A test for block circular symmetric covariance structure with divergent dimension

2019 ◽  
Vol 23 ◽  
pp. 672-696
Author(s):  
Junshan Xie ◽  
Gaoming Sun
Keyword(s):  
Numerical Simulations ◽  
Sample Size ◽  
Asymptotic Distribution ◽  
Null Hypothesis ◽  
Covariance Structure ◽  
Moderate Deviation ◽  
Test Method ◽  
Test Statistic ◽  
Lr Test ◽  
Structure Test

The paper considers the likelihood ratio (LR) test on the block circular symmetric covariance structure of a multivariate Gaussian population with divergent dimension. When the sample size n, the dimension of each block p and the number of blocks u satisfy pu < n − 1 and p = p(n) → ∞ as n → ∞, the asymptotic distribution and the moderate deviation principle of the logarithmic LR test statistic under the null hypothesis are established. Some numerical simulations indicate that the proposed LR test method performs well in the divergent-dimensional block circular symmetric covariance structure test.

Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

1987 ◽  
Vol 3 (1) ◽  
pp. 69-97 ◽  
Author(s):  
M. Hashem Pesaran
Keyword(s):  
Probability Density ◽  
Asymptotic Distribution ◽  
Null Hypothesis ◽  
Probability Density Functions ◽  
Density Functions ◽  
Local Alternatives ◽  
Hypotheses Testing ◽  
Local Power ◽  
Test Statistic ◽  
Local Alternative

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

scholarly journals REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction

2021 ◽  
Author(s):  
Zaheer Ahmed ◽  
Alberto Cassese ◽  
Gerard van Breukelen ◽  
Jan Schepers
Keyword(s):  
Null Hypothesis ◽  
Type I Error ◽  
Type I ◽  
The Novel ◽  
Simulation Studies ◽  
Test Statistic ◽  
Clustering Model ◽  
Novel Method ◽  
Main Effects ◽  
Empirical Case Studies

AbstractWe present a novel method, REMAXINT, that captures the gist of two-way interaction in row by column (i.e., two-mode) data, with one observation per cell. REMAXINT is a probabilistic two-mode clustering model that yields two-mode partitions with maximal interaction between row and column clusters. For estimation of the parameters of REMAXINT, we maximize a conditional classification likelihood in which the random row (or column) main effects are conditioned out. For testing the null hypothesis of no interaction between row and column clusters, we propose a $$max-F$$ m a x - F test statistic and discuss its properties. We develop a Monte Carlo approach to obtain its sampling distribution under the null hypothesis. We evaluate the performance of the method through simulation studies. Specifically, for selected values of data size and (true) numbers of clusters, we obtain critical values of the $$max-F$$ m a x - F statistic, determine empirical Type I error rate of the proposed inferential procedure and study its power to reject the null hypothesis. Next, we show that the novel method is useful in a variety of applications by presenting two empirical case studies and end with some concluding remarks.

scholarly journals Parallelized calculation of permutation tests

2020 ◽  
Author(s):  
Markus Ekvall ◽  
Michael Höhle ◽  
Lukas Käll
Keyword(s):  
Dynamic Programming ◽  
Sample Size ◽  
Permutation Test ◽  
Statistical Tests ◽  
Permutation Tests ◽  
Supplementary Information ◽  
Attractive Alternative ◽  
Test Statistic ◽  
Sample Distribution ◽  
Running Time

Abstract Motivation Permutation tests offer a straightforward framework to assess the significance of differences in sample statistics. A significant advantage of permutation tests are the relatively few assumptions about the distribution of the test statistic are needed, as they rely on the assumption of exchangeability of the group labels. They have great value, as they allow a sensitivity analysis to determine the extent to which the assumed broad sample distribution of the test statistic applies. However, in this situation, permutation tests are rarely applied because the running time of naïve implementations is too slow and grows exponentially with the sample size. Nevertheless, continued development in the 1980s introduced dynamic programming algorithms that compute exact permutation tests in polynomial time. Albeit this significant running time reduction, the exact test has not yet become one of the predominant statistical tests for medium sample size. Here, we propose a computational parallelization of one such dynamic programming-based permutation test, the Green algorithm, which makes the permutation test more attractive. Results Parallelization of the Green algorithm was found possible by non-trivial rearrangement of the structure of the algorithm. A speed-up—by orders of magnitude—is achievable by executing the parallelized algorithm on a GPU. We demonstrate that the execution time essentially becomes a non-issue for sample sizes, even as high as hundreds of samples. This improvement makes our method an attractive alternative to, e.g. the widely used asymptotic Mann-Whitney U-test. Availabilityand implementation In Python 3 code from the GitHub repository https://github.com/statisticalbiotechnology/parallelPermutationTest under an Apache 2.0 license. Supplementary information Supplementary data are available at Bioinformatics online.

The Numbers Will Love You Back in Return—I Promise

2016 ◽  
Vol 11 (4) ◽  
pp. 551-554 ◽  
Author(s):  
Martin Buchheit
Keyword(s):  
Sample Size ◽  
Null Hypothesis ◽  
Clinical Medicine ◽  
Statistical Significance ◽  
Significance Testing ◽  
Null Hypothesis Significance Testing ◽  
Sport Science ◽  
Size Dependent ◽  
Research Questions ◽  
Per Se

The first sport-science-oriented and comprehensive paper on magnitude-based inferences (MBI) was published 10 y ago in the first issue of this journal. While debate continues, MBI is today well established in sport science and in other fields, particularly clinical medicine, where practical/clinical significance often takes priority over statistical significance. In this commentary, some reasons why both academics and sport scientists should abandon null-hypothesis significance testing and embrace MBI are reviewed. Apparent limitations and future areas of research are also discussed. The following arguments are presented: P values and, in turn, study conclusions are sample-size dependent, irrespective of the size of the effect; significance does not inform on magnitude of effects, yet magnitude is what matters the most; MBI allows authors to be honest with their sample size and better acknowledge trivial effects; the examination of magnitudes per se helps provide better research questions; MBI can be applied to assess changes in individuals; MBI improves data visualization; and MBI is supported by spreadsheets freely available on the Internet. Finally, recommendations to define the smallest important effect and improve the presentation of standardized effects are presented.

scholarly journals A Comparison Study of Goodness of Fit Tests of Logistic Regression in R: Simulation and Application to Breast Cancer Data

2020 ◽  
pp. 50-59
Author(s):  
El-Housainy A. Rady ◽  
Mohamed R. Abonazel ◽  
Mariam H. Metawe’e
Keyword(s):  
Breast Cancer ◽  
Logistic Regression ◽  
Sample Size ◽  
Null Hypothesis ◽  
Goodness Of Fit ◽  
Quadratic Term ◽  
Breast Cancer Dataset ◽  
Cancer Data ◽  
Interaction Term ◽  
Test Package

Goodness of fit (GOF) tests of logistic regression attempt to find out the suitability of the model to the data. The null hypothesis of all GOF tests is the model fit. R as a free software package has many GOF tests in different packages. A Monte Carlo simulation has been conducted to study two situations; the first, studying the ability of each test, under its default settings, to accept the null hypothesis when the model truly fitted. The second, studying the power of these tests when assumptions of sufficient linear combination of the explanatory variables are violated (by omitting linear covariate term, quadratic term, or interaction term). Moreover, checking whether the same test in different R packages had the same results or not. As the sample size supposed to affect simulation results, so the pattern of change of GOF tests results under different sample sizes as well as different model settings was estimated. All tests accept the null hypothesis (more than 95% of simulation trials) when the model truly fitted except modified Hosmer-Lemeshow test in "LogisticDx" package under all different model settings and Osius and Rojek’s (OsRo) test when the true model had an interaction term between binary and categorical covariates. In addition, le Cessie-van Houwelingen-Copas-Hosmer unweighted sum of squares (CHCH) test gave unexpected different results under different packages. Concerning the power study, all tests had a very low power when a departure of missing covariate existed. Generally, stukel’s test (package ’LogisticDX) and CHCH test (package "RMS") reached a power in detecting a missing quadratic term greater than 80% under lower sample size while OsRo test (package ’LogisticDX’) was better in detecting missing interaction term. Beside the simulation study, we evaluated the performance of GOF tests using the breast cancer dataset.

scholarly journals The Effects of Manifest Residual Variances, Indicator Communality, and Sample Size on the χ2-Test Statistic of the Metric Invariance Model

2019 ◽  
Author(s):  
Eric Klopp ◽  
Stefan Klößner
Keyword(s):  
Sample Size ◽  
Measurement Invariance ◽  
Signal To Noise Ratio ◽  
Practical Implication ◽  
Residual Variance ◽  
Test Statistic ◽  
Monte Carlo Studies ◽  
Key Factor ◽  
Metric Measurement ◽  
Invariance Model

In this contribution, we investigate the effects of manifest residual variance, indicator communality and sample size on the χ2-test statistic of the metric measurement invariance model, i.e. the model with equality constraints on all loadings. We demonstrate by means of Monte Carlo studies that the χ2-test statistic relates inversely to manifest residual variance, whereas sample size and χ2-test statistic show the well-known pro- portional relation. Moreover, we consider indicator communality as a key factor for the size of the χ2-test statistic. In this context, we introduce the concept of signal-to-noise ratio as a tool for studying the effects of manifest residual error and indicator commu- nality and demonstrate its use with some examples. Finally, we discuss the limitations of this contribution and its practical implication for the analysis of metric measurement invariance models.

scholarly journals Role of Cooperative Societies in Boosting Agricultural Production & Entrepreneurship in the Kebbi State of Nigeria.

2017 ◽  
pp. 234-351
Author(s):  
Kamelshewer Lohana Et al.,
Keyword(s):  
Local Government ◽  
Sample Size ◽  
Agricultural Production ◽  
Null Hypothesis ◽  
Food Production ◽  
Sampling Technique ◽  
Added Value ◽  
Cluster Sampling ◽  
Survey Results

The study Assess the Role & contributions of cooperative societies in boosting agricultural production & Entrepreneurship in the Kebbi State of Nigeria. A total of 120 sample size was used for the study. Cluster sampling technique was used to obtaining information from sample respondents (members of farmers’ cooperative societies). Sixty (60) questionnaires were administered to sixty respondents, each in both Zuru and Yauri Local Government Areas. Data collected was analysed and interpreted using simple percentage and descriptive methods. The major conclusions drawn from this research were: survey results, regarding effectiveness of cooperative societies in improving agricultural production & Entrepreneurship, have shown that 33.3% and 25% of the respondents in Zuru and Yauri Local Government Areas reported promoting farmers’ participation in agriculture, while 25% and 46% agreed to boost agricultural production in the study areas. About 36.6% and 35% believed in the effectiveness of cooperative societies in increasing food production. Sample respondents in the two Local Government Areas 5% and 3.3% reported all of the above indicators increase the effectiveness of cooperatives to agriculture. Survey results regarding the role of cooperatives in boosting Entrepreneurship in the study areas shows that 75% Zuru 88.3% Yauri agreed that cooperatives have added value to boosting Agric production & Entrepreneurship and only 15% and 11.6% did not agree with the above opinion. Many problems were identified that affects the smooth functioning of cooperatives and solutions for addressing the problems were recommended. Therefore it was concluded that Null Hypothesis HO is rejected and Alternate Hypothesis HA is accepted.

Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers

2017 ◽  
Vol 28 (4) ◽  
pp. 1019-1043 ◽  
Author(s):  
Shi-Fang Qiu ◽  
Xiao-Song Zeng ◽  
Man-Lai Tang ◽  
Wai-Yin Poon
Keyword(s):  
Sample Size ◽  
Null Hypothesis ◽  
Test Procedure ◽  
Sample Size Determination ◽  
Double Sampling ◽  
Score Statistic ◽  
Wald Statistic ◽  
Test Procedures ◽  
Practical Applications ◽  
Logit Transformation

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example.

scholarly journals Profile Inferences on Restricted Additive Partially Linear EV Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiuli Wang
Keyword(s):  
Least Squares ◽  
Asymptotic Distribution ◽  
The Other ◽  
Finite Sample ◽  
Test Statistic ◽  
Two Stage ◽  
Chi Square ◽  
Partially Linear ◽  
Profile Least Squares ◽  
Restricted Estimator

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

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