Nonparametric two-sample tests for increasing convex order
6
Citation
13
Reference
10
Related Paper
Citation Trend
Abstract:
Given two independent samples of non-negative random variables with unknown distribution functions $F$ and $G$, respectively, we introduce and discuss two tests for the hypothesis that $F$ is less than or equal to $G$ in increasing convex order. The test statistics are based on the empirical stop-loss transform, critical values are obtained by a bootstrap procedure. It turns out that for the resampling a size switching is necessary. We show that the resulting tests are consistent against all alternatives and that they are asymptotically of the given size $α$. A specific feature of the problem is the behavior of the tests ‘inside’ the hypothesis, where $F≠G$. We also investigate and compare this aspect for the two tests.Keywords:
Resampling
Cite
Citations (1)
Resampling
Jackknife resampling
Cite
Citations (444)
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the private setting. We compare our tests to prior work, both on parametric and nonparametric tests. We find that in all cases our new nonparametric tests achieve large improvements in statistical power, even when the assumptions of parametric tests are met.
Categorical variable
Semiparametric regression
Goldfeld–Quandt test
Cite
Citations (4)
Researchers have preferred normal-theory tests over nonparametric procedures, despite evidence that the statistical properties of the latter are sometimes superior for variables and subject populations frequently encountered in educational and psychological research. Two ongoing concerns among researchers are that non-parametric tests exist only in simple cases (e.g., univariate one-, two-, and J-sample tests) and that these tests are often not available in statistical computing programs. The nonparametric hypothesis-testing model of Puri and Sen (1969, 1985) circumvents these concerns by permitting a variety of statistical hypotheses to be tested using existing computing programs. The breadth and flexibility of this model is illustrated with several examples.
Univariate
Cite
Citations (6)
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the private setting. We compare our tests to prior work, both on parametric and nonparametric tests. We find that in all cases our new nonparametric tests achieve large improvements in statistical power, even when the assumptions of parametric tests are met.
Categorical variable
Semiparametric regression
Goldfeld–Quandt test
Cite
Citations (0)
Statistic
Statistical power
Null (SQL)
Cite
Citations (7,796)
Resampling
Neurophysiology
Cite
Citations (29)
Abstract In several fields of applications, the underlying theoretical distribution is unknown and cannot be assumed to have a specific parametric distribution such as a normal distribution. Nonparametric statistical methods are preferable in these cases. Nonparametric testing hypotheses have been one of the primarily used statistical procedures for nearly a century, and the power of the test is an important property in nonparametric testing procedures. This review discusses the unbiasedness of nonparametric tests. In nonparametric hypothesis, the best‐known Wilcoxon–Mann–Whitney (WMW) test has both robustness and power performance. Therefore, the WMW test is widely used to determine the location parameter. In this review, the unbiasedness and biasedness of the WMW test for the location parameter family of the distribution is mainly investigated. An overview of historical developments, detailed discussions, and works on the unbiasedness/biasedness of several nonparametric tests are presented with references to numerous studies. Finally, we conclude this review with a discussion on the unbiasedness/biasedness of nonparametric test procedures. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Goldfeld–Quandt test
Robustness
Cite
Citations (1)
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the private setting. We compare our tests to prior work, both on parametric and nonparametric tests. We find that in all cases our new nonparametric tests achieve large improvements in statistical power, even when the assumptions of parametric tests are met.
Categorical variable
Goldfeld–Quandt test
Semiparametric regression
Normality test
Cite
Citations (28)
Statistical Inference
Semiparametric regression
Alternative hypothesis
Statistical power
Score test
Cite
Citations (97)