Pub Date : 2015-09-01DOI: 10.1016/j.stamet.2015.04.004
B.L.S. Prakasa Rao
We introduce a class of processes termed as filtered fractional Poisson processes (FFPP) and study their properties and give some applications of these to stochastic models. In addition, we study filtered fractional Levy processes (FFLP) as a generalization of these models.
{"title":"Filtered fractional Poisson processes","authors":"B.L.S. Prakasa Rao","doi":"10.1016/j.stamet.2015.04.004","DOIUrl":"10.1016/j.stamet.2015.04.004","url":null,"abstract":"<div><p>We introduce a class of processes termed as filtered fractional Poisson processes (FFPP) and study their properties and give some applications of these to stochastic models. In addition, we study filtered fractional Levy processes (FFLP) as a generalization of these models.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"26 ","pages":"Pages 124-134"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.04.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092967","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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2015.02.002
Anne Philip, P. Yageen Thomas
In this paper, we consider concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and develop its distribution theory. Using ranked set sample obtained from the above distribution, unbiased estimators of the parameters associated with the study variate involved in it are generated. The best linear unbiased estimators (BLUEs) based on observations in the ranked set sample of those parameters as well have been derived. The efficiencies of the BLUEs relative to the respective unbiased estimators generated also have been evaluated.
{"title":"On concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and its application in estimation","authors":"Anne Philip, P. Yageen Thomas","doi":"10.1016/j.stamet.2015.02.002","DOIUrl":"10.1016/j.stamet.2015.02.002","url":null,"abstract":"<div><p><span>In this paper, we consider concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate </span>logistic distribution<span><span> and develop its distribution theory. Using ranked set sample obtained from the above distribution, </span>unbiased estimators<span> of the parameters associated with the study variate involved in it are generated. The best linear unbiased estimators (BLUEs) based on observations in the ranked set sample of those parameters as well have been derived. The efficiencies of the BLUEs relative to the respective unbiased estimators generated also have been evaluated.</span></span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"25 ","pages":"Pages 59-73"},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.02.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55092828","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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2015.02.003
Hironori Fujisawa , Toshihiro Abe
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 for a skew distribution is discussed. A numerical study is also conducted.
{"title":"A family of skew distributions with mode-invariance through transformation of scale","authors":"Hironori Fujisawa , 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":"25 ","pages":"Pages 89-98"},"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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2014.12.003
Dian-tong Kang
Di Crescenzo and Longobardi (2002) introduced the past entropy, Sunoj et al. (2013) gave a quantile 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.
Di Crescenzo和Longobardi(2002)引入了过去熵,Sunoj等人(2013)给出了过去熵的分位数版本,称为过去分位数熵(PQE)。在PQE函数的基础上,他们定义了一种新的随机阶,称为少PQE (LPQE)阶,并研究了该阶的一些性质。在本文中,我们关注于这一新阶的进一步闭包性质。研究了LPQE阶的一些性质,得到了闭包和反闭包性质。讨论了比例故障率和反向故障率模型中LPQE顺序的保持问题。
{"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":"25 ","pages":"Pages 23-35"},"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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2015.02.001
K.K. Sudheesh , P. Anisha , C.M. Deemat
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.
{"title":"A simple approach for testing constant failure rate against different ageing classes for discrete data","authors":"K.K. Sudheesh , P. Anisha , 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":"25 ","pages":"Pages 74-88"},"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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2014.12.001
Sangyeol Lee , Byungsoo Kim
In this paper, we study the problem of testing for a copula 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 null distribution under regularity conditions. For illustration, we conduct a simulation study with an emphasis on STAR–STGARCH models. A real data analysis applied to the S&P 500 index and IBM stock price is also considered.
{"title":"Copula parameter change test for nonlinear AR models with nonlinear GARCH errors","authors":"Sangyeol Lee , 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&P 500 index and IBM stock price is also considered.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"25 ","pages":"Pages 1-22"},"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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2014.12.002
Zhensheng Huang , Quanxi Shao , Zhen Pang , Bingqing Lin
Adaptive testing for the partially linear single-index model (PLSIM) with error-prone linear covariates 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 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.
{"title":"Adaptive testing for the partially linear single-index model with error-prone linear covariates","authors":"Zhensheng Huang , Quanxi Shao , Zhen Pang , 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":"25 ","pages":"Pages 51-58"},"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}
In this article we construct bivariate discrete distributions in . 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.
{"title":"On some distributions arising from a generalized trivariate reduction scheme","authors":"Christophe Chesneau , Maher Kachour , 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":"25 ","pages":"Pages 36-50"},"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}
Pub Date : 2015-07-01DOI: 10.1016/j.stamet.2015.02.004
Bernard Chalmond
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.
{"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":"25 ","pages":"Pages 99-118"},"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}
Pub Date : 2015-05-01DOI: 10.1016/j.stamet.2014.11.001
Tony Siu Tung Wong
Justification of heavy tail is an important open problem. A systematic approach is proposed to verify heavy tail in linear time series. 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.
{"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":"24 ","pages":"Pages 1-11"},"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}