European Journal of Statistics最新文献

{"title":"A Data-Based Adjustment for Fisher Exact Test","authors":"Guo-Guang Zhao, Huiyu Yang, Junxia Yang, Liufeng Zhang, Xiaoang Yang","doi":"10.28924/ada/stat.1.74","DOIUrl":"https://doi.org/10.28924/ada/stat.1.74","url":null,"abstract":"Fisher exact test is one of most popularly used methods in modern data analyses. However, it is conservative because of discreteness. The mid-p method may reduce the conservativeness but it is defined by the factor 1/2, an extra term beyond data. This paper considers an adjustment defined by a data-based factor. The adjusted test is compared with other ten tests. Special attention is given to the comparison between the data-based factor and the factor 1/2. The standardized version of the adjusted test is asymptotically standard normal. The adjustment reduces the conservativeness, as evidenced by increasing test size and power and decreasing p-values. The adjusted test holds such properties as the significance level under control of nominal α, the same modification in the left- and right-sided p-values, and the proportional reduction from Fisher test, which the mid-p method lacks. The mid-p method is more powerful than the adjusted test but the increment of power comes from the factor 1/2 and is not controlled by α. The unconditional tests are also more powerful but the power comes partly from the unobserved samples. The proper choice of an adjustment is based largely upon a consideration of both the power of test and the origin of power so that the adjusted test is an option in data analyses. It is easy to implement for 2 × 2 and r × c contingency tables. Two real examples are given for analyzing 2 × 2 tables and another example for r × c tables.","PeriodicalId":153849,"journal":{"name":"European Journal of Statistics","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132722106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiple Upper Outlier Detection Procedure in Generalized Exponential Sample","authors":"A. Singh, Abhinav Singh, Rohit Patawa","doi":"10.28924/ada/stat.1.58","DOIUrl":"https://doi.org/10.28924/ada/stat.1.58","url":null,"abstract":"Hawkins [6] defined an outlier as an observation that is significantly different from the remaining observations in a dataset so as to arouse suspicion that it was generated by different mechanism. Barnett and Lewis [2] defined an outlier as an observation that deviates significantly in the sample in which it occurs. Spatial outliers are different from outliers and many authors like Singh and Lalitha [9]. Outlier detection procedures for two parameter gamma distribution have been discussed by many authors. But one major disadvantage of the gamma distribution is that the distribution (or survival) function cannot be expressed in a closed form if the shape parameter is not an integer. Since it is in terms of an incomplete gamma function, one needs to obtain the distribution/survival function or the failure rate by numerical integration. This is a limitation in the usage of gamma distribution. It is observed that the generalized exponential distribution can be used as an alternative to the gamma distribution in many situations. Different properties like monotonicity of the hazard functions and tail behaviours of the gamma distribution and that of the generalized exponential distribution are quite similar in nature. But the latter one has a nice compact distribution (or survival) function. It is observed that for a given gamma distribution there exists a generalized exponential distribution so that the two distribution functions are almost identical. Since the gamma distribution function does not have a compact form, efficiently generating gamma random numbers is known to be problematic. It was observed that for all practical purposes it is possible to generate approximate gamma random numbers using generalized exponential distribution and the random samples thus obtained cannot be differentiated using any statistical tests. Many authors proposed a location and scale invariant test based on the test statistic Zk for testing the upper outliers in two-parameter exponential sample. Kumar et. al. [7] and Singh and Lalitha [10] have proposed test statistics for testing multiple upper outlier detection in gamma sample. Various test statistics have been proposed to detect outliers in an exponential sample. Likes [8] also proposed a new test statistics to detect outlier in the exponential case. In this paper, the test statistic proposed by Likes has been used to detect outliers in a generalized exponential sample and the critical value of the test statistics has been obtained. A simulation study is carried out to compare the theoretical developments.","PeriodicalId":153849,"journal":{"name":"European Journal of Statistics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128207849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statistics of SPDEs: From Linear to Nonlinear","authors":"J. Bishwal","doi":"10.28924/ada/stat.1.1","DOIUrl":"https://doi.org/10.28924/ada/stat.1.1","url":null,"abstract":"We study statistical inference for stochastic partial differential equations (SPDEs). Though inference linear SPDEs have been studied well (with lot of problems still remain to be investigated) in the last two decades, inference for nonlinear SPDEs is in its infancy. The inference methods use both inference for finite-dimensional diffusions and inference for classical i.i.d. sequences. Solving 2D Navier-Stokes equation is one of the challenging problem of the last century. However, with additive white noise, the equation has a strong solution. We estimate the viscosity coefficient of the 2D stochastic Navier-Stokes (SNS) equation by minimum contrast method. We show $n$ consistency in contrast to $sqrt n$ consistency in the classical i.i.d. case where $n$ is the number of observations. We consider both continuous and discrete observations in time. We also obtain the Berry-Esseen bounds. Then we estimate and control the Type I and Type II error of a simple hypothesis testing problem of the viscosity coefficient of the SNS equation. We study a class of rejection regions and provide thresholds that guarantee that the statistical errors are smaller than the given upper bound. The tests are of likelihood ratio type. The proofs are based on the large deviation bounds. Finally we give Monte Carlo test procedure for simulated data.","PeriodicalId":153849,"journal":{"name":"European Journal of Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130138846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Consensus as a Nash Equilibrium of a Stochastic Differential Game","authors":"P. Pramanik","doi":"10.28924/ada/stat.3.10","DOIUrl":"https://doi.org/10.28924/ada/stat.3.10","url":null,"abstract":"In this paper a consensus has been constructed in a social network which is modeled by a stochastic differential game played by agents of that network. Each agent independently minimizes a cost function which represents their motives. A conditionally expected integral cost function has been considered under an agent’s opinion filtration. The dynamic cost functional is minimized subject to a stochastic differential opinion dynamics. As opinion dynamics represents an agent’s differences of opinion from the others as well as from their previous opinions, random influences and stubbornness make it more volatile. An agent uses their rate of change of opinion at certain time point as a control input. This turns out to be a non-cooperative stochastic differential game which have a feedback Nash equilibrium. A Feynman-type path integral approach has been used to determine an optimal feedback opinion and control. This is a new approach in this literature. Later in this paper an explicit solution of a feedback Nash equilibrium opinion is determined.","PeriodicalId":153849,"journal":{"name":"European Journal of Statistics","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121170368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}