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A New Definition of p-value Involving the Maximum Likelihood Estimator

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Open Journal of Statistics 2024年第5期14卷 546-552页

作者： H. W. Corley Center on Stochastic Modeling Optimization and Statistics (COSMOS) The University of Texas at Arlington Arlington USA

We present here an alternative definition of the p-value for statistical hypothesis test of a real-valued parameter for a continuous random variable X. Our approach uses neither the notion of Type I error nor the assumption that null hypothesis is true. Instead, the new p-value involves the maximum likelihood estimator, which is usually available for a parameter such as the mean μ or standard deviation σ of a random variable X with a common distribution.

关键词： Hypothesis Testing p-value Evidence Statistics

The earth's rotation-dominated seismicity preceding the 2023 M_(W) 7.8 Gaziantep, Türkiye, earthquake

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Geodesy and Geodynamics 2024年第6期15卷 592-601页

作者： Yane Li Xuezhong Chen Lijuan Chen Institute of Geophysics China Earthquake AdministrationBeijing 100081China Chongqing Earthquake Administration Chongqing 401147China

For earthquakes (M≥4.0) occurring along and around the East Anatolian fault zone and the Dead Sea fault zone within ten years immediately before the MW7.8 Gaziantep earthquake,Türkiye,of February 6,2023,we explored the correlation between seismicity and the earth's *** statistically evaluated the correlation using the Schuster's *** results are quantitatively assessed by a *** found a clear downward trend in the p-values from early 2020 to late 2022 in the studied *** also obtained a spatial distribution of the p-values showing a low p-value area near the northeastern end of the aftershock *** the stress induced by the rotation of the earth is very weak,it could control the earthquake occurrence when the focal medium is loaded to the critical state to release a large *** decrease in the b-value in the Gutenberg-Richter (G-R) relation is considered in the form of the tectonic stress increase in the *** investigated the b-value as a function of time in the study *** found that the b-value had decreased for about eleven years before the p-value started to decrease,with a relative reduction of 57%.Therefore,the result of the lower p-values obtained in the present study infers that the earthquakes were dominated by the earth's rotation prior to the MW7.8 Türkiye earthquake due to a critical state of the focal region.

关键词： Earth's rotation M_(W)7.8 Türkiye earthquake p-value b-value

An Exact Generalized Test for Homogeneity of Inverse Gaussian Scale parameters

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 761-769页

作者： Xu-hua LIU Xing-zhong XU Wei-yan MU Department of Mathematics China Agricultural University Beijing 100083 China College of Mathematics Beijing Institute of Technology Beijing 100081 China School of Science Beijing University of Civil Engineering and Architecture Beijing 100044 China

In this paper, we propose a new generalized p-value for testing homogeneity of scale parameters λi from k independent inverse Gaussian populations. The proposed generalized p-value is proved to have exact frequentist property, and it is also invariant under the group of scale transformation. Simulation results indicate that the proposed test is better than existing approximate χ^2 test.

关键词： Inverse Gaussian distribution Generalized p-value Exact frequentist property

Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects

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Computers, Materials & Continua 2021年第6期67卷 3215-3227页

作者： Muhammad Farman Aqeel Ahmad Ali Akgül Muhammad Umer Saleem Muhammad Naeem Dumitru Baleanu Department of Mathematics and Statistics University of LahorePakistan Department of Mathematics Faculty of Art and ScienceSiirt UniversitySiirt56100Turkey Department of Mathematics University of EducationLahorePakistan Department of Economics and Business Administration University of EducationLahorePakistan Department of Mathematics Cankaya UniversityBalgat06530Turkey Institute of Space Sciences Magurele-BucharestR76900Romania Department of Medical Research China Medical UniversityTaichung40402Taiwan

Today,coronavirus appears as a serious challenge to the whole *** data of coronavirus is collected through media and web sources for the purpose of *** data on COVID-19 are available daily,yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited,and uncertainty remains around nearly all its parameters’*** research provides the scientic and public health communities better resources,knowledge,and tools to improve their ability to control the infectious *** the publicly available data on the ongoing pandemic,the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 *** of the testing hypotheses for different countries with a 95%level of condence,and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different *** results will be helpful in decision making as well as in further mathematical analysis and control *** tools are used to investigate this pandemic,which will be useful for further *** testing of the hypothesis is done for the differences in various effects including standard *** in states’variables are observed over *** rapid outbreak of coronavirus can be stopped by reducing its *** should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.

关键词： Covid-19 infectious disease statistical analysis p-value epidemiology hypothesis

FDR Control for pairwise Comparisons of Normal Means Based on Goodness of Fit Test

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 701-712页

作者： pei JIN Xing-zhong XU Na LI School of Mathematics and Statistics Beijing Institute of Technology School of Economics and Management University of the Chinese Academy of Sciences

This study is undertaken to apply a bootstrap method of controlling the false discovery rate （FDR） when performing pairwise comparisons of normal means. Due to the dependency of test statistics in pairwise comparisons, many conventional multiple testing procedures can＇t be employed directly. Some modified pro- cedures that control FDR with dependent test statistics are too conservative. In the paper, by bootstrap and goodness-of-fit methods, we produce independent p-values for pairwise comparisons. Based on these indepen- dent p-values, plenty of procedures can be used, and two typical FDR controlling procedures are applied here. An example is provided to illustrate the proposed approach. Extensive simulations show the satisfactory FDR control and power performance of our approach. In addition, the proposed approach can be easily extended to more than two normal, or non-normal, balance or unbalance cases.

关键词： multiple testing false discovery rate goodness-of-fit test pairwise comparisons p-value resampling

Bridging the semantic gap with human perception based features for scene categorization

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International Journal of Intelligent Computing and Cybernetics 2017年第3期10卷 387-406页

作者： padmavati Shrivastava K.K.Bhoyar A.S.Zadgaonkar Dr.C.V.Raman University BilaspurIndia Department of Information Technology Yeshwantrao Chavan College of EngineeringNagpurIndia

purpose–The purpose of this paper is to build a classification system which mimics the perceptual ability of human vision,in gathering knowledge about the structure,content and the surrounding environment of a real-world natural scene,at a quick glance *** paper proposes a set of novel features to determine the gist of a given scene based on dominant color,dominant direction,openness and roughness ***/methodology/approach–The classification system is designed at two different *** the first level,a set of low level features are extracted for each semantic *** the second level the extracted features are subjected to the process of feature evaluation,based on inter-class and intra-class *** most discriminating features are retained and used for training the support vector machine(SVM)classifier for two different data ***–Accuracy of the proposed system has been evaluated on two data sets:the well-known Oliva-Torralba data set and the customized image data set comprising of high-resolution images of natural *** experimentation on these two data sets with the proposed novel feature set and SVM classifier has provided 92.68 percent average classification accuracy,using ten-fold cross validation *** set of proposed features efficiently represent visual information and are therefore capable of narrowing the semantic gap between low-level image representation and high-level human ***/value–The method presented in this paper represents a new approach for extracting low-level features of reduced dimensionality that is able to model human perception for the task of scene *** methods of mapping primitive features to high-level features are intuitive to the user and are capable of reducing the semantic *** proposed feature evaluation technique is general and can be applied across any domain.

关键词： Openness Roughness Human perception JND p-value Scene classification Semantic gap Feature elevation Dominant direction

Hypothesis testing of poisson rates in COVID-19 offspring distributions

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Infectious Disease Modelling 2023年第4期8卷 980-1001页

作者： Rui Luo Department of Systems Engineering City University of Hong KongKowloon TownHong Kong Special Administrative Region

In the present study,we undertake the task of hypothesis testing in the context of poissondistributed *** primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same poisson *** delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this *** these are the conditional test,the likelihood ratio test,and the Bayes ***,we employ the posterior predictive p-value in our analysis,coupled with its corresponding calibration *** the culmination of our investigation,we apply these diverse methodologies to test both simulated datasets and real-world *** latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies-Hong Kong and *** allows us to provide a practical demonstration of the methodologies’applications and their potential implications in the field of epidemiology.

关键词： poisson distribution Hypothesis testing Bayes factor posterior predictive p-value COVID-19

A Note on the Nonparametric Least-squares Test for Checking a polynomial Relationship

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 511-520页

作者： Chang-lin Mei, Shu-yuan He, Yan-hua WangLMAM, Institute of Mathematics, peking University, Beijing 100871, China School of Sciences, Xi’an Jiaotong University, Xi’an 710049, China LMAM Institute of Mathematics Peking University Beijing China School of Sciences Xi’an Jiaotong University Xi’an China

Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in mo... 详细信息

Recently, Gijbels and Roussonp>[6]p> suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson’s approach. Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory.

关键词： Local polynomial fitting polynomial regression derivative estimation p-value

A sea change in statistics:A reconsideration of what is important in the age of big data

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Journal of Management Analytics 2014年第4期1卷 241-248页

作者： Wenbo Guo Detmar Straub pengzhu Zhang Antai College of Economics and Management Shanghai Jiao Tong UniversityShanghai 200052China J.Mack Robinson College of Business Georgia State UniversityAtlantaGA 30303USA

The development of information technology(IT)in the last decade has ushered us into the‘big data’*** sampling error has been of high interest in such studies over the last century,extremely large datasets will virtually rule out the possibility that statistics generated from samples are not also true of the *** critical discussion must move on to how much the exogenous and endogenous variables explain ultimate *** stress will have to move from generalizability to explanatory *** examining the three common statistical tests–the T-value,the F-value and the beta coefficient(or‘b’in the sample)–this paper aims to show how important effect size analysis is with the trend toward larger and larger samples and big *** the end,the paper points out the gap of what the acceptable ranges of effects that appears in our sundry scientific literatures *** call for studies in this regard so that social sciences can move forward and strengthen weak theory bases,and recognize strong theories when they do appear.

关键词： p-value effect size sample size big data