Showing papers on "Nonparametric statistics published in 1973"
Book•
01 Mar 1973
TL;DR: An ideal text for an upper-level undergraduate or first-year graduate course, Nonparametric Statistical Methods, Second Edition is also an invaluable source for professionals who want to keep abreast of the latest developments within this dynamic branch of modern statistics.
Abstract: This Second Edition of Myles Hollander and Douglas A. Wolfe's successful Nonparametric Statistical Methods meets the needs of a new generation of users, with completely up-to-date coverage of this important statistical area. Like its predecessor, the revised edition, along with its companion ftp site, aims to equip readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for a given situation. An extensive array of examples drawn from actual experiments illustrates clearly how to use nonparametric approaches to handle one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. An ideal text for an upper-level undergraduate or first-year graduate course, Nonparametric Statistical Methods, Second Edition is also an invaluable source for professionals who want to keep abreast of the latest developments within this dynamic branch of modern statistics.
7,240 citations
Book•
01 Jan 1973
TL;DR: In this article, a thoroughly revised edition presents important methods in the quantitative analysis of geologic data, such as probability, nonparametric statistics, and Fourier analysis, as well as data analysis methods such as the semivariogram and the process of kriging.
Abstract: From the Publisher:
This thoroughly revised edition presents important methods in the quantitative analysis of geologic data. Retains the basic arrangement of the previous edition but expands sections on probability, nonparametric statistics, and Fourier analysis. Contains revised coverage of eigenvalues and eigenvectors, and new coverage of data analysis methods, such as the semivariogram and the process of kriging.
5,956 citations
2,137 citations
TL;DR: In this article, the authors proposed a nonparametric spectrum factorization method for time series, where the model is formulated explicitly in terms of the spectral density function, and may also be viewed as a spectrum factorisation method.
Abstract: SUMMARY Existing procedures for obtaining linear prediction formulae for time series may be placed in two categories. The first consists of methods which involve fitting parametric models of the autoregressive or autoregressive moving average type. The second involves the factorization of an estimated spectral density function; this is essentially a nonparametric procedure. The procedure suggested in this paper contains elements of both of the above. Formally, it involves fitting a model with a finite number of parameters. However, the model is formulated explicitly in terms of the spectral density function, and may also be viewed as a spectrum factorization method. The model has been fitted to various series considered by other authors, and the quality of the fit is compared with that obtained with conventional models using the same number of parameters. Asymptotie properties of the parameter estimates have been used to assess the nonparametric spectrum factorization techniques proposed by other authors.
580 citations
TL;DR: In this article, the authors introduce Probability One-Dimension Random Variables Functions of One Random Variable and Expectation Joint Probability Distributions Some Important Discrete Distributions some Important Continuous Distributions The Normal Distribution Random Samples and Sampling Distributions Parameter Estimation Tests of Hypotheses Design and Analysis of Single Factor Experiments: The Analysis of Variance Design of Experiments with Several Factors Simple Linear Regression and Correlation Multiple Regression Nonparametric Statistics Statistical Quality Control and Reliability Engineering Stochastic Processes and Queueing Statistical Decision Theory References
Abstract: Introduction and Data Description An Introduction to Probability One-Dimension Random Variables Functions of One Random Variable and Expectation Joint Probability Distributions Some Important Discrete Distributions Some Important Continuous Distributions The Normal Distribution Random Samples and Sampling Distributions Parameter Estimation Tests of Hypotheses Design and Analysis of Single-Factor Experiments: The Analysis of Variance Design of Experiments with Several Factors Simple Linear Regression and Correlation Multiple Regression Nonparametric Statistics Statistical Quality Control and Reliability Engineering Stochastic Processes and Queueing Statistical Decision Theory References Appendix Answers to Selected Exercises Index.
531 citations
TL;DR: MCCALL and APPELBAUM as discussed by the authors consider several alternatives when heterogeneity of covariance exists, including nonparametric tests, randomization and matching procedures, Box and Greenhouse-Geisser corrections, and multivariate analysis.
Abstract: MCCALL, ROBERT B., and APPELBAUM, MARK I. Bias in the Analysis of Repeated-Measures Designs: Some Alternative Approaches. CHILD DEVELOPMENT, 1973, 44, 401-415. The conventional analysis of variance applied to designs in which each subject is measured repeatedly requires stringent assumptions regarding the variance-covariance (i.e., correlations among repeated measures) structure of the data. Violation of these assumptions results in too many rejections of the null hypothesis for the stated significance level. This paper considers several alternatives when heterogeneity of covariance exists, including nonparametric tests, randomization and matching procedures, Box and Greenhouse-Geisser corrections, and multivariate analysis. The presentation is from an applied rather than theoretical standpoint. Multivariate techniques that make no covariance assumptions and provide exact probability statements represent the most versatile solution.
394 citations
01 Jan 1973
TL;DR: A nonparametric clustering technique incorporating the concept ofsimilarity based sharing of near-neighbors is presented, proving its applicability to a class of practical problems involving large sample size and high dimensionality.
Abstract: A nonparametric clustering technique incorporating the concept ofsimilarity basedonthesharing ofnearneighbors ispre- sented. Inaddition tobeing anessentially paraliel approach, thecom- putational elegance ofthemethodissuchthattheschemeisapplicable toawideclass ofpractical problems involving large sample size andhigh dimensionality. No attempt ismadetoshowhowapriori problem knowledge canbeintroduced into theprocedure. IndexTerms-Clustering, nonparametric, pattern recognition, shared nearneighbors, similarity measure.
90 citations
TL;DR: In this article, a general class of rank order tests for progressive censoring is proposed along with a basic martinga:le property and a Brownian motion approximation for a related rank order process, asymptotic distribution theory of the proposed statistics is developed.
Abstract: SummaryProgressive censoring schemes (allowing a continuous monitoring of experimentation until a terminal decision is reached) are often adopted in clinical trials and life testing problems. In this paper, a general class of rank order tests for progressive censoring is proposed. Along with a basic martinga:le property and a Brownian motion approximation for a related rank order process, asymptotic distribution theory of the proposed statistics is developed. Asymptotic performance characteristics of the proposed tests (in the light of Bahadur efficiency and the stochastic smallness of the stopping variables) are studied.
88 citations
TL;DR: This paper develops a direct implementation of a nonparametric representation of a curve, f(x, y) = 0, that allows steps to be taken to any point adjacent to the current one, and uses decision variables closely related to an error criterion.
Abstract: Generation of curves using incremental steps along fixed coordinate axes is important in such diverse areas as computer displays, digital plotters, and numerical control. Direct implementation of a nonparametric representation of a curve, f(x, y) = 0, has been shown to be attractive for digital generation. The algorithm in this paper is developed directly from the nonparametric representation of the curve, allows steps to be taken to any point adjacent to the current one, and uses decision variables closely related to an error criterion. Consequently, the algorithm is more general and produces curves closer to the actual curve than do previously reported algorithms.
87 citations
TL;DR: A new nonparametric method of estimating the Bayes risk using an unclassified test sample set as well as a classified design sample set is introduced, which provides unbiased estimates of the k -NN classification error, thus providing an upper bound on the Baye error.
Abstract: A new nonparametric method of estimating the Bayes risk using an unclassified test sample set as well as a classified design sample set is introduced. The classified design set is used to obtain nonparametric estimates of the conditional Bayes risk of classification at each point of the unclassified test set. The average of these risk estimates is the error estimate. For large numbers of design samples the new error estimate has less variance than does an error-count estimate for classified test samples using the optimum Bayes classifier. The first application of the nonparametric method uses k -nearest neighbor ( k -NN) estimates of the posterior probabilities to form the risk estimate. A large-sample analysis is made of this estimate. The expected value of this estimate is shown to be a lower bound on the Bayes error. A simple modification provides unbiased estimates of the k -NN classification error, thus providing an upper bound on the Bayes error. The second application of the method uses Parzen approximation of the density functions to obtain estimates of the risk and subsequently the Bayes error. Results of experiments on simulated data illustrate the small-sample behavior.
86 citations
TL;DR: In this paper, the authors show that the computation for randomization test counterparts of the t test and one-way analysis of variance can be relatively inexpensive when performed by a high-speed computer.
Abstract: Summary Even though randomization tests are the most powerful of nonparametric tests and are the only valid tests to employ when there has been random assignment, but not random selection, of subjects in experiments (a common practice in psychology), such tests are rarely used by psychologists. The limited adoption of randomization tests is primarily a consequence of the great amount of computation they require. The present study shows, however, that the computation for randomization test counterparts of the t test and one-way analysis of variance can be relatively inexpensive when performed by a high-speed computer.
TL;DR: In this paper, a measure of interaction in factorial experiments is introduced and the problem of estimating it and testing it for nullity is considered, and the asymptotic power efficiencies are studied and Monte Carlo power comparisons are made when samples are drawn from normal and scale contaminated compound normal distributions.
Abstract: A measure of interaction in factorial experiments is introduced and the problem of estimating it and testing it for nullity is considered. The asymptotic power efficiencies are studied and Monte Carlo power comparisons are made when samples are drawn from normal and scale contaminated compound normal distributions. The proposed test showed improved power over the normal theory F test and other rank tests for moderately large samples taken from the heavy tailed distributions.
TL;DR: Inference procedures based on simple rank statistics are proposed and studied for the statistical analysis of longitudinal data in this article, which do not require the basic assumption of multivariate normality of the underlying distributions.
Abstract: Inference procedures based on some simple rank statistics are proposed and studied for the statistical analysis of longitudinal data. These robust and asymptotically efficient procedures do not require the basic assumption of multivariate normality of the underlying distributions. The theory is illustrated with two examples.
TL;DR: In this article, the Reed-Muench and Dragstedt-Behrens estimators are shown to be estimators of the mean, not the median, tolerance and to be nearly equivalent to the Spearman-Karber estimator.
Abstract: SUMMARY Theoretical properties of the Spearman-Karber estimator of the mean tolerance in a quantal response bioassay are discussed, and its limiting distribution is studied under three different limiting processes. The Reed-Muench and Dragstedt-Behrens estimators are shown to be estimators of the mean, not the median, tolerance and to be nearly equivalent to the Spearman-Karber estimator. The limiting distributions of the Reed-Muench estimator are considered in detail.
Journal Article•
TL;DR: In this paper, the authors consider the problem of estimating the mode of an unknown multivariate probability density function and establish conditions under which their estimate of the population mode is strongly consistent and asymptotically normal.
Abstract: The problem of estimating the mode of a probability density function is a matter of both theoretical and practical interest. This problem was first considered by Parzen (1962) in the univariate situation. He has shown that under certain regularity conditions the estimate of the population mode obtained by maximizing an estimate of the true probability density function is consistent and asymptotically normal. The strongest result in this direction is due to Nadaraya (1965) who has proved that under certain regularity conditions the estimate con verges to the theoretical mode with probability one. In this paper we consider the problem of estimating the mode of an unknown multivariate probability density function. We establish conditions under which our estimate of the . population mode is strongly consistent and asymptotically normal.
01 Jan 1973
TL;DR: In this paper, the authors present a general theory regarding classification into known distributions, rules based on ranks, rules on tolerance regions and distance between empirical CDFs, nearest neighbor rules, rules with density estimates, nonparametric or distribution-free methods, classification into more than two multivariate normal populations with different covariance matrices, compounddecision and empirical Bayes approaches, and general theory of classification when the information about the distribution is based on samples.
Abstract: Publisher Summary This chapter discusses the theories and methods used in classification. It presents a general theory regarding classification into known distributions, rules based on ranks, rules based on tolerance regions, rules based on distances between empirical CDFs, nearest neighbor rules, rules with density estimates, nonparametric or distribution-free methods, classification into more than two multivariate normal populations, classification into two multivariate normal populations with different covariance matrices, compound-decision and empirical Bayes approaches, and general theory of classification when the information about the distribution is based on samples. A best-of-class or constructive rule is given by the one that optimizes certain specified criteria in a given class. The so-called nonparametric or distribution-free methods are used in statistical inference when one is concerned with a wide class of distributions that usually cannot be expressed as a parametric family with a finite number of parameters.
TL;DR: In this paper, three statistics that could be used to test that hypothesis using a ratio of linear combinations of independent Chi-square statistics were examined for a number of con-figurations of nuisance parameters.
Abstract: When an experiment is run with a factorial layout and some of the factors are random effects, there may not be an exact test for some effect of interest. This paper considers three statistics that could be used to test that hypothesis using a ratio of linear combinations of independent Chi-square statistics. The common case, utilizing four Chi-square statistics, is examined for a number of con-figurations of nuisance parameters. Both the power and the probability of a type I error are used in the comparison. Two statistics appear to be equally good over a large region and, in certain situations, the statistics involving the subtraction of Chi-square statistics is shown to be more stable.
TL;DR: In this article, a modification of Wesolowsky's approach was shown to result in a nonparametric linear program, and further, a different approach to the problem will yield a simpler formulation as a smaller linear program.
Abstract: In a recent edition of this journal, Wesolowsky (Trans. Sci. 6, 103–113) presents a formulation of a multifoxility minimax location problem for rectilinear distances as a parametric linear program. It is shown here that a modification of Wesolowsky's approach will result in a nonparametric linear program, and further, that a different approach to the problem will yield a simpler formulation as a smaller linear program.
TL;DR: Sign-bit semblance as mentioned in this paper is a nonparametric detector that uses only the sign bits of the seismic data and, hence, requires less storage and is faster to compute than other detection statistics.
Abstract: By casting the problem of seismic signal detection as one of statistical detection theory, one can develop a myriad of detection statistics or detectors. Of these, one of the most promising appears to be sign‐bit semblance. This nonparametric detector makes use of only the sign bits of the seismic data and, hence, requires less storage and is faster to compute than other detection statistics. In addition, it is independent of the noise statistics, as are all nonparametric detectors. An automatic velocity analysis and interpretation program has been developed using sign‐bit semblance as the detection statistic. The statistical properties of sign‐bit semblance were such that this system could do a velocity analysis and an interpretation with no human intervention. In this mode of operation it yielded state‐of‐the‐art accuracy at greatly increased speed and with greatly reduced storage requirements. These results indicate that sign‐bit semblance can be used to advantage for certain other seismic‐data process...
TL;DR: In this article, a class of permutationally distribution-free tests has been proposed and their asymptotic optimality has been established for ungrouped data, and an alternative test to the problem of paired comparison has been considered.
Abstract: In a previous paper [5], the author has proposed a class of asymptotically optimal (in the sense of Wald [11]) nonparametric tests for testing the hypothesis of no regression in a multiple linear regression model. In the present paper, we are interested in testing that the intercept in the multiple (linear) regression model is zero along with the absence of regression. A class of permutationally distribution-free tests has been proposed and their asymptotic optimality has been established. These results generalize analogus findings of Puri and Sen [9] for ungrouped data. As an important application, an alternative test to the problem of paired comparison has been considered.
TL;DR: The results of computer experiments with artificially generated data and with handprinted alphanumeric characters are given to show that the approach proposed is quite useful for recognition of Markovian patterns.
TL;DR: In this paper, a new nonparametric selection procedure (conjectured to be better than BS) is proposed, which is substantially better than reasonable competitors designed specifically for 2-point populations.
Abstract: A nonparametric selection procedure bs was proposed by Bechhofer and Sobel (1958) and studied by Dudewicz (1971) in comparison with other procedures under normal and uniform alternatives. He found BS always required larger sample sizes, sometimes substantially so. For 2-point populations we find more extreme results. We also find that BS may be substantially better than reasonable competitors designed specifically for 2-point populations. Finally, a new nonparametric selection procedure (conjectured to be better than BS) is proposed.