes, is introduced and is shown to constitute a conjugate class. To arrive at these, a nonparametric time-discrete framework for survival data, which has some independent interest, is studied first. An important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated, for example, time-inhomogeneous Markov chains. We find posterior distributions and derive Bayes estimators in such models and also present a semiparametric Bayesian analysis of the Cox regression model. The Bayes estimators are easy to interpret and easy to compute. In the limiting case of a vague prior the Bayes solution for a cumulative hazard is the Nelson-Aalen estimator and the Bayes solution for a survival probability is the Kaplan-Meier estimator.
515 citations
01 Jan 1990
TL;DR: In order to lessen the dependence of statistical inference on that assumption statisticians developed methods based on rank tests whose sampling distribution, under the null hypothesis, do not depend on the form of the underlying density function.
Abstract: Basic statistics and econometrics courses stress methods based on assuming that the data or error term in regression models follow the normal distribution. Indeed, the efficiency of least squares estimates relies on the assumption of normality. In order to lessen the dependence of statistical inference on that assumption statisticians developed methods based on rank tests whose sampling distribution, under the null hypothesis, do not depend on the form of the underlying density function.
493 citations
Book•
01 Aug 1990
TL;DR: This chapter discusses informetric models, the dual approach between sources and items giving rise to the definition of Information Production Processes, and some science policy applications.
Abstract: I Statistics
This part begins with elementary descriptive statistics and elements of probability It continues with a chapter on inferential statistics, including regression, correlation and nonparametric statistics Next, there is a chapter on sampling theory, including overlap problems Part I concludes with a short description of several techniques of multivariate statistics: multiple regression, principal component analysis, multidimensional scaling and cluster techniques
II Operations research and library management
The second part deals with applications of linear programming, including transportation and assignment problems, and basic queueing theory Special attention is paid to book circulation interference
III Citation analysis
Citer motivations, citation networks, bibliographic coupling and co-citation analysis are introduced here Citation measures such as the impact factor are defined This part ends with some science policy applications
IV Informetric models
Informetric models and their relations are studied At the heart of this theory is the dual approach between sources and items giving rise to the definition of Information Production Processes Explanations and applications of the classical informetric laws as well as fitting methods are provided
474 citations
Book•
18 Dec 1990
TL;DR: Probability and statistics normal distribution binomial poisson hypergeometric, and negative binomial distributions student's t-distribution Chi-square distribution f -distribution order statistics range and studentized range correlation coefficient nonparametric statistics quality control miscellaneous statistics tables miscellaneous mathematics tables.
Abstract: Probability and statistics normal distribution binomial poisson hypergeometric, and negative binomial distributions student's t-distribution Chi-square distribution f-distribution order statistics range and studentized range correlation coefficient non-parametric statistics quality control miscellaneous statistics tables miscellaneous mathematics tables. (partial)
TL;DR: In this article, it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators for nonlinear models in an i.i.d. environment.
Abstract: This paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i.i.d. environment. The class of models includes nonlinear simultaneous equations models and other models of interest. A problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation, calculation of which can require functional form assumptions for the conditional distribution of endogenous variables, as well as integration. Nonparametric methods provide a way of avoiding this difficulty. Here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators. Also, ways of choosing the nonparametric estimate in applications are discussed. Two types of nonparametric estimates of the optimal instruments are considered. Each involves nonparametric regression, one by nearest neighbor and the other by series approximation. The finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model.
TL;DR: The authors classified bias measures according to two characteristics: sensitivity (the ability of an observer to reflect a stimulus-response correspondence defined by the experimenter) and response bias (the tendency to favor 1 response over others).
Abstract: Models of discrimination based on statistical decision theory distinguish sensitivity (the ability of an observer to reflect a stimulus-response correspondence defined by the experimenter) from response bias (the tendency to favor 1 response over others). Measures of response bias have received less attention than those of sensitivity. Bias measures are classified here according to 2 characteristics. The various bias statistics are compared on pragmatic and theoretical grounds, and it is concluded that criterion location measures have many advantages in empirical work
TL;DR: In this paper, the authors provide a survey of nonparametric methods for estimating the robustness of single-sample estimators using the McNemar's test and the sign test.
Abstract: PREFACEINTRODUCING NONPARAMETRIC METHODSBasic StatisticsSamples and PopulationsHypothesis TestsEstimationEthical IssuesComputers and Nonparametric MethodsFurther ReadingCENTRALITY INFERENCE FOR SINGLE SAMPLESUsing Measurement DataInferences about Medians Based on RanksThe Sign TestTransformation of RanksAsymptotic ResultsRobustnessOTHER SINGLE-SAMPLE INFERENCEInferences for Dichotomous DataTests Related to the Sign TestMatching Samples to DistributionsAngular DataA Runs Test for RandomnessMETHODS FOR PAIRED SAMPLESComparisons in PairsA Less Obvious Use of the Sign TestPower and Sample SizeMETHODS FOR TWO INDEPENDENT SAMPLESCentrality Tests and EstimatesRank Based TestsThe Median TestNormal ScoresTests for Survival DataAsymptotic ApproximationPower and Sample SizeTests for Equality of VarianceTests for a Common DistributionTHREE OR MORE SAMPLESComparisons with Parametric MethodsCentrality Tests for Independent SamplesCentrality Tests for Related SamplesMore Detailed Treatment ComparisonsTests for Heterogeneity of VarianceSome MiscellaneousConsiderationsCORRELATION AND CONCORDANCECorrelation and Bivariate DataRanked Data for Several VariablesAgreementREGRESSIONBivariate Linear RegressionMultiple RegressionNonparametric Regression ModelsOther Multivariate Data ProblemsCATEGORICAL DATACategories and CountsNominal Attribute CategoriesOrdered Categorical DataGoodness-of-Fit Tests for Discrete DataExtension of McNemar'sTestASSOCIATION IN CATEGORICAL DATAThe Analysis of AssociationSome Models for Contingency TablesCombining and Partitioning of TablesPowerROBUST ESTIMATIONWhen Assumptions Break DownOutliers and InfluenceThe BootstrapM-Estimators and Other Robust EstimatorsAPPENDIXREFERENCESSOLUTIONS TO ODD-NUMBERED EXERCISESINDEXEach chapter also includes Fields of Application, Summary, and Exercises
TL;DR: In this article, a bootstrap method for estimating mean squared error and smoothing parameter in nonparametric problems is described, which involves using a resample of smaller size than the original sample.
TL;DR: In this article, it is shown that kernel estimators with a Guassian kernel are asymptotically suboptimal for smoothing parameter selection, and a method for choosing the smoothing parameters is proposed.
Abstract: For an estimator of quantiles, the efficiency of the sample quantile can be improved by considering linear combinations of order statistics, that is, L estimators. A variety of such methods have appeared in the literature; an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a Guassian kernel, and the bandwidths are identified. It is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal. In addition, the theory of this article suggests a method for choosing the smoothing parameter. How much reliance should be placed on the theoretical results is investigated through a simulation study. Over a variety of distributions little consistent difference is found between various estimators. An important conclusion, made during the theoretical analysis, is that all of these estimators usually provide only modest improvement over the sample quantile. The results indicate that even if one knew the best estimator ...
Book•
17 Jan 1990
TL;DR: Experimental design descriptive statistics probability random variables and distributions samples and sampling distributions estimation hypothesis testing analysis of variance repeated measures chi-square tests correlation and regression nonparametric methods.
Abstract: Experimental design descriptive statistics probability random variables and distributions samples and sampling distributions estimation hypothesis testing analysis of variance repeated measures chi-square tests correlation and regression nonparametric methods.
TL;DR: In this article, a number of sensitivity analysis techniques are compared in the case of non-linear model responses in the context of the risk analysis for the disposal of radioactive waste, where sensitivity analysis plays a crucial role.
Journal Article•
TL;DR: It is demonstrated that the rejection of the two one-sided hypotheses at nominal alpha-level by means of nonparametric Mann-Whitney-Wilcoxon tests is equivalent to the inclusion of the corresponding distribution-free (1-2 alpha) 100%-confidence interval in the bioequivalence range.
Abstract: In bioequivalence assessment, the consumer risk of erroneously accepting bioequivalence is of primary concern. In order to control the consumer risk, the decision problem is formulated with bioinequivalence as hypothesis and bioequivalence as alternative. In the parametric approach, a split into two one-sided test problems and application of two-sample t-tests have been suggested. Rejection of both hypotheses at nominal alpha-level is equivalent to the inclusion of the classical (shortest) (1-2 alpha) 100%-confidence interval in the bioequivalence range. This paper demonstrates that the rejection of the two one-sided hypotheses at nominal alpha-level by means of nonparametric Mann-Whitney-Wilcoxon tests is equivalent to the inclusion of the corresponding distribution-free (1-2 alpha) 100%-confidence interval in the bioequivalence range. This distribution-free (nonparametric) approach needs weaker model assumptions and hence presents an alternative to the parametric approach.
TL;DR: In this article, a Cox-regression-like model for nonparametric analysis of data under a time-dependent covariate effects determined by a regression function is presented and a computational approach is outlined.
Abstract: Techniques are developed for nonparametric analysis of data under a Cox-regression-like model permitting time-dependent covariate effects determined by a regression function $\beta_0(t)$. Estimators resulting from maximization of an appropriate penalized partial likelihood are shown to exist and a computational approach is outlined. Weak uniform consistency (with a rate of convergence) and pointwise asymptotic normality of the estimators are established under regularity conditions. A consistent estimator of a common baseline hazard function is presented and used to construct a consistent estimator of the asymptotic variance of the estimator of the regression function. Extensions to multiple covariates, general relative risk functions and time-dependent covariates are discussed.
TL;DR: In this article, a comparison of nonparametric regression curves is considered, where the authors assume that there are parametric transformations of the axes which map one curve into the other.
Abstract: The comparison of nonparametric regression curves is considered. It is assumed that there are parametric (possibly nonlinear) transformations of the axes which map one curve into the other. Estimation and testing of the parameters in the transformations are studied. The rate of convergence is $n^{-1/2}$ although the nonparametric components of the model typically have a rate slower than that. A statistic is provided for testing the validity of a given completely parametric model.
TL;DR: In this paper, the conditional mean and variance are used for identifying nonlinear time series using nonparametric estimates of the conditional Mean and Conditional Variance (CVM) of the time series and a criterion for determining the order of a general nonlinear model.
Abstract: SUMMARY We study the possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance. It is shown that most nonlinear models satisfy the assumptions needed to apply nonparametric asymptotic theory. Sampling variations of the conditional quantities are studied by simulation and explained by asymptotic arguments for a number of first-order nonlinear autoregressive processes. The conditional mean and variance can be used for identification purposes, but one must be aware of bias and misspecification effects. We also propose a criterion for determining the order of a general nonlinear model. The criterion is justified in parts by heuristics, but encouraging results are obtained from a limited set of simulation experiments. Several
TL;DR: In this paper, the authors study the robustness properties of randomization tests by studying their asymptotic validity in situations where the basis for their construction breaks down, i.e., when the underlying populations differ only in location.
Abstract: Fisher's randomization construction of hypothesis tests is a powerful tool to yield tests that are nonparametric in nature in that their level is exactly equal to the nominal level in finite samples over a wide range of distributional assumptions. For example, the usual permutation t test to test equality of means is valid without a normality assumption of the underlying populations. On the other hand, Fisher's randomization construction is not applicable in this example unless the underlying populations differ only in location. In general, the basis for the randomization construction is invariance of the probability distribution of the data under a transformation group. It is the goal of this article to understand the robustness properties of randomization tests by studying their asymptotic validity in situations where the basis for their construction breaks down. Here, asymptotic validity refers to whether the probability of a Type I error tends asymptotically to the nominal level. In particula...
TL;DR: In this article, a review of the use of nonparametric analysis of variance in the design of experiments in the behavioral and social sciences that focused on interaction effects is presented, where the authors show that non-parametric methods lack statistical power and that there is a paucity of techniques in more complicated research designs.
Abstract: Until recently the design of experiments in the behavioral and social sciences that focused on interaction effects demanded the use of the parametric analysis of variance. Yet, researchers have been concerned by the presence of nonnormally distributed variables. Although nonparametric statistics are recommended in these situations, researchers often rely on the robustness of parametric tests. Further, often it is assumed that nonparametric methods lack statistical power and that there is a paucity of techniques in more complicated research designs, such as in testing for interaction effects. This paper reviewed (a) research in the past decade and a half that addressed concerns in selecting parametric and nonparametric statistics and (b) 10 recently developed nonparametric techniques for the testing of interactions in experimental design. The review shows that these new techniques are robust, powerful, versatile, and easy to compute. An application of selected nonparametric techniques on fabricated data is...
TL;DR: In this paper, a survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines, and the resulting log hazard ratio estimates are compared with those from nonparametric methods.
Abstract: The Cox proportional hazards model restricts the log hazard ratio to be linear in the covariates. A smooth nonlinear covariate effect may go undetected in this model but can be well approximated by a spline function. A survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines, and the resulting log hazard ratio estimates are compared with those from nonparametric methods. We remove the linear restriction on the log hazard ratio by transforming a continuous covariate into a vector of fixed knot basis splines (B-splines). B-splines are known to produce better-conditioned systems of equations than the truncated power basis when used as interpolants, and show similar behavior when fitting proportional hazards models. We describe the procedures for, and the issues arising in, the estimation and the testing of the B-spline coefficients. Although inference is not well developed for some nonparametric methods that estimate covariate effects, the...
TL;DR: In this article, the authors compared the Fourier series, harmonic mean, minimum convex polygon, and 2 95% ellipse home-range estimators using computer-simulated data with a known home range area.
Abstract: We compared the Fourier series, harmonic mean, minimum convex polygon, and 2 95% ellipse home-range estimators using computer-simulated data with a known home-range area. Data were generated to simulate home ranges with 1 or 2 centers of activity and with topographic barriers causing irregular shapes. Estimators performed with different precision and bias according to the type of data simulated and the number of observations taken. Overall, the harmonic mean was the least biased, but was also one of the least precise. Home-range estimators are only general measures of animal activity. J. WILDL. MANAGE. 54(2):310-315 Many statistical home-range estimators have been proposed. All have different underlying models (assumptions) providing different operating characteristics and therefore can produce dissimilar results for a specific set of data. Rarely have the statistical properties of these estimators been compared or have guidelines on the selection of a specific estimator for a particular set of data been proposed. Application of different estimators produces confusion in the interpretation of home-range estimates because some of the differences observed between studies are due to the estimators themselves, and not to the behavior of the animals being studied. We used computer simulated data to address the differences among estimators by comparing 3 nonparametric estimators: harmonic mean (Dixon and Chapman 1980), Fourier series (Anderson 1982), and minimum convex polygon (Mohr 1947); and 2 parametric estimators: 95% ellipse estimators of Jennrich and Turner (1969) and Koeppl et al. (1975). Two types of animal movements were simulated: (1) an animal with a center of activity (e.g., a nesting bird) and (2) an animal with a uniform distribution (no center of activity). Data from a normal distribution were used to simulate center-of-activity movements, and data from a uniform distribution were used for movements without a center of activity. In addition, home ranges with irregular This content downloaded from 207.46.13.114 on Thu, 26 May 2016 06:08:42 UTC All use subject to http://about.jstor.org/terms J. Wildl. Manage. 54(2):1990 HOME-RANGE ESTIMATORS * Boulanger and White 311 shapes, as would be caused by topographic barriers and/or habitat heterogeneity, were simulated. Advantages of using computer-simulated data are that a true home range is known, and thus bias and precision of each estimator can be evaluated. The statistical properties of an estimator cannot be determined with field telemetry data because true replicate observations cannot be constructed. Replicated, simulated data sets also allow powerful statistical comparisons of esti-