Showing papers on "Nonparametric statistics published in 1974"

Biostatistics: A Foundation for Analysis in the Health Sciences

Abstract: Introduction to Biostatistics Descriptive Statistics Some Basic Probability Concepts Probability Distributions Some Important Sampling Distributions Estimation Hypothesis Testing Analysis of Variance Simple Linear Regression and Correlation Multiple Regression and Correlation Regression Analysis - Some Additional Techniques The Chi-Square Distribution and the Analysis of Frequencies Nonparametric and Distribution-Free Statistics Vital Statistics.

Statistical techniques in business and economics

Abstract: What is statistics? summarizing data - frequency distributions and graphic presentation describing data - measure of central tendency measures of dispersion and skewness a survey of probability concepts discrete probability distributions the normal probability distribution sampling methods and sampling distributions tests of hypotheses - large samples tests of hypotheses - small samples analysis of variance linear regression and correlation multiple regression and correlation nonparametric methods - chi square applications nonparametric methods - analysis of ranked data statistical quality control index numbers time series and forecasting an introduction to decision making under uncertainty.

Nonparametric Estimation of a Survivorship Function with Doubly Censored Data

Abstract: A simple iterative procedure is proposed for obtaining estimates of a response time distribution when some of the data are censored on the left and some on the right. The procedure is based on the product-limit method of Kaplan and Meier [15], and it also uses the idea of self-consistency due to Efron [8]. Under fairly general assumptions, the method is shown to yield unique consistent maximum likelihood estimators. Asymptotic expressions for their variances and covariances are derived and an extension to the case of arbitrary censoring is suggested.

Adaptive Robust Procedures: A Partial Review and Some Suggestions for Future Applications and Theory

Abstract: After providing some background for the need to consider estimates other than those resulting from normal theory, there is a brief review of some nonadaptive robust estimators. We introduce adaptive estimators using those of Tukey and McLaughlin, Jaeckel, Johns, Birnbaum and Mike, Takeuchi, Hajek, van Eeden, and Beran. Adaptive estimators based on preliminary testing and Stein-like procedures are then considered, and recommendations are made on how to select the amount of trimming. Various proposals for estimating regression coefficients are also considered. Adaptive distrubution-free tests look very promising for improving the power of nonparametric tests, and some of these techniques can be used effectively in data analysis. Asymmetric trimmed means, adapted to the particular sample, can easily be used with data and provide good descriptive statistics having an approximate error structure. Finally, it is conjectured that estimators based on “cliff-hangers” might be extremely effective if there ...

Nonparametric Statistical Methods

Abstract: The Dichotomous Data Problem. The One--Sample Location Problem. The Two--Sample Location Problem. The Two--Sample Dispersion Problem and Other Two--Sample Problems. The One--Way Layout. The Two--Way Layout. The Independence Problem. Regression Problems. Comparing Two Success Probabilities. Life Distributions and Survival Analysis. Appendix. Bibliography. Answers to Selected Problems. Indexes.

A statistical analysis of telephone noise

Abstract: The results of a statistical analysis of telephone noise are presented. The analysis consists of two stages: an exploratory data analysis stage, where the data are characterized through various nonparametric statistics and a model-building stage, where the data are matched to models. The exploratory data analysis stage involved examination of noise waveforms, power spectra, and covariance estimates. The results show that telephone noise consists of a deterministic component (sinusoids at various frequencies) and a stochastic component. It is assumed that these components add. The data are filtered to remove the deterministic component. Next, central moment estimates are presented, as well as first-order amplitude statistics (histograms and empirical cumulative distributions) for these filtered data. The results indicate that the filtered data appear wide-sense stationary over short periods of time (typically 1 second) and, although close to gaussian, are distinctly nongaussian. The model-building stage involved fitting the filtered data to two classes of models. The first class of models is based on symmetric stable distributions that arise from the central limit theorem. The second class of models assumes two different physical processes that contribute to the random component of telephone noise: The low-variance process is assumed to be gaussian, while the high-variance component is assumed to be a filtered Poisson process. Both classes of models agree intuitively with the physical processes generating telephone noise and are mathematically tractable. Based largely on graphical tests, both models appear to fit the filtered data reasonably well.

Edgeworth Expansions in Nonparametric Statistics

Abstract: This is a survey of recent work on Edgeworth expansions for $(M)$ estimates, rank tests and some other statistics arising in nonparametric models. A Berry-Esseen theorem for $U$-statistics which seems to be new is also proved.

Asymptotic Normality of Nonparametric Tests for Independence

Abstract: Asymptotic normality of linear rank statistics for testing the hypothesis of independence is established under fixed alternatives. A generalization of a result of Bhuchongkul [I) is obtained both with respect to the conditions concerning the orders of magnitude of the score functions and with respect to the smoothness conditions on these functions.

Evaluation of a transformation method for estimation of normal range.

Abstract: We have evaluated a recently proposed method for estimating normal limits by prior transformation of data to gaussian-like form. Computer simulation techniques are used to generate random data from frequency distributions having various shapes. For each such distribution, the transformation method is compared with the method of nonparametric percentile estimation. We conclude that the nonparametric method should continue to be the method of choice unless data have a nearly symmetrical frequency distribution. The present state of methods for estimating normal ranges is discussed.

A non-parametric test of whether two simple regression lines are parallel'

Abstract: 1. Summary and initial remarks. If one desires to test whether two simple regression lines have the same slope, then one can, of course, use the standard test derived from least-squares theory if one is willing to assume that the distributions of the two sets of error terms are both normal and that they have the same variance. If the two distributions in question are both normal but have different variances, the tests of [1] and [10] are available. In soine cases, though, the experimenter may need a test which is valid for two arbitrary distributions of the two sets of error terms. The present paper presents such a test. The test bears a close resemblance to the Wilcoxon two-sample test [13, 7], and may be considered as an extension of the idea developed in [8] concerning the use of the Wilcoxon statistic with respect to a generalized Behrens-Fisher problem.

Nonparametric Estimation of Location

Abstract: A sequence of asymptotically normally distributed estimators of location is presented having the property that, for any ∈ > 0, all estimators in the sequence beyond an appropriate point have asymptotic variances within ∈ of the Cramer-Rao lower bound, uniformly for all symmetric distributions in a nonparametric family constrained only by regularity conditions. The simplest estimator in this sequence is the familiar trimmed mean. The next simplest estimator examined in some detail is shown to possess good efficiency-robustness properties, both asymptotically and for small sample sizes. This estimator is much easier to compute than previously proposed estimators having similar properties, and a good nonparametric estimate of the variance of the location estimator is produced as a by-product.

Asymptotic Normality of a New Nonparametric Statistic for Use in Organ Transplant Studies

Abstract: This article presents a proof of the asymptotic normality of a recently proposed nonparametric test statistic which has been used in analyzing heart transplant data.

Nonparametric Partial Correlation and Causal Analysis

Abstract: The properties of Quade's "index of matched correlation"are explored in the context of causal analysis Quade's approach is tested on data with specified characteristics generated through a computer simulation Although nonparametric partial correlation must be used with caution, it supplies an easily interpreted and applied method for analyzing categorized data

The ANOVA F-Test Versus The Kruskal-Wallis Test: A Robustness Study.

Abstract: Betty J. Feir, Oklahoma State University Larry E. Toothaker, University of Oklahoma Researchers are often in a dilemma as to whether parametric or nonparametric procedures should be cited when assumptions of the parametric methods are thought to be violated. Therefore, the Kruskal-Wallis test and the ANOVA F-test were empirically compared in terns of probability of a Type I error and power under various patterns of mean differences in combination with patterns of variance inequality, and patterns of sample size inequality. The Kruskal-Wallis test was found to be competitive with the ANOVA F-test in terms of alpha but not for power. Power of the KruskalWallis test was grossly affected in all but one situation for nonstepwise mean differences when sample sizes and variances were negatively related and when small levels of significance were utilized. The ANOVA Ftest, however, was found to be generally robust for the types of specified mean differences. (,)

Stopping Times of Some One-Sample Sequential Rank Tests

Abstract: Two models for modified, one-sample, sequential probability ratio tests based on Lehmann alternatives are considered, one developed by Weed and Bradley and one by Govindarajulu. It is shown how they are related. Sure termination of the SPRT's is established under very general conditions.

Nonparametric Subset Selection Procedures for the t Best Populations.

Abstract: : In this paper the authors propose some nonparametric selection procedures based on one-sample Hodges-Lehmann type estimators of the parameters for the symmetric location parameter populations. Some investigations of the efficiency are also discussed. (Author)

Some Nonparametric Multiple-Comparison Tests

Abstract: Some nonparametric multiple-comparison tests are described for making both pairwise comparisons and a limited number of comparisons with k independent and k matched groups when the data consist of “bad” numbers and ranks or frequencies.