Article
Statistics & Probability
Taewoong Uhm, Seongbaek Yi
Summary: This study compares and evaluates the power and performance of different normality testing methods, taking into account factors such as significance levels, sample sizes, and alternative distributions.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2023)
Article
Statistics & Probability
Pere Grima, Jose A. Sanchez-Espigares, Pedro Delicado
Summary: This article introduces the use of a Skewed Exponential Power Distribution to create a bidimensional array of graphics. The kurtosis varies horizontally and the skewness varies vertically. By testing the null hypotheses that a sample comes from each distribution in the array, the corresponding cell is filled with a color based on the obtained p-value. This generates a dark area on the mosaic to indicate the compatible distributions with the sample.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Article
Mathematics, Applied
Katarzyna Maraj-Zygmat, Grzegorz Sikora, Marcin Pitera, Agnieszka Wylomanska
Summary: In this paper, a new framework for efficient stochastic process discrimination is introduced. The framework is based on even empirical moments and is a generalization of the time-averaged mean-squared displacement framework. It allows for statistical testing of processes with stationary increments and a finite-moment distribution. The effectiveness of the framework is demonstrated through simulations and application to real data analysis of metal prices.
Article
Statistics & Probability
Simos Meintanis, Bojana Milosevic, Marko Obradovic
Summary: In this study, we examine the Bahadur efficiency of weighted L2-type goodness-of-fit tests based on the empirical characteristic function. We consider tests for normality, exponentiality, and goodness-of-fit to the logistic distribution. Our findings provide insight into the efficiency of these tests, assisting practitioners in selecting the most appropriate one.
Article
Computer Science, Information Systems
Alexander Shapiro, Yao Xie, Rui Zhang
Summary: The research develops a general theory for the goodness-of-fit test to non-linear models, where the residual of the model fit follows a chi(2) distribution related to the model order and problem dimension. A sequential method for selecting model orders is presented, demonstrating broad applications in machine learning and signal processing.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Mathematics
A. Pekgor
Summary: Recently, new goodness-of-fit tests based on Kullback-Leibler divergence and likelihood ratio have been introduced for the Cauchy distribution, claiming to be more powerful than traditional tests. This study proposes a novel test for the Cauchy distribution and derives its asymptotic null distribution. Critical values are determined through Monte Carlo simulation for various sample sizes, and power analysis reveals the superiority of the proposed test under certain conditions.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Chioneso S. Marange, Yongsong Qin, Raymond T. Chiruka, Jesca M. Batidzirai
Summary: A new blockwise empirical likelihood moment-based procedure is proposed to test the Gaussianity of a stationary autoregressive process. The proposed test utilizes skewness and kurtosis moment constraints to construct the test statistic. The test shows good control of type I error and outperforms competitor tests for log-normal and chi-square alternatives across different sample sizes. Real data studies also demonstrate the applicability and robustness of the proposed test.
Article
Biochemical Research Methods
Mengqi Zhang, Sahar Gelfman, Cristiane Araujo Martins Moreno, Janice M. McCarthy, Matthew B. Harms, David B. Goldstein, Andrew S. Allen
Summary: Gene set-based signal detection analysis is used to detect the association between a trait and a set of genes by accumulating signals across the genes in the set. This study presents a flexible framework based on tail-focused GOF statistics, which depends on two critical parameters. Guidance on statistic selection is provided and the methods are implemented in the user-friendly R package wHC. The methods are applied to a study on amyotrophic lateral sclerosis.
BRIEFINGS IN BIOINFORMATICS
(2022)
Article
Mathematics
Jurgita Arnastauskaite, Tomas Ruzgas, Mindaugas Brazenas
Summary: The testing of multivariate normality is a significant scientific problem, and a new method has been introduced showing strong empirical power, especially for smaller samples.
Article
Computer Science, Interdisciplinary Applications
Alessandra Cipriani, Christian Hirsch, Martina Vittorietti
Summary: In many fields, such as materials science, 3D information is often obtained by extrapolating from 2D slices. Persistence vineyards have emerged as a powerful tool in topological data analysis to consider topological features across multiple slices. This article demonstrates how persistence vineyards can be used to design statistical hypothesis tests for 3D microstructure models based on 2D slice data. The testing methodology is illustrated through simulations and an example from materials science.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Statistics & Probability
Jiawei Zhang, Jie Ding, Yuhong Yang
Summary: The article proposes a methodology called BAGofT for assessing the goodness of fit of a general classification procedure. The method splits the data into a training set and a validation set, and identifies the most severe regions of underfitting by adaptingively grouping the training set. A test statistic is then calculated based on this grouping and a comparison between the estimated success probabilities and the actual observed responses from the validation set. The BAGofT has a broader scope than existing methods in testing parametric classification models.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Statistics & Probability
Piotr Sulewski
Summary: The paper aims to apply the corrected Lilliefors goodness-of-fit test for normality (LF) into practice by modifying the formula of calculating the empirical distribution function (EDF) to increase the test power. It also proposes a similarity measure between the normal distribution and alternative distributions, and introduces two new alternative distributions to achieve desired skewness and excess kurtosis values. Furthermore, it calculates the power of tests for new alternative distributions. The results demonstrate the influence of constant values in the EDF formula on the LF test power, and illustrate the performance of the new proposals through the analysis of real data sets.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2022)
Article
Statistics & Probability
Jose A. Sanchez-Espigares, Pere Grima, Lluis Marco-Almagro
Summary: A procedure is proposed for jointly visualizing the compatibility of a sample with a family of Skewed Exponential Power Distributions, with distributions such as Normal, Exponential, Laplace, and Uniform as particular cases. The procedure involves constructing a mosaic where asymmetry varies from left to right and kurtosis varies from top to bottom. By examining the shaded area that appears on the mosaic, one can identify which distributions are compatible with the sample and assess the power of the test performed.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2021)
Article
Computer Science, Interdisciplinary Applications
Chihiro Watanabe, Taiji Suzuki
Summary: This study developed a new goodness-of-fit test for latent block models to test whether an observed data matrix fits a given set of row and column cluster numbers, or it consists of more clusters in at least one direction of the row and the column.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2021)
Article
Statistics & Probability
Shulin Zhang, Qian M. Zhou, Huazhen Lin
Summary: In this paper, we propose a goodness-of-fit test, named pseudo in-and-out-of-likelihood (PIOL) ratio test, for checking for misspecification in semi-parametric copula models for univariate time series. The test not only extends the idea of IOS and PIOS tests, but also provides an integrated framework for both independent data and time series data. Asymptotic properties and finite-sample performance are discussed, and the proposed method is demonstrated through the analysis of a daily transactions time series of Apple trade.
STATISTICAL PAPERS
(2021)
Article
Health Care Sciences & Services
Albert Vexler, Jihnhee Yu, Yang Zhao, Alan D. Hutson, Gregory Gurevich
STATISTICAL METHODS IN MEDICAL RESEARCH
(2018)
Article
Statistics & Probability
Alan D. Hutson, Albert Vexler
AMERICAN STATISTICIAN
(2018)
Article
Computer Science, Interdisciplinary Applications
Gregory Gurevich, Albert Vexler
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2018)
Article
Statistics & Probability
Albert Vexler, Georgios Afendras, Marianthi Markatou
Article
Mathematical & Computational Biology
Li Zou, Albert Vexler, Jihnhee Yu, Hongzhi Wan
STATISTICS IN MEDICINE
(2019)
Article
Mathematical & Computational Biology
Jihnhee Yu, Albert Vexler, Kabir Jalal
STATISTICS IN MEDICINE
(2019)
Article
Computer Science, Interdisciplinary Applications
Albert Vexler, Li Zou, Alan D. Hutson
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2019)
Article
Statistics & Probability
Albert Vexler
Summary: The focus is on valid definitions of p-values and how they can be used to make decisions at a prefixed level-alpha. New test procedures are exemplified, with practical reasons advocated for implementing VpV mechanisms. The VpV framework extends the EPV tool for measuring test performance. The Bayes Factor test statistic is explored in relation to the BF of test statistics.
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
(2021)
Article
Statistics & Probability
Albert Vexler
JOURNAL OF MULTIVARIATE ANALYSIS
(2020)
Article
Health Care Sciences & Services
Mingmei Tian, Jihnhee Yu, Denise F. Lillvis, Albert Vexler
Summary: This study introduces a robust method for relative risk estimation using data from the 2000-2016 US Medical Expenditure Panel Survey (MEPS). By employing influence function methods and data-balancing techniques, the study demonstrates the method's efficacy in providing reliable RR estimates across various model assumptions. The proposed method shows promising potential for health services research, particularly for nonexperimental and imbalanced data.
HEALTH SERVICES RESEARCH
(2022)
Article
Statistics & Probability
Albert Vexler, Li Zou
Summary: The need for analyzing multivariate aspects of joint data distributions is growing, and various contexts of joint symmetry of data distributions have been extensively studied in theory and practice. Univariate characterizations of multivariate distributions can simplify the original problem. In this study, the authors focus on scenarios where vectors x and Ax are identically distributed and establish projections of joint symmetry and independence. The linear projections are shown to be the most informative in multivariate data distribution. The authors demonstrate the usefulness of linear projections by constructing an efficient nonparametric exact test for joint treatment effects.
JOURNAL OF MULTIVARIATE ANALYSIS
(2022)
Article
Statistics & Probability
Albert Vexler, Alan D. Hutson
Summary: Data-driven most powerful tests are statistical hypothesis decision-making tools that provide the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. By applying the likelihood ratio principle, it is possible to conduct most powerful tests when the underlying data distributions are known. This study examines how to improve the power of a test and compares test statistics based on the attribute of a desired most powerful decision-making procedure.
AMERICAN STATISTICIAN
(2023)
Article
Computer Science, Interdisciplinary Applications
Albert Vexler, Xinyu Gao, Jiaojiao Zhou
Summary: The aim of this study is to address the limitations of the one-sample Wilcoxon signed rank test when the center of symmetry is unknown, and propose correct schemes for applying the test with an estimated center of symmetry. It is found that the test and the sign test for symmetry do not provide meaningful results when unknown centers of symmetry are estimated using the data. We propose simple corrections and develop new customized procedures for estimating density values, which significantly improve the performance of the test. The proposed algorithms can be used to modify Wilcoxon tests in various statistical software.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jeffrey C. Miecznikowski, En-shuo Hsu, Yanhua Chen, Albert Vexler
Article
Biochemical Research Methods
Albert Vexler, Jihnhee Yu
JOURNAL OF COMPUTATIONAL BIOLOGY
(2018)
