Showing papers on "Nonparametric statistics published in 1980"

Principles and Procedures of Statistics: A Biometrical Approach

Abstract: Observations probability sampling from a normal distribution comparisons involving two sample means principles of experimental design analysis of variance I - the one-way classification mutiple comparisons analysis of variance II - multiway classification linear regression linear correlation matrix notation linear regression in matrix notation multiple and partial regression and correlation analysis of variance III - factorial experiments analysis of variance analysis of covariance IV analysis of covariance analysis of variance V - unequal subclass numbers some uses of chi-square enumeration data I - one-way classifications enumeration data II - contingency tables categorical models some discrete distributions nonparametric statistics sampling finite populations.

Statistical Reasoning for the Behavioral Sciences

Abstract: Preface. I. RESEARCH AND THE ROLE OF STATISTICS. 1. Research Design in the Behavioral Sciences. 2. Statistics in Context: Research on Teacher Expectancy. II. DESCRIPTIVE STATISTICS FOR UNIVARIATE DISTRIBUTIONS. 3. Frequency Distributions. 4. Measures of Central Tendency and Variability. 5. The Normal Distribution. III. DESCRIPTIVE STATISTICS FOR JOINT DISTRIBUTIONS. 6. Joint Distributions and Correlation Coefficients. 7. Linear Regression. IV. REASONING BEHIND STATISTICAL INFERENCE. 8. Statistical Inference: By Intuition. 9. Probability Theory and Mathematical Distributions. 10. Statistical Inference Using the Normal Distribution. 11. Decisions, Error, and Power. V. STATISTICAL TESTS FOR BETWEEN-SUBJECTS DESIGNS. 12. Tests for Case I and Case II Research. 13. One-Way Analysis of Variance. 14. Factorial Analysis of Variance. VI. STATISTICAL TESTS FOR WITHIN-SUBJECTS AND MIXED DESIGNS. 15. Randomized-Blocks Analysis of Variance. 16. Split-Plot Analysis of Variance. 17. Analysis of Covariance. VII. ADDITIONAL TOPICS: CORRELATIONAL AND NONPARAMETRIC STATISTICAL ANALYSIS. 18. Multiple Regression Analysis. 19. Chi Square Tests. 20. Additional Nonparametric Tests. Appendix I. Review of Summation Notation. Appendix II. Miscellaneous Tables. Appendix III. Glossary of Formulas. References. Index.

Schaum's Outline of Theory and Problems of Probability and Statistics

Abstract: Part I: Probability Chapter 1: Basic Probability Chapter 2: Random Variables and Probability Distributions Chapter 3: Mathematical Expectation Chapter 4: Special Probability Distributions Part II: Statistics Chapter 5: Sampling Theory Chapter 6: Estimation Theory Chapter 7: Tests of Hypotheses and Significance Chapter 8: Curve Fitting, Regression, and Correlation Chapter 9: Analysis of Variance Chapter 10: Nonparametric Tests Appendices Index Index for Solved Problems

On simulating non-normal distributions

Abstract: Six different algorithms to generate widely different non-normal distributions are reviewed. These algorithms are compared in terms of speed, simplicity and generality of the technique. The advantages and disadvantages of using these algorithms are briefly discussed.

Estimation of the failure rate-a survey of nonparametric methods Part I: Non-Bayesian Methods

Abstract: In this paper several nonparametric, non-Bayesian methods for estimating the failure rate function on which no monotonicity conditions have been imposed are surveyed. The survey attempts to consolidate and synthesize literature from several diverse areas of application, and endeavors to be as up-to-date as is feasible.

Developments in Nonparametric Density-Estimation

Abstract: Summary The object of the present study is to summarize recent developments in nonparametric density estimation. The study covers the period of time from 1956 to 1978. Most of the important types of nonparametric density estimations are discussed. These include Parzen or kernel estimators, series estimators, penalized maximum likelihood estimators, and various other types of nonparametric density estimation techniques.

Towards a unified definition of maximum likelihood

Abstract: A unified definition of maximum likelihood (ml) is given. It is based on a pairwise comparison of probability measures near the observed data point. This definition does not suffer from the usual inadequacies of earlier definitions, i.e., it does not depend on the choice of a density version in the dominated case. The definition covers the undominated case as well, i.e., it provides a consistent approach to nonparametric ml problems, which heretofore have been solved on a more less ad hoc basis. It is shown that the new ml definition is a true extension of the classical ml approach, as it is practiced in the dominated case. Hence the classical methodology can simply be subsumed. Parametric and nonparametric examples are discussed.

Some results on estimating a change-point using non-parametric type statistics

Abstract: A Mann-Whitney type statistic is used to estimate a change-point when a change, at an unknown point in a sequence of random variables, has taken place. This estimate is compared, using Monte Carlo techniques, with the normal theory maximum likelihood estimate, when a location change has occurred, for different underlying distributions ranging from the normal to the long tailed “normal over uniform” distribution. The distribution of the Mann-Whitney type estimate remains fairly constant over the various distributions. Two generalisations of the statistic are considered and investigated.

A Survey of Approaches to Solving Inverse Problems for Lossless Layered Media Systems

Abstract: In this paper, we survey approaches to solving inverse problems for lossless layered systems Such systems can be modeled in two different ways, by nonparametric or parametric models We review both models, but concentrate our attention on inverse and estimation procedures for parametric models Algebraic inverse procedures are described for determining the reflection coefficient parameters when measurements are noise free An extension of these procedures to the case of noisy data is also discussed; but, resulting reflection coefficient values are suboptimal Finally, we describe two procedures for estimating reflection coefficients from noisy data One of these, which is very promising, is a maximum-likelihood procedure, which is not only able to provide estimates of reflection coefficients, but is also able to provide estimates of another set of parameters, layer travel times These maximum-likelihood estimates are optimal

On Approximating Parametric Bayes Models by Nonparametric Bayes Models

Abstract: Let $\tau$ be a prior distribution over the parameter space $\Theta$ for a given parametric model $P_\theta, \theta \in \Theta$. For the sample space $\mathscr{X}$ (over which $P_\theta$'s are probability measures) belonging to a general class of topological spaces, which include the usual Euclidean spaces, it is shown that this parametric Bayes model can be approximated by a nonparametric Bayes model of the form of a mixture of Dirichlet processes prior, so that (i) the nonparametric prior assigns most of its weight to neighborhoods of the parametric model, and (ii) the Bayes rule for the nonparametric model is close to the Bayes rule for the parametric model in the no-sample case. Moreover, any prior parametric or nonparametric, may be approximated arbitrarily closely by a prior which is a mixture of Dirichlet processes. These results have implications in Bayesian inference.

Distribution-free partially sequential piacment procedures

Abstract: The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample Exact and asymptotic, as the fixed sample size in¬creases to infinity, properties of these sequential placements procedures are obtained, including statements about the power and expected number of sequentially obtained observations The results of a Monte Carlo study are used to differentiate be¬tween various placement scoring schemes

Nonparametric Testing for Time Series: a Bibliography

Abstract: This bibliography brings together and classifies a wide variety of nonparametric methods which are pocentially useful for the analysis of time series data, in particular for testing randomness. Inference on Markov chain models is also extensively surveyed.

$(k - 1)$-Mean Significance Levels of Nonparametric Multiple Comparisons Procedures

Abstract: We consider the nonparametric pairwise comparisons procedures derived from the Kruskal-Wallis $k$-sample test and from Friedman's test. For large samples the $(k - 1)$-mean significance level is determined, i.e., the probability of concluding incorrectly that some of the first $k - 1$ samples are unequal. We show that in general this probability may be larger than the simultaneous significance level $\alpha$. Even when the $k$th sample is a shift of the other $k - 1$ samples, it may exceed $\alpha$, if the distributions are very skew. Here skewness is defined with Van Zwet's $c$-ordering of distribution functions.

Nonparametric Tests of Independence for Censored Data.

Abstract: : The work accomplished by six Tech Reports already issued. Papers based on two of them are accepted for publication and are soon to be published in two of the leading journals in statistics. One other is submitted for publication. And yet another will appear in Proceedings of a conference on nonparametric statistics. (Author)

Bootstrapping a basic inequality in the analysis of joint action of two drugs.

Abstract: This communication discusses the relevance of a basic inequality for bivariate probability distributions for general nonparametric modelling of independent action of two drugs. A bootstrap method is used to estimate a measure of agreement between observed data and this model.

Small sample behaviour of some nonparametric multi-sample location tests in the presence of dispersion differences

Abstract: Summary This paper describes the small and moderate sample behaviour of three studentized non-parametric statistics by Sen and a modified Wilcoxon statistic by Potthoff for testing the equality of location parameters in the presence of dispersion differences. Based on the agreement between the asymptotic and small sample distributions of the statistics as well as a comparison of their power under heteroscedasticity, the studentized Wilcoxon and the studentized Brown and Mood tests arc preferred in the two-sample and c-sample situations, respectively.

Asymptotically Minimal Multivariate Tolerance Sets

Abstract: Multivariate β-content tolerance sets with asymptotic confidence level γ(0<γ⩽1) are defined and the requirement of asymptotic minimality for such sets is formulated. A method of construction of asymptotically minimal tolerance sets baFed on uniformly consistent density estimates ia developed. Application of the method in certain parametric situations based on parameter estimates and certain nonparametric situations based on window estimates of the density is considered.

Interpretation of research data: selected statistical procedures.

Abstract: Selected statistical procedures used in the analysis of research data are presented. The relationship of significance testing to research hypotheses is explained in terms of tests of differences and correlation. Also, the differences, assumptions, and advantages and disadvantages of parametric and nonparametric statistics are discussed. With regard to each statistic presented, emphasis is placed on the hypotheses that would be tested, the kinds of data for which the statistic is appropriate, the method of calculation, and how to test for "significance." The selected statistical procedures include the Student's t-test and chi square. An explanation of the concept of correlation is provided, and several correlation coefficients are discussed, including the Pearson r, Spearman rho, Kendall's tau, the point biserial, biserial, phi coefficient, and contingency coefficient. Pharmacists must know basic statistical procedures in order to be able to effectively interpret the results of published research or to appropriately analyze data that have been collected in their own research endeavors.

Nonparametric Bayesian Estimation of the Horizontal Distance between two Populations.

Abstract: : The horizontal distance delta (X) =1/G (F(x)) -x has been shown by Doksum (1974) to be a useful measure of difference, at each x, between the populations defined by continuous distribution functions F(x) and G(x).

Robust and nonparametric subset selection procedures

Abstract: Subset selection procedures based on ranks have been investigated by a number of authors previously. Their methods are based on ranking the samples from all the populations jointly. However, as was pointed out by Rizvi and Woodworth (1970), the procedures they proposed cannot control the probability of a correct selection over the entire parameter space. In this paper, we propose a subset selection procedure based on pairwise rather than joint ranking of the samples. It is shown that this procedure controls the probability of a correct selection over the entire parameter space. It is also shown that the Pitman efficiency of this nonparametric procedure relative to the multivariate t procedure of Gupta (1956, 1965) is the same as the Pitman efficiency of the Mann-Whitney-Wilcoxon test relative to the t-test.

Parametric Assumptions of Some "Nonparametric" Measures of Sensory Efficiency:

Abstract: Nonparametric measures of sensory efficiency suggested by Craig (1979) for use in sustained monitoring tasks are shown to be dependent on distributional assumptions when based on one point in ROC space.