# Optimal tolerance regions for some functions of multiple regression model with Student-t errors

(2006) Optimal tolerance regions for some functions of multiple regression model with Student-t errors. Journal of Statistics and Management Systems, 9 (3). pp. 699-715. ISSN 0972-0510 Preview
PDF
opt-tr-regVec-t.pdf

## Abstract

This paper considers the multiple regression model to determine optimal beta-expectation tolerance regions for the future regression vector (FRV) and future residual sum
of squares (FRSS) by using the prediction distributions of some appropriate functions of future responses. It is assumed that the errors of the regression model follow a multivariate Student-t distribution with unknown shape parameter, nu. The prediction distribution
of the FRV, conditional on the observed responses, is a
multivariate Student-t distribution but its shape parameter does not depend on the unknown degrees of freedom of the Student-t model. Similarly, the prediction distribution of the FRSS is a beta distribution. The optimal beta- expectation tolerance regions for the FRV and FRSS have been obtained based on the F-distribution and beta distribution respectively. Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C) Yes Live Archive Full text of paper available for subscribers to the journal at http://www.tarupublications.com/jsms/FullText/JSMS-2006/JSMS-9-3-2006/jsms159.pdf. Author's final manuscript version deposited with permission of publisher. Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) 11 Oct 2007 00:49 02 May 2017 00:36 Multiple regression model, prediction distribution, tolerance region, invariant differential, non-informative prior multivariate Student-t, beta and \$F\$ distributions. 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory01 Mathematical Sciences > 0104 Statistics > 010401 Applied Statistics 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490509 Statistical theory49 MATHEMATICAL SCIENCES > 4905 Statistics > 490501 Applied statistics http://eprints.usq.edu.au/id/eprint/1703 Archive Repository Staff Only
{"ft_lang_label":"__label__en","ft_lang_prob":0.67500174,"math_prob":0.5534898,"size":2493,"snap":"2021-31-2021-39","text_gpt3_token_len":585,"char_repetition_ratio":0.12334271,"word_repetition_ratio":0.11692308,"special_character_ratio":0.2515042,"punctuation_ratio":0.120987654,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97501266,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,3,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-20T02:55:11Z\",\"WARC-Record-ID\":\"<urn:uuid:fc07c37b-e86d-4c97-bdc8-10f37085c578>\",\"Content-Length\":\"21931\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f6b7f78b-3d64-413c-8cef-14dc33d472ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:b7911589-ee85-4e9a-ac23-01a46274bb86>\",\"WARC-IP-Address\":\"139.86.7.154\",\"WARC-Target-URI\":\"https://eprints.usq.edu.au/1703/\",\"WARC-Payload-Digest\":\"sha1:OYQEI4SWQVQAZXIUKDH7KJDQK4ULAQQ2\",\"WARC-Block-Digest\":\"sha1:OCJQF33MLLPZZONLTQOWUHK2XQKICS66\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056974.30_warc_CC-MAIN-20210920010331-20210920040331-00305.warc.gz\"}"}