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A family of skew distributions with mode-invariance through transformation of scale 通过尺度变换得到一类模不变的偏态分布
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2015.02.003
Hironori Fujisawa , Toshihiro Abe
{"title":"A family of skew distributions with mode-invariance through transformation of scale","authors":"Hironori Fujisawa ,&nbsp;Toshihiro Abe","doi":"10.1016/j.stamet.2015.02.003","DOIUrl":"10.1016/j.stamet.2015.02.003","url":null,"abstract":"<div><p>Recently, a new family of skew distributions was proposed using a specific class of transformation of scale, in which the normalizing constant remains unchanged and unimodality is readily assured. In this paper, we introduce the mode invariance in this family, which allows us to easily study certain properties, including monotonicity of skewness, and incorporate various favorable properties. The entropy maximization<span> for a skew distribution is discussed. A numerical study is also conducted.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.02.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092837","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: 6
Further results on closure properties of LPQE order LPQE序闭包性质的进一步结果
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2014.12.003
Dian-tong Kang
{"title":"Further results on closure properties of LPQE order","authors":"Dian-tong Kang","doi":"10.1016/j.stamet.2014.12.003","DOIUrl":"10.1016/j.stamet.2014.12.003","url":null,"abstract":"<div><p>Di Crescenzo and Longobardi (2002) introduced the past entropy, Sunoj et al. (2013) gave a quantile<span> version for the past entropy, termed as the past quantile entropy (PQE). Based on the PQE function, they defined a new stochastic order called as less PQE (LPQE) order and studied some properties of this order. In the present paper, we focus our interests on further closure properties of this new order. Some characterizations of the LPQE order are investigated, closure and reversed closure properties are obtained. The preservation of the LPQE order in the proportional failure rate and reversed failure rate models is discussed.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.12.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092670","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: 7
A simple approach for testing constant failure rate against different ageing classes for discrete data 对离散数据的不同老化类别测试恒定故障率的简单方法
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2015.02.001
K.K. Sudheesh , P. Anisha , C.M. Deemat
{"title":"A simple approach for testing constant failure rate against different ageing classes for discrete data","authors":"K.K. Sudheesh ,&nbsp;P. Anisha ,&nbsp;C.M. Deemat","doi":"10.1016/j.stamet.2015.02.001","DOIUrl":"10.1016/j.stamet.2015.02.001","url":null,"abstract":"<div><p>In this paper, we develop simple non-parametric test based on U-statistics for testing constant failure rate against IFR, IFRA, DMRL, NBU and NBUE alternatives. The asymptotic properties of the test statistics are studied. In particular, the test statistics are shown to be asymptotically normal and consistent against the relevant alternatives. Some numerical results are presented to demonstrate the performance of the proposed tests.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.02.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092816","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: 5
Copula parameter change test for nonlinear AR models with nonlinear GARCH errors 具有非线性GARCH误差的非线性AR模型的Copula参数变化检验
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2014.12.001
Sangyeol Lee , Byungsoo Kim
{"title":"Copula parameter change test for nonlinear AR models with nonlinear GARCH errors","authors":"Sangyeol Lee ,&nbsp;Byungsoo Kim","doi":"10.1016/j.stamet.2014.12.001","DOIUrl":"10.1016/j.stamet.2014.12.001","url":null,"abstract":"<div><p><span><span>In this paper, we study the problem of testing for a copula<span> parameter change in nonlinear autoregressive (AR) models with nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) errors. To perform a test, we propose the cusum test based on pseudo maximum likelihood estimates of copula parameters. We derive its limiting </span></span>null distribution under </span>regularity conditions. For illustration, we conduct a simulation study with an emphasis on STAR–STGARCH models. A real data analysis applied to the S&amp;P 500 index and IBM stock price is also considered.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.12.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092641","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: 6
Adaptive testing for the partially linear single-index model with error-prone linear covariates 带有易出错线性协变量的部分线性单指标模型的自适应检验
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2014.12.002
Zhensheng Huang , Quanxi Shao , Zhen Pang , Bingqing Lin
{"title":"Adaptive testing for the partially linear single-index model with error-prone linear covariates","authors":"Zhensheng Huang ,&nbsp;Quanxi Shao ,&nbsp;Zhen Pang ,&nbsp;Bingqing Lin","doi":"10.1016/j.stamet.2014.12.002","DOIUrl":"10.1016/j.stamet.2014.12.002","url":null,"abstract":"<div><p>Adaptive testing for the partially linear single-index model (PLSIM) with error-prone linear covariates<span> is considered. This is a fundamentally important and interesting problem for the current model because existing literature often assumes that the model structure is known before making inferences. In practice, this may result in an incorrect inference on the PLSIM. In this study, we explore whether the link function satisfies some special shape constraints by using an efficient penalized estimating method. For this we propose a model structure selection method by constructing a new testing statistic<span> in the current setting with measurement error, which may enhance the flexibility and predictive power of this model under the case that one can correctly choose an adaptive shape and model structure. The finite sample performance of the proposed methodology is investigated by using some simulation studies and a real example from the Framingham Heart Study.</span></span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.12.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092654","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: 1
On some distributions arising from a generalized trivariate reduction scheme 关于由广义三元约化格式引起的一些分布
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2015.01.001
Christophe Chesneau , Maher Kachour , Dimitris Karlis
{"title":"On some distributions arising from a generalized trivariate reduction scheme","authors":"Christophe Chesneau ,&nbsp;Maher Kachour ,&nbsp;Dimitris Karlis","doi":"10.1016/j.stamet.2015.01.001","DOIUrl":"10.1016/j.stamet.2015.01.001","url":null,"abstract":"<div><p><span>In this article we construct bivariate discrete distributions in </span><span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We make use of a generalized trivariate reduction technique. The special case leading to a generalization of a bivariate Skellam distribution is studied in detail. Properties of the derived models as well as estimation are examined. Real data application is provided. Discussion of extensions to different models is also mentioned.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.01.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092802","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: 3
A macro-DAG structure based mixture model 基于宏观dag结构的混合模型
Statistical Methodology Pub Date : 2015-07-01 DOI: 10.1016/j.stamet.2015.02.004
Bernard Chalmond
{"title":"A macro-DAG structure based mixture model","authors":"Bernard Chalmond","doi":"10.1016/j.stamet.2015.02.004","DOIUrl":"10.1016/j.stamet.2015.02.004","url":null,"abstract":"<div><p>In the context of unsupervised classification of multidimensional data, we revisit the classical mixture model in the case where the dependencies among the random variables are described by a DAG structure. This structure is considered at two levels, the original DAG and its macro-representation. This two-level representation is the main base of the proposed mixture model. To perform unsupervised classification, we propose a dedicated algorithm called EM-mDAG, which extends the classical EM algorithm. In the Gaussian case, we show that this algorithm can be efficiently implemented. This approach has two main advantages. It favors the selection of a small number of classes and it allows a semantic interpretation of the classes based on a clustering within the macro-variables.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.02.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092849","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: 1
Diagnostic check for heavy tail in linear time series 线性时间序列中重尾的诊断检查
Statistical Methodology Pub Date : 2015-05-01 DOI: 10.1016/j.stamet.2014.11.001
Tony Siu Tung Wong
{"title":"Diagnostic check for heavy tail in linear time series","authors":"Tony Siu Tung Wong","doi":"10.1016/j.stamet.2014.11.001","DOIUrl":"10.1016/j.stamet.2014.11.001","url":null,"abstract":"<div><p>Justification of heavy tail is an important open problem. A systematic approach is proposed to verify heavy tail in linear time series<span>. It consists of three parts, each of which is guided by statistical tests. The analysis is supplemented by an application to ozone concentration. The methodology has the advantage that the threshold selection is data-driven. Simulations show that test results are accurate even under model misspecification. The power is good under two heavy-tailed alternatives. The test is invariant when the time series clusters at extreme level in the study of the max-autoregressive process. It also gives a preliminary measure of tail heaviness if the underlying process is heavy-tailed.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.11.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092600","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: 1
Approximating moments of continuous functions of random variables using Bernstein polynomials 用Bernstein多项式逼近随机变量连续函数的矩
Statistical Methodology Pub Date : 2015-05-01 DOI: 10.1016/j.stamet.2014.11.004
A.I. Khuri , S. Mukhopadhyay , M.A. Khuri
{"title":"Approximating moments of continuous functions of random variables using Bernstein polynomials","authors":"A.I. Khuri ,&nbsp;S. Mukhopadhyay ,&nbsp;M.A. Khuri","doi":"10.1016/j.stamet.2014.11.004","DOIUrl":"10.1016/j.stamet.2014.11.004","url":null,"abstract":"<div><p><span>Bernstein polynomials<span> have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function </span></span><span><math><mi>g</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> of a random variable <span><math><mi>X</mi></math></span>, and (2) proving <em>Jensen’s inequality</em><span> concerning a convex function<span> without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the </span></span><span><em>delta method</em></span>, which is used to approximate the variance of <span><math><mi>g</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.11.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092631","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: 5
A uniqueness result for L-estimators, with applications to L-moments l估计量的唯一性结果，及其在l矩上的应用
Statistical Methodology Pub Date : 2015-05-01 DOI: 10.1016/j.stamet.2014.08.002
J.R.M. Hosking , N. Balakrishnan
{"title":"A uniqueness result for L-estimators, with applications to L-moments","authors":"J.R.M. Hosking ,&nbsp;N. Balakrishnan","doi":"10.1016/j.stamet.2014.08.002","DOIUrl":"10.1016/j.stamet.2014.08.002","url":null,"abstract":"<div><p><span>We show that if a linear combination<span> of expectations of order statistics has mean zero across all random variables that have finite mean, then the linear combination is identically zero. A consequence of this result is that any functional of a probability distribution can have essentially only one unbiased </span></span><span><math><mi>L</mi></math></span>-estimator (i.e., an estimator that has the form of a linear combination of order statistics): if two such linear combinations have the same expectation then they must be algebraically identical. We use this result to prove the equivalence of two statistics that have been proposed as estimators of the <em>L</em>-moments introduced by Hosking (1990), and to provide alternative means of computing estimators of the trimmed <em>L</em>-moments introduced by Elamir and Seheult (2003). We also make comparisons of the speed of various methods for computing estimators of <em>L</em>-moments and trimmed <em>L</em>-moments.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.08.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092453","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: 8
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