Showing papers on "Nonparametric statistics published in 1998"
TL;DR: The authors presented conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very general forms of spatial and temporal dependence as the time dimension becomes large.
Abstract: Many panel data sets encountered in macroeconomics, international economics, regional science, and finance are characterized by cross-sectional or “spatial” dependence. Standard techniques that fail to account for this dependence will result in inconsistently estimated standard errors. In this paper we present conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very general forms of spatial and temporal dependence as the time dimension becomes large. We illustrate the relevance of this approach using Monte Carlo simulations and a number of empirical examples.
3,763 citations
Book•
24 Jul 1998
TL;DR: In this paper, the use of Bayesian methods for reliability data is discussed and a detailed discussion of the application of these methods in the context of automated life test planning is presented.
Abstract: Partial table of contents: Reliability Concepts and Reliability Data. Nonparametric Estimation. Other Parametric Distributions. Probability Plotting. Bootstrap Confidence Intervals. Planning Life Tests. Degradation Data, Models, and Data Analysis. Introduction to the Use of Bayesian Methods for Reliability Data. Failure--Time Regression Analysis. Accelerated Test Models. Accelerated Life Tests. Case Studies and Further Applications. Epilogue. Appendices. References. Indexes.
2,341 citations
TL;DR: In this paper, the authors provide a general methodology of bootstrapping in nonparametric frontier models and some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants.
Abstract: Efficiency scores of production units are generally measured relative to an estimated pro-duction frontier. Nonparametric estimators (DEA, FDH,···) are based on a finite sample of observed production units. The bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. The main point in order to validate the bootstrap is to define a reasonable data-generating process in this complex framework and to propose a reasonable estimator of it. This paper provides a general methodology of bootstrapping in nonparametric frontier models. Some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants.
2,024 citations
Book•
30 Jan 1998
TL;DR: One-sample problems as mentioned in this paper have been used to evaluate the robustness of estimates of location in linear models with respect to the number of false positives and false negatives of the estimated locations.
Abstract: One-Sample Problems Introduction Location Model Geometry and Inference in the Location Model Examples Properties of Norm-Based Inference Robustness Properties of Norm-Based Inference Inference and the Wilcoxon Signed-Rank Norm Inference Based on General Signed-Rank Norms Ranked Set Sampling L1 Interpolated Confidence Intervals Two-Sample Analysis Two-Sample Problems Introduction Geometric Motivation Examples Inference Based on the Mann-Whitney-Wilcoxon General Rank Scores L1 Analyses Robustness Properties Proportional Hazards Two-Sample Rank Set Sampling (RSS) Two-Sample Scale Problem Behrens-Fisher Problem Paired Designs Linear Models Introduction Geometry of Estimation and Tests Examples Assumptions for Asymptotic Theory Theory of Rank-Based Estimates Theory of Rank-Based Tests Implementation of the R Analysis L1 Analysis Diagnostics Survival Analysis Correlation Model High Breakdown (HBR) Estimates Diagnostics for Differentiating between Fits Rank-Based Procedures for Nonlinear Models Experimental Designs: Fixed Effects Introduction One-Way Design Multiple Comparison Procedures Two-Way Crossed Factorial Analysis of Covariance Further Examples Rank Transform Models with Dependent Error Structure Introduction General Mixed Models Simple Mixed Models Arnold Transformations General Estimating Equations (GEE) Time Series Multivariate Multivariate Location Model Componentwise Spatial Methods Affine Equivariant and Invariant Methods Robustness of Estimates of Location Linear Model Experimental Designs Appendix: Asymptotic Results References Index
505 citations
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TL;DR: In this article, a brief overview of the class of models under study and central theoretical issues such as the curse of dimensionality, the bias-variance trade-off and rates of convergence are discussed.
Abstract: This introduction to nonparametric regression emphasizes techniques that might be most accessible and useful to the applied economist. The paper begins with a brief overview of the class of models under study and central theoretical issues such as the curse of dimensionality, the bias-variance trade-off and rates of convergence. The paper then focuses on kernel and nonparametric least squares estimation of the nonparametric regression model, and optimal differencing estimation of the partial linear model. Constrained estimation and hypothesis testing is also discussed. Empirical examples include returns to scale in electricity distribution and hedonic pricing of housing attributes.
458 citations
TL;DR: The authors examined the results of nonparametric tests with small sample sizes published in a recent issue of Animal Behaviour and found that in more than half of the articles concerned, the asymptotic variant had apparently been inappropriately used and incorrect P values had been presented.
438 citations
TL;DR: In this paper, the authors investigated the consistency and the speed of convergence of the estimated efficiency scores in the very general setup of a multioutput and multi-input case, and they showed that the convergence speed depends on the smoothness of the unknown frontier and on the number of inputs and outputs.
Abstract: Efficiency scores of production units are measured by their distance to an estimated production frontier. Nonparametric data envelopment analysis estimators are based on a finite sample of observed production units, and radial distances are considered.We investigate the consistency and the speed of convergence of these estimated efficiency scores ~or of the radial distances! in the very general setup of a multioutput and multi-input case. It is shown that the speed of convergence relies on the smoothness of the unknown frontier and on the number of inputs and outputs. Furthermore, one has to distinguish between the output- and the input-oriented cases.
399 citations
01 Jan 1998
TL;DR: This paper discusses various statistics for testing hypotheses regarding returns to scale in the context of non-parametric models of technical efficiency and presents bootstrap estimation procedures which yield appropriate critical values for the test statistics.
Abstract: This paper discusses various statistics for testing hypotheses regarding returns to scale in the context of nonparametric models of technical eciency. In addition, the paper presents bootstrap estimation procedures which yield appropriate critical values for the test statistics. Evidence on the true sizes and power of the various proposed tests is obtained from Monte Carlo experiments. This paper is an extension of earlier work in Simar and Wilson (1998a).
371 citations
TL;DR: The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a non-parametric fit, and neither dominates in experiments as mentioned in this paper.
Abstract: The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bear closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banach-valued random elements and applying the Banach central limit theorem and law of iterated logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted.
346 citations
TL;DR: In this article, the authors define a single-index model and propose a set of extensions of the maximum score and smoothed maximum score estimators, which are then used to reduce the dimension of the data.
Abstract: 1. Introduction.- 2. Single-Index Models.- 2.1 Definition of a Single-Index Model.- 2.2 Why Single-Index Models Are Useful.- 2.3 Other Approaches to Dimension Reduction.- 2.4 Identification of Single-Index Models.- 2.5 EstimatingGin a Single-Index Modei.- 2.6 Optimization Estimators ofss.- 2.7 Direct Semiparametric Estimators.- 2.8 Bandwidth Selection.- 2.9 An Empirical Example.- 3. Binary Response Models.- 3.1 Random-Coefficients Models.- 3.2 Identification.- 3.3 Estimation.- 3.4 Extensions of the Maximum Score and Smoothed Maximum Score Estimators.- 3.5 An Empirical Example.- 4. Deconvolution Problems.- 4.1 A Model of Measurement Error.- 4.2 Models for Panel Data.- 4.3 Extensions.- 4.4 An Empirical Example.- 5. Transformation Models.- 5.1 Estimation with ParametricTand NonparametricF.- 5.2 Estimation with NonparametricTand ParametricF.- 5.3 Estimation when BothTandFare Nonparametric.- 5.4 Predicting Y Conditional onX.- 5.5 An Empirical Example.- Appendix: Nonparametric Estimation.- A.1 Nonparametric Density Estimation.- A.2 Nonparametric Mean Regression.- References.
TL;DR: A related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties.
Abstract: This paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations. In the first part, a related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties. In the second part a parametric model for the RLDS is identified. Convergence in probability of this model to the RLDS is proven. A function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate.
TL;DR: It is proposed that robust statistical analysis can be of great use for determinations of reference intervals from limited or possibly unreliable data.
Abstract: We propose a new methodology for the estimation of reference intervals for data sets with small numbers of observations or for those with substantial numbers of outliers. We propose a prediction interval that uses robust estimates of location and scale. The SAS software can be readily modified to do these calculations. We compared four reference interval procedures (nonparametric, transformed, robust with a nonparametric lower limit, and transformed robust) for sample sizes of 20, 40, 60, 80, 100, and 120 from chi 2 distributions of 1, 4, 7, and 10 df. chi 2 distributions were chosen because they simulate the skewness of distributions often found in clinical chemistry populations. We used the root mean square error as the measure of performance and used computer simulation to calculate this measure. The robust estimator showed the best performance for small sample sizes. As the sample size increased, the performance values converged. The robust method for calculating upper reference interval values yields reasonable results. In two examples using real data for haptoglobin and glucose, the robust estimator provides slightly smaller upper reference limits than the other procedures. Lastly, the robust estimator was compared with the other procedures in a population where 5% of the values were multiplied by a factor of 5. The reference intervals were calculated with and without outlier detection. In this case, the robust approach consistently yielded upper reference interval values that were closer to those of the true underlying distributions. We propose that robust statistical analysis can be of great use for determinations of reference intervals from limited or possibly unreliable data.
TL;DR: In this article, the authors consider the nonparametric estimation of the densities of the latent variable and the error term in the standard measurement error model when two or more measurements are available.
TL;DR: In this article, a unified approach to selecting a bandwidth and constructing confidence intervals in local maximum likelihood estimation is presented, which is then applied to least squares nonparametric regression and to non-parametric logistic regression.
Abstract: Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local maximum likelihood estimation. The approach is then applied to least squares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powerful and encouraging.
TL;DR: In this paper, nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose-response experiment, which can also be applied to data collected from a completely randomized design experiment.
Abstract: Nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose–response experiment. The methods can also be applied to data collected from a completely randomized design experiment. Methods are developed for the detection and description of the effects of dose, time, and their interaction. The methods allow for individual variation in the timing and number of observations. A generalization allowing baseline covariates to be incorporated is addressed. These results may be used in an exploratory fashion in the process of building a random-effects model for longitudinal data.
Book•
01 Apr 1998
TL;DR: The High School and Beyond Data Set and SPSS 7.5 Measurement and Descriptive Statistics Data Entry, Checking Data and Data Descriptives More descriptive statistics, and Checking the Normal Distribution Data Transformations - Count, Recode, Compute Selecting and Interpreting Inferential Statistics Crosstabulation and Nonparametric Association Correlation and Scatterplots Factor Analysis - Data Reduction with Principle Components Analysis Several Measures of Reliability Multiple Regression Logistic Regression and Discriminant Analysis Independent and Paired Samples t Tests and Equivalent Non-Param
Abstract: Research Problem, Approaches and Questions Overview of the High School and Beyond Data Set and SPSS 7.5 Measurement and Descriptive Statistics Data Entry, Checking Data and Descriptives More Descriptive Statistics, and Checking the Normal Distribution Data Transformations - Count, Recode, Compute Selecting and Interpreting Inferential Statistics Crosstabulation and Nonparametric Association Correlation and Scatterplots Factor Analysis - Data Reduction with Principle Components Analysis Several Measures of Reliability Multiple Regression Logistic Regression and Discriminant Analysis Independent and Paired Samples t Tests and Equivalent Non-Parametric Tests One-Way ANOVA with Multiple Comparisons for Between Groups Designs Factorial ANOVA, Including Interactions and ANOVA Repeated Measures and Mixed ANOVA Multivariate Analysis of Variance (MANOVA).
TL;DR: In this article, a general family of nonparametric mixed effects models is proposed, where smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function, and the random effects are modeled parametrically by assuming that the covariance function depends on a parsimonious set of parameters.
Abstract: We propose a general family of nonparametric mixed effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a connection between a nonparametric mixed effects model and a linear mixed effects model. This connection suggests a way of fitting a nonparametric mixed effects model by using existing programs. The classical two-way mixed models and growth curve models are used as examples to demonstrate how to use smoothing spline analysis-of-variance decompositions to build nonparametric mixed effects models. Similarly to the classical analysis of variance, components of these nonparametric mixed effects models can be interpreted as main effects and interactions. The penalized likelihood estimates of the fixed effects in a two-way mixed model are extensions of James-Stein shrinkage estimates to correlated observations. In an example three nested nonparametric mixed effects models are fitted to a longitudinal data set.
TL;DR: In this paper, a nonparametric test for I(0) against fractional alternatives is proposed, which makes no assumptions on spectral behaviour away from zero frequency, and seems likely to have good efficiency.
Abstract: There is frequently interest in testing that a scalar or vector time series is I(0), possibly after first- differencing or other detrending, while the I(0) assumption is also taken for granted in autocorrelation-consistent variance estimation. We propose a test for I(0) against fractional alternatives. The test is non-parametric, and indeed makes no assumptions on spectral behaviour away from zero frequency. It seems likely to have good efficiency against fractional alternatives, relative to other nonparametric tests. The test is given large samle justification, subjected to a Monte Carlo analysis of finite sample behaviour, and applied to various empirical data series.
TL;DR: In this paper, the authors conducted a simulation study to provide counterexamples to some commonly held generalizations about the benefits of nonparametric tests, and found that non-parametric methods are not always acceptable substitutes for parametric methods such as the t test and the F test when parametric assumptions are not satisfied.
Abstract: To provide counterexamples to some commonly held generalizations about the benefits of nonparametric tests, the author concurrently violated in a simulation study 2 assumptions of parametric statistical significance tests—normality and homogeneity of variance. For various combinations of nonnormal distribution shapes and degrees of variance heterogeneity, the Type I error probability of a non-parametric rank test, the Wilcoxon-Mann-Whitney test, was found to be biased to a far greater extent than that of its parametric counterpart, the Student t test. The Welch-Satterthwaite separate-variances version of the t test, together with a preliminary outlier detection and downweighting procedure, protected the statistical significance level more consistently than the nonparametric test did. Those findings reveal that nonparametric methods are not always acceptable substitutes for parametric methods such as the t test and the F test in research studies when parametric assumptions are not satisfied. They ...
TL;DR: This paper shows how a kernel density estimate of the joint distribution of disaggregate flow variables can form the basis for conditional simulation based on an input aggregate flow variable, and shows how this conditional simulation procedure preserves a variety of statistical attributes.
Abstract: Synthetic simulation of streamflow sequences is important for the analysis of water supply reliability Disaggregation models are an important component of the stochastic streamflow generation methodology They provide the ability to simulate multiseason and multisite streamflow sequences that preserve statistical properties at multiple timescales or space scales In recent papers we have suggested the use of nonparametric methods for streamflow simulation These methods provide the capability to model time series dependence without a priori assumptions as to the probability distribution of streamflow They remain faithful to the data and can approximate linear or nonlinear dependence In this paper we extend the use of nonparametric methods to disaggregation models We show how a kernel density estimate of the joint distribution of disaggregate flow variables can form the basis for conditional simulation based on an input aggregate flow variable This methodology preserves summability of the disaggregate flows to the input aggregate flow We show through applications to synthetic data and streamflow from the San Juan River in New Mexico how this conditional simulation procedure preserves a variety of statistical attributes
TL;DR: An algorithm is suggested and it is shown that this algorithm converges to the solution of the minimization problem and a simulation study is presented, showing the superiority of the algorithm compared to the EM algorithm in the interval censoring case 2 setting.
Abstract: The problem of minimizing a smooth convex function over a specific cone in IRn is frequently encountered in nonparametric statistics. For that type of problem we suggest an algorithm and show that this algorithm converges to the solution of the minimization problem. Moreover, a simulation study is presented, showing the superiority of our algorithm compared to the EM algorithm in the interval censoring case 2 setting.
TL;DR: In this article, the authors present an outline of relative distribution methods, with an application to recent changes in the U.S. wage distribution, using a nonparametric statistical framework.
Abstract: We present an outline of relative distribution methods, with an application to recent changes in the U.S. wage distribution. Relative distribution methods are a nonparametric statistical framework ...
TL;DR: In this article, the bias of the nonparametric function is estimated using the sandwich method, in an automatic fashion, without the need to derive asymptotic formulas and plug-in an estimate of a density function.
Abstract: Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric estimators of a “parameter” depending on a predictor. The nonparametric component is estimated via local polynomials with loess or kernel weighting; asymptotic theory is derived for the latter. In keeping with the estimating equation paradigm, variances of the nonparametric function estimate are estimated using the sandwich method, in an automatic fashion, without the need (typical in the literature) to derive asymptotic formulas and plug-in an estimate of a density function. The same philosophy is used in estimating the bias of the nonparametric function; that is, an empirical method is used without deriving asymptotic theory on a case-by-case basis. The methods are applied to a series of examples. The applicatio...
TL;DR: In this article, the authors explore the possibility of approximating the Ferguson-Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures, based on the constructive definition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule.
Abstract: We explore the possibility of approximating the Ferguson-Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures. The proposed procedure is based on the constructive definition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule. This allows us to set in advance the closeness to the distributions of interest. The distribution of the stopping rule is derived, and the practicability of the simulating procedure is discussed. Sufficient conditions for convergence of random functionals are provided. The numerical applications provided just sketch the idea of the variety of nonparametric procedures that can be easily and safely implemented in a Bayesian setting.
TL;DR: In this article, bias-corrected confidence bands for general nonparametric regression models are considered and local polynomial fitting is used to construct the confidence bands and combine the cross-validation method and the plug-in method to select the bandwidths.
Abstract: Summary. Bias-corrected confidence bands for general nonparametric regression models are considered. We use local polynomial fitting to construct the confidence bands and combine the cross-validation method and the plug-in method to select the bandwidths. Related asymptotic results are obtained. Our simulations show that confidence bands constructed by local polynomial fitting have much better coverage than those constructed by using the Nadaraya‐Watson estimator. The results are also applicable to nonparametric autoregressive time series models.
TL;DR: Kernel weighted local linear regression smoothing of sample variogram ordinates and of squared residuals are considered to provide a nonparametric estimator for the covariance structure without assuming stationarity.
Abstract: In longitudinal studies, the effect of various treatments over time is usually of prime interest. However, observations on the same subject are usually correlated and any analysis should account for the underlying covariance structure. A nonparametric estimate of the covariance structure is useful, either as a guide to the formulation of a parametric model or as the basis for formal inference without imposing parametric assumptions. The sample covariance matrix provides such an estimate when the data consist of a short sequence of measurements at a common set of time points on each of many subjects but is impractical when the data are severely unbalanced or when the sequences of measurements on individual subjects are long relative to the number of subjects. The variogram of residuals from a saturated model for the mean response has previously been suggested as a nonparametric estimator for covariance structure assuming stationarity. In this paper, we consider kernel weighted local linear regression smoothing of sample variogram ordinates and of squared residuals to provide a nonparametric estimator for the covariance structure without assuming stationarity. The value of the estimator as a diagnostic tool is demonstrated in two applications, one to a set of data concerning the blood pressure of newborn babies in an intensive care unit and the other to data on the time evolution of CD4 cell numbers in HIV seroconverters. The use of the estimator in more formal statistical inferences concerning the mean profiles requires further study.
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TL;DR: This work suggests two improved methods for conditional density estimation based on locally fitting a log-linear model and a constrained local polynomial estimator, both of which always produce non-negative estimators.
Abstract: We suggest two new methods for conditional density estimation. The first is based on locally fitting a log-linear model, and is in the spirit of recent work on locally parametric techniques in density estimation. The second method is a constrained local polynomial estimator. Both methods always produce non-negative estimators. We propose an algorithm suitable for selecting the two bandwidths for either estimator. We also develop a new bootstrap test for the symmetry of conditional density functions. The proposed methods are illustrated by both simulation and application to a real data set.
TL;DR: The analysis shows that as long as a reduced dimension subvector of the regressor vector is PE, then a specialized form of exponential convergence will be achieved, which is critical since the general PE conditions are not practical in most control applications.
Abstract: This paper investigates nonparametric nonlinear adaptive control under passive learning conditions. Passive learning refers to the normal situation in control applications in which the system inputs cannot be selected freely by the learning system. This article also analyzes the stability of both the system state and approximator parameter estimates. Stability results are presented for both parametric (known model structure with unknown parameters) and nonparametric (unknown model structure resulting in /spl epsiv/-approximation error) adaptive control applications. Upper bounds on the tracking error are developed. The article also analyzes the persistence (PE) of excitation conditions required for parameter convergence. In addition, to a general PE analysis, the article presents a specific analysis pertinent to approximators that are composed of basis elements with local support. In particular, the analysis shows that as long as a reduced dimension subvector of the regressor vector is PE, then a specialized form of exponential convergence will be achieved. This condition is critical, since the general PE conditions are not practical in most control applications. In addition to the PE results, this article explicitly defines the regions over which the approximator converges when locally supported basis elements are used. The results are demonstrated throughout via examples.
TL;DR: In this article, a nonparametric, kernel-based test of parametric quantile regression models is proposed, which has a limiting standard normal distribution and diverges to infinity for any misspecification of the parametric model.
Abstract: This paper proposes a nonparametric, kernel-based test of parametric quantile regression models. The test statistic has a limiting standard normal distribution if the parametric quantile model is correctly specified and diverges to infinity for any misspecification of the parametric model. Thus the test is consistent against any fixed alternative. The test also has asymptotic power 1 against local alternatives converging to the null at proper rates. A simulation study is provided to evaluate the finite-sample performance of the test.