Mathematical Methods of Statistics最新文献

Estimation of Parameters of Misclassified Size Biased Uniform Poisson Distribution and Its Application 误分类大小偏差均匀泊松分布参数估计及其应用

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Mathematical Methods of Statistics Pub Date : 2024-07-15 DOI: 10.3103/s106653072470008x

B. S. Trivedi, D. R. Barot, M. N. Patel

{"title":"Estimation of Parameters of Misclassified Size Biased Uniform Poisson Distribution and Its Application","authors":"B. S. Trivedi, D. R. Barot, M. N. Patel","doi":"10.3103/s106653072470008x","DOIUrl":"https://doi.org/10.3103/s106653072470008x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Statistical data analysis is of great interest in every field of\u0000management, business, engineering, medicine, etc. At the time of\u0000classification and analysis, errors may arise, like a\u0000classification of observation in the other class instead of the\u0000actual class. All fields of science and economics have substantial\u0000problems due to misclassification errors in the observed data. Due\u0000to a misclassification error in the data, the sampling process may\u0000not suggest an appropriate probability distribution, and in that\u0000case, inference is impaired. When these types of errors are\u0000identified in variables, it is expected to consider the problem’s\u0000solution regarding classification errors. This paper presents the\u0000situation where specific counts are reported erroneously as\u0000belonging to other counts in the context of size biased Uniform\u0000Poisson distribution, the so-called misclassified size biased\u0000Uniform Poisson distribution. Further, we have estimated the\u0000parameters of misclassified size biased Uniform Poisson\u0000distribution by applying the method of moments, maximum likelihood\u0000method, and approximate Bayes estimation method. A simulation\u0000study is carried out to assess the performance of estimation\u0000methods. A real dataset is discussed to demonstrate the\u0000suitability and applicability of the proposed distribution in the\u0000modeling count dataset. A Monte Carlo simulation study is\u0000presented to compare the estimators. The simulation results show\u0000that the ML estimates perform better than their corresponding\u0000moment estimates and approximate Bayes estimates.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"6 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717516","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}

引用次数: 0

On Aggregation of Uncensored and Censored Observations 关于未删减和删减观测数据的聚合

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Mathematical Methods of Statistics Pub Date : 2024-07-15 DOI: 10.3103/s1066530724700078

Sam Efromovich

{"title":"On Aggregation of Uncensored and Censored Observations","authors":"Sam Efromovich","doi":"10.3103/s1066530724700078","DOIUrl":"https://doi.org/10.3103/s1066530724700078","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In survival analysis a random right-censoring partitions data into uncensored and censored observations of the lifetime of interest. The dominance of uncensored observations is a familiar methodology in nonparametric estimation motivated by the classical Kaplan–Meier product-limit and Cox partial likelihood estimators. Nonetheless, for high rate censoring it is of interest to understand what, if anything, can be done by aggregating uncensored and censored observations for the staple nonparametric problems of density and regression estimation. The oracle, who knows distribution of the censoring lifetime, can use each subsample for consistent estimation and hence may shed light on the aggregation. The oracle’s asymptotic theory reveals that density estimation, based on censored observations, is an ill-posed problem with slower rates of risk convergence, the ill-posedness occurs in frequency-domain, its severity increases with frequency, and accordingly a special aggregation on low frequencies may be beneficial. On the other hand, censored observations are not ill-posed for nonparametric regression and the aggregation is feasible. Based on these theoretical results, methodology of aggregation in frequency domain is developed and proposed estimators are tested on simulated and real examples.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"36 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717518","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}

引用次数: 0

Asymptotic Properties of Extrema of Moving Sums of Independent Non-identically Distributed Variables 独立非同分布变量移动和的渐近特性

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Mathematical Methods of Statistics Pub Date : 2024-07-15 DOI: 10.3103/s1066530724700091

Narayanaswamy Balakrishnan, Alexei Stepanov

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Stochastic Comparisons of the Smallest Claim Amounts from Two Heterogeneous Portfolios Following Exponentiated Weibull Distribution 两种异质投资组合的最小索赔额的随机比较，遵循幂次韦布尔分布

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Mathematical Methods of Statistics Pub Date : 2024-07-15 DOI: 10.3103/s1066530724700108

Suheir Kareem Ramani, Habib Jafari, Ghobad Saadat Kia

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Rates of the Strong Uniform Consistency with Rates for Conditional U-Statistics Estimators with General Kernels on Manifolds 曲面上具有一般核的条件 U 统计估计器的强均匀一致率与率

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Mathematical Methods of Statistics Pub Date : 2024-07-15 DOI: 10.3103/s1066530724700066

Salim Bouzebda, Nourelhouda Taachouche

{"title":"Rates of the Strong Uniform Consistency with Rates for Conditional U-Statistics Estimators with General Kernels on Manifolds","authors":"Salim Bouzebda, Nourelhouda Taachouche","doi":"10.3103/s1066530724700066","DOIUrl":"https://doi.org/10.3103/s1066530724700066","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>\u0000<span>(U)</span>-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. <span>(U)</span>-statistics generalize the empirical mean of a random variable <span>(X)</span> to sums over every <span>(m)</span>-tuple of distinct observations of <span>(X)</span>. Stute [103] introduced a class of so-called conditional <span>(U)</span>-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to:</p><span>$$r^{(k)}(varphi,tilde{mathbf{t}}):=mathbb{E}[varphi(Y_{1},ldots,Y_{k})|(X_{1},ldots,X_{k})=tilde{mathbf{t}}]quadtextrm{for}quadtilde{mathbf{t}}=left(mathbf{t}_{1},ldots,mathbf{t}_{k}right)inmathbb{R}^{dk}.$$</span><p>In the analysis of modern machine learning algorithms, sometimes we need to manipulate kernel estimation within the nonconventional setting with intricate kernels that might even be irregular and asymmetric. In this general setting, we obtain the strong uniform consistency result for the general kernel on Riemannian manifolds with Riemann integrable kernels for the conditional <span>(U)</span>-processes. We treat both cases when the class of functions is bounded or unbounded, satisfying some moment conditions. These results are proved under some standard structural conditions on the classes of functions and some mild conditions on the model. Our findings are applied to the regression function, the set indexed conditional <span>(U)</span>-statistics, the generalized <span>(U)</span>-statistics, and the discrimination problem. The theoretical results established in this paper are (or will be) key tools for many further developments in manifold data analysis.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"24 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717517","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}

引用次数: 0

Functional Uniform-in-Bandwidth Moderate Deviation Principle for the Local Empirical Processes Involving Functional Data 涉及函数数据的局部经验过程的函数统一带宽适度偏差原理

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Mathematical Methods of Statistics Pub Date : 2024-04-25 DOI: 10.3103/s1066530724700030

Nour-Eddine Berrahou, Salim Bouzebda, Lahcen Douge

{"title":"Functional Uniform-in-Bandwidth Moderate Deviation Principle for the Local Empirical Processes Involving Functional Data","authors":"Nour-Eddine Berrahou, Salim Bouzebda, Lahcen Douge","doi":"10.3103/s1066530724700030","DOIUrl":"https://doi.org/10.3103/s1066530724700030","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Our research employs general empirical process methods to investigate and establish moderate deviation principles for kernel-type function estimators that rely on an infinite-dimensional covariate, subject to mild regularity conditions. In doing so, we introduce a valuable moderate deviation principle for a function-indexed process, utilizing intricate exponential contiguity arguments. The primary objective of this paper is to contribute to the existing literature on functional data analysis by establishing functional moderate deviation principles for both Nadaraya–Watson and conditional distribution processes. These principles serve as fundamental tools for analyzing and understanding the behavior of these processes in the context of functional data analysis. By extending the scope of moderate deviation principles to the realm of functional data analysis, we enhance our understanding of the statistical properties and limitations of kernel-type function estimators when dealing with infinite-dimensional covariates. Our findings provide valuable insights and contribute to the advancement of statistical methodology in functional data analysis.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"57 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803620","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}

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Controlling Separation in Generating Samples for Logistic Regression Models 在生成逻辑回归模型样本时控制分离度

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Mathematical Methods of Statistics Pub Date : 2024-04-25 DOI: 10.3103/s1066530724700017

Huong T. T. Pham, Hoa Pham

{"title":"Controlling Separation in Generating Samples for Logistic Regression Models","authors":"Huong T. T. Pham, Hoa Pham","doi":"10.3103/s1066530724700017","DOIUrl":"https://doi.org/10.3103/s1066530724700017","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Separation has a significant impact on parameter estimates for logistic regression models in frequentist approach and in Bayesian approach. When separation presents in a sample, the maximum likelihood estimation (MLE) does not exist through standard estimation methods. The existence of posterior means is affected by the presence of separation and also depended on the forms of prior distributions. Therefore, controlling the appearance of separation in generating samples from the logistic regression models has an important role for parameter estimation techniques. In this paper, we propose necessary and sufficient conditions for separation occurring in the logistic regression samples with two dimensional models and multiple dimensional models of independent variables. By using the technique of rotating Castesian coordinates of p dimensions, the characteristic of separation occurring in general cases is presented. Using these results, we propose algorithms to control the probability of separation appearance in generated samples for given sample sizes and multiple dimensional models of independent variables. The simulation studies show that the proposed algorithms can effectively generate the designed random samples with controlling the probability of separation appearance.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":"124 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803675","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}

引用次数: 0

Assessing Monotonicity: An Approach Based on Transformed Order Statistics 评估单调性：基于变换阶次统计的方法

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Mathematical Methods of Statistics Pub Date : 2024-04-25 DOI: 10.3103/s1066530724700054

Aleksandr Chen, Nadezhda Gribkova, Ričardas Zitikis

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Truncated Estimators for a Precision Matrix 精确矩阵的截断估计器

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Mathematical Methods of Statistics Pub Date : 2024-04-25 DOI: 10.3103/s1066530724700029

Anis M. Haddouche, Dominique Fourdrinier

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Characterizing Existence and Location of the ML Estimate in the Conway–Maxwell–Poisson Model 确定康威-麦克斯韦-泊松模型中 ML 估计值的存在性和位置