[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-290182-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-290182-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","preliminary-test-methodology-in-view-ofasymmetry-with-elliptically-contoureddistribution","PRELIMINARY TEST METHODOLOGY IN VIEW OFASYMMETRY WITH ELLIPTICALLY CONTOUREDDISTRIBUTION","","This paper investigates the preliminary test estimator (PTE) for parameters of elliptically contoured distributions under an asymmetric linex loss function. Analytical and graphical risk functions of the PTE and a sample-information-based unrestricted estimator are derived and compared. The study identifies conditions under which the PTE achieves superior performance relative to the unrestricted estimator, emphasizing the role of asymmetric loss in risk assessment.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/preliminary-test-methodology-in-view-ofasymmetry-with-elliptically-contoureddistribution/290182/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/preliminary-test-methodology-in-view-ofasymmetry-with-elliptically-contoureddistribution/290182.png","ImageObject",300,407,{"name":42,"@type":43},"Logic","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-06","2026-09-17",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What estimator does the paper focus on?","Question",{"text":62,"@type":63},"The paper studies the preliminary test estimator (PTE) for parameters of elliptically contoured distributions.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Why is an asymmetric linex loss function used?",{"text":67,"@type":63},"It reflects situations where over-estimation and under-estimation have different implications, unlike symmetric losses such as squared error loss.",{"name":69,"@type":60,"acceptedAnswer":70},"How are the estimators compared?",{"text":71,"@type":63},"Risk functions are derived and analyzed both analytically and graphically, comparing the PTE against a sample-information-based unrestricted estimator.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},290182,1792160911,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145,"preview_page_count":4},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","# PRELIMINARY TEST METHODOLOGY IN VIEW OFASYMMETRY WITH ELLIPTICALLY CONTOUREDDISTRIBUTION\n\nM.ARASHI  \nFaculty of Mathematical Sciences,Shahrood University of Technology,IranEmail:m-arashi-stat@yahoo.com  \nZ.HoQUE  \nDepartment of Analytics and Digital Era,College of Business and Economics,UAE University,P.O.Box 15551,Al Ain,UAEEmail:Zahirul.Hoque@uaeu.ac.ae  \n## SUMMARY\n\nThis paper studies the preliminary test estimator(PTE)of the parameters ofelliptically contoured distribution.The risk functions of the PTE and the sampleinformation based unrestricted estimator have been derived under asymmetriclinex loss function.These risk functions have been analysed both analyticallyand graphically to compare with each other.It has been revealed that undercertain conditions PTE outperforms the sample information based estimator.  \nKeywords and phrases:Elliptically contoured distribution,Preliminary test esti-mator,Linex loss and risk function.  \n2010 Mathematics Subject Classification:Primary 62F03,secondary 62J05.  \n## 1 Introduction\n\nThe class of elliptical distributions contains a wide variety of distributions.It includes themultivariate normal(multinormal,henceforth)distribution as a special case,as well as manynon-normal distributions including Cauchy,multivariate exponential,multivariate ellipticalanalogue of Student's t and non-normal variance mixtures of multinormal distributions.Elliptical distributions are symmetric and unimodal but are not constrained regarding kur-tosis.This class of distributions has recently gained a lot of attention to the practitionersof statistics in different areas,especially in financial statistics.Particular use of this distri-bution is visible in risk management.Therefore,the estimation of parameters of ellipticaldistribution is of interest to its users in many areas.  \nIn statistical literature different estimation strategies are suggested.Sample informationbased maximum likelihood estimator(MLE)is the best linear unbiased estimator and oneof the most popular estimators.However,if the objective of any study is to minimize therisk of the estimator,MLE may not be an ideal choice as there are other estimators thatoutperform MLE.Khan et al.(2005)compared five different estimators of the interceptparameter of simple linear regression model under squared error loss and suggested thatthe least squares estimator (LSE)is not admissible as there are other estimators that out-perform the LSE.Khan(2005)studied the different estimation strategies of parameters ofthe simple multivariate linear model with Student-t error with squared error loss.LaterKhan(2008)investigated the estimation strategies of the intercept parameters of two linearregression models with normal errors,when it is a priori suspected that the two regressionlines are parallel.An extensive investigation on the properties of alternative estimators ofthe parameters of various models is available in Saleh(2006).  \nRisk of the estimator depends on the choice of the loss function.In statistical literaturethere are various loss functions.Some loss functions are symmetric in nature and someare asymmetric.Symmetric losses,e.g.squared error loss,assigns equal weight to bothunder-and over-estimation.On the other hand,asymmetric losses such as linex loss assignsappropriate wight to under-and over-estimations.In real life there are situations whereover-estimation is more severe than under-estimation and vice-versa.For example,in adam construction underestimation of the peak water level is more serious than its over-estimation.In such situation the choice of an appropriate asymmetric loss is necessary forthe study of the risk.  \nIn an applied study of real estate assessment,Varian(1975)proposed the linex lossfunction.It includes the symmetric squared error loss as a special case.Hoque et al.(2009)investigated the performance of preliminary test estimator of simple linear regressionmodel under asymmetric linex loss.In a recent study,Hoque et al.(2018)studied th","cbCaig6sXSR40nHG","https://ap.wps.com/l/cbCaig6sXSR40nHG","pdf",4900566,11,"English","# Summary\n# 1 Introduction\n# 2 Preliminaries\n## 2.1 Linex Loss Function","[{\"question\":\"What estimator does the paper focus on?\",\"answer\":\"The paper studies the preliminary test estimator (PTE) for parameters of elliptically contoured distributions.\"},{\"question\":\"Why is an asymmetric linex loss function used?\",\"answer\":\"It reflects situations where over-estimation and under-estimation have different implications, unlike symmetric losses such as squared error loss.\"},{\"question\":\"How are the estimators compared?\",\"answer\":\"Risk functions are derived and analyzed both analytically and graphically, comparing the PTE against a sample-information-based unrestricted estimator.\"}]","PRELIMINARY TEST METHODOLOGY IN VIEW OFASYMMETRY WITH ELLIPTICALLY CONTOUREDDISTRIBUTION | PDF",1789640882,28]