Topic
Sample maximum and minimum
About: Sample maximum and minimum is a research topic. Over the lifetime, 70 publications have been published within this topic receiving 1660 citations.
Papers published on a yearly basis
Papers
TL;DR: This article studies the small sample behavior of several test statistics that are based on maximum likelihood estimator, but are designed to perform better with nonnormal data.
Abstract: Structural equation modeling is a well-known technique for studying relationships among multivariate data. In practice, high dimensional nonnormal data with small to medium sample sizes are very common, and large sample theory, on which almost all modeling statistics are based, cannot be invoked for model evaluation with test statistics. The most natural method for nonnormal data, the asymptotically distribution free procedure, is not defined when the sample size is less than the number of nonduplicated elements in the sample covariance. Since normal theory maximum likelihood estimation remains defined for intermediate to small sample size, it may be invoked but with the probable consequence of distorted performance in model evaluation. This article studies the small sample behavior of several test statistics that are based on maximum likelihood estimator, but are designed to perform better with nonnormal data. We aim to identify statistics that work reasonably well for a range of small sample sizes and distribution conditions. Monte Carlo results indicate that Yuan and Bentler's recently proposed F-statistic performs satisfactorily.
637 citations
Book•
1 Jan 1986
TL;DR: In this paper, the Pearson Product-Moment Correlation Coefficient is used to measure the correlation between two distributions and its relation to the correlation coefficient of the mean and the standard deviation of the distribution.
Abstract: Part I: Descriptive Statistics. 1. The Study Of Statistics. Why Study Statistics? Descriptive and Inferential Statistics. Measurement. Summation sign. Summary. 2. Frequency Distributions And Graphing. Types of Frequency Distributions. Constructing Frequency Distributions with Class Intervals. Graphs of Frequency Distributions. How Distributions Differ. Summary. 3. Characteristics Of Distributions. Indicators of Central Tendency. Indicators of Variability. Populations and Samples. A Note on Calculators and Computers. Summary. 4. Elements Of Exploratory Data Analysis. Stem and Leaf Displays. Resistant Indicators. Summary. 5. Indicators Of Relative Standing. Percentiles. Changing the Properties of Scales. Standard Scores and the Normal Distribution. Summary. 6. Regression. Linear Relationships. Regression Constants and the Regression Line. Standard Error of Estimate. Summary. 7. Correlation. The Pearson Product-Moment Correlation Coefficient. Properties of the Correlation Coefficient. Sampling Factors that Change the Correlation Coefficient. Causality and Correlation. Summary. Part II: Inferential Statistics. 8. Sampling, Sampling Distributions, And Probability. Methods of Sampling. Sampling Distributions and Sampling Error. Probability and its Application to Hypothesis Testing. Estimation. Summary. 9. Introduction To Hypothesis Testing: Terminology And Theory. Statistical Terminology. Hypothesis Testing When Alpha X is Estimated by Sigma X. Summary. 10. Elementary Techniques Of Hypothesis Testing. Inferences About the Difference Between Means. Inferences About Correlation Coefficients. A Comparison of the Difference Between Means and Correlation. Statistics in the Journals. Summary. 11. Beyond Hypothesis Testing: Effect Size And Interval Estimation. Beyond Hypothesis Testing. Indices of Size. Interval Estimation. Summary. Part III: Special Topics. 12. Introduction To Research Design. Scientific Questions. Operationalizing. Data Collection and Data Analysis. Conclusions and Interpretations. The Research Report. Ethical Considerations. Summary. 13. Topics On Probability. Set Theory. Simple Classical Probability. Probability of Complex Events. Methods of Counting. Summary. 14. Simple Analysis Of Variance. Logic of the Analysis of Variance. Computational Procedures. Comparisons Between Specific Means. Size of Relationship. Summary. 15. Two-Factor Analysis Of Variance. Two-Factor Classification. Logic of Two-Factor Analysis of Variance. Computational Procedures. Summary. 16. Nonparametric Techniques. Parametric and Nonparametric Tests. Tests on Independent Samples. Tests on Correlated Samples. Rank-Order Correlation. Summary. Appendix 1: Math Review. Appendix 2: Tables. Appendix 3: Symbols. Appendix 4: Terms. Appendix 5: Answers. Index.
443 citations
TL;DR: In this article, an approximation to the mathematical relation between the variate value z and the unknown distribution function F of the continuous, univariate population from which a sample is available is obtained in which z is expressed as a series of polynomials in F; the coefficients are the expectations of linear combinations of the order statistics of the sample.
Abstract: SUMMARY Approximations to the mathematical relation between the variate value z and the unknown distribution function F of the continuous, univariate population from which a sample is available are obtained in which z is expressed as a series of polynomials in F; the coefficients are the expectations of linear combinations of the order statistics of the sample. A particular system of orthogonal polynomials and a particular system of n linearly independent linear systematic statistics of a sample of n emerge naturally as apt for the purpose. General relations are found for the variances and covariances of these statistics, thus enabling them to be used as a vector basis in terms of which other linear combinations of the order statistics can be expressed and their variances and mutual covariances investigated.
78 citations
Abstract: Abstract Suppose A is a bounded set in ℛ d and f a real function defined on A. Suppose m = min{f(x; | x ∈ A} exists. Using a random sample X 1, X 2. …, X n from a uniform distribution over A we construct a confidence interval for m using asymptotic theory. Our results contain some statistical results valid in general extreme value theory (estimation of the main parameter of extreme value distributions).
76 citations
TL;DR: In this article, a Monte Carlo method was developed to obtain the p values of function-indexed statistics, and the moderate sample size properties of this method were evaluated in a data analysis of the Beta-Blocker Heart Attack Trial.
Abstract: Two-sample weighted log-rank statistics are used in the presence of right censoring to test whether failure times from two populations have different survival distributions. Kosorok has showed that large families of these statistics form stochastic processes indexed by weight functions, and that these function-indexed statistics can be used to construct versatile test procedures simultaneously sensitive to a wide array of both ordered hazards and stochastic ordering alternatives. The complexity of the asymptotic distribution of these statistics precludes obtaining p values through analytical means. In this article we develop a Monte Carlo method for accurately obtaining these p values, and we evaluate the moderate sample size properties of this method and compare the power of function-indexed statistics with previously developed weighted log-rank tests. These statistics are also examined in a data analysis of the Beta-Blocker Heart Attack Trial (BHAT). The results of this article demonstrate that...
59 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 3 |
| 2016 | 2 |
| 2015 | 3 |
| 2014 | 3 |
| 2013 | 3 |
| 2012 | 3 |