MARGINAL CURVATURES FOR FUNCTIONS OF PARAMETERS IN NONLINEAR REGRESSION

The marginal curvature by Clarke (1987) for individual parameters in nonlinear models not only improves the inference on each parameter but also has been found useful in experimental design for nonlinear models. In this article we develop the marginal curvature for functions of parameters. We show t...

Full description

Saved in:
Bibliographic Details
Published in:Statistica Sinica 1998-04, Vol.8 (2), p.467-476
Main Authors: Kang, Gunseog, Rawlings, John O.
Format: Article
Language:English
Subjects:
Curvature
Experiment design
Inference
Linear approximation
Mathematical independent variables
Mathematical transformations
Nonlinearity
Parametric models
Point estimators
Regression analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 476
container_issue 2
container_start_page 467
container_title Statistica Sinica
container_volume 8
creator Kang, Gunseog
Rawlings, John O.
description The marginal curvature by Clarke (1987) for individual parameters in nonlinear models not only improves the inference on each parameter but also has been found useful in experimental design for nonlinear models. In this article we develop the marginal curvature for functions of parameters. We show that, for a given reparametrization, the marginal curvatures for the transformed parameters can be computed without determining the inverse transformation. Furthermore, the marginal curvature for a function of parameters depends only on the marginal curvatures of the original parameters and on the derivatives of the function with respect to the parameters involved in that function. We also present a more efficient computing algorithm of Clarke's marginal curvature measure. The resulting expression enables us to compare Clarke's measure with other available measures.
format article
fullrecord <record><control><sourceid>jstor</sourceid><recordid>TN_cdi_jstor_primary_24306503</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>24306503</jstor_id><sourcerecordid>24306503</sourcerecordid><originalsourceid>FETCH-LOGICAL-j175t-ff8d99f58eacb0881b35a4174546747b60a1fe96cc6079827e4ccb519688485e3</originalsourceid><addsrcrecordid>eNotjM1KxDAYAIMouKz7CEJeoPBlky8_x1DSWugmkrZel7YmsIuitHvx7S3oaeYwzB3ZMWNkoRHU_ebAVAEC8JEc1vUyARhApoHvSH2ysW68bWk5xDfbD9F1tAqRVoMv-yb4joaKvtpoT653saONpz74tvHORhpdvfXdlj2Rhzx-rOnwzz0ZKteXL0Ub6qa0bXFlCm9FzvrdmIw6jfMEWrOJ4yiYEiikEmqSMLKcjJxnCcroo0pinidkRmotNCa-J89_3-t6-1rO38vlc1x-zkfBQSJw_guewEAq</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>MARGINAL CURVATURES FOR FUNCTIONS OF PARAMETERS IN NONLINEAR REGRESSION</title><source>JSTOR</source><creator>Kang, Gunseog ; Rawlings, John O.</creator><creatorcontrib>Kang, Gunseog ; Rawlings, John O.</creatorcontrib><description>The marginal curvature by Clarke (1987) for individual parameters in nonlinear models not only improves the inference on each parameter but also has been found useful in experimental design for nonlinear models. In this article we develop the marginal curvature for functions of parameters. We show that, for a given reparametrization, the marginal curvatures for the transformed parameters can be computed without determining the inverse transformation. Furthermore, the marginal curvature for a function of parameters depends only on the marginal curvatures of the original parameters and on the derivatives of the function with respect to the parameters involved in that function. We also present a more efficient computing algorithm of Clarke's marginal curvature measure. The resulting expression enables us to compare Clarke's measure with other available measures.</description><identifier>ISSN: 1017-0405</identifier><identifier>EISSN: 1996-8507</identifier><language>eng</language><publisher>Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association</publisher><subject>Curvature ; Experiment design ; Inference ; Linear approximation ; Mathematical independent variables ; Mathematical transformations ; Nonlinearity ; Parametric models ; Point estimators ; Regression analysis</subject><ispartof>Statistica Sinica, 1998-04, Vol.8 (2), p.467-476</ispartof><rights>1998 Statistica Sinica</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/24306503$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/24306503$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,58237,58470</link.rule.ids></links><search><creatorcontrib>Kang, Gunseog</creatorcontrib><creatorcontrib>Rawlings, John O.</creatorcontrib><title>MARGINAL CURVATURES FOR FUNCTIONS OF PARAMETERS IN NONLINEAR REGRESSION</title><title>Statistica Sinica</title><description>The marginal curvature by Clarke (1987) for individual parameters in nonlinear models not only improves the inference on each parameter but also has been found useful in experimental design for nonlinear models. In this article we develop the marginal curvature for functions of parameters. We show that, for a given reparametrization, the marginal curvatures for the transformed parameters can be computed without determining the inverse transformation. Furthermore, the marginal curvature for a function of parameters depends only on the marginal curvatures of the original parameters and on the derivatives of the function with respect to the parameters involved in that function. We also present a more efficient computing algorithm of Clarke's marginal curvature measure. The resulting expression enables us to compare Clarke's measure with other available measures.</description><subject>Curvature</subject><subject>Experiment design</subject><subject>Inference</subject><subject>Linear approximation</subject><subject>Mathematical independent variables</subject><subject>Mathematical transformations</subject><subject>Nonlinearity</subject><subject>Parametric models</subject><subject>Point estimators</subject><subject>Regression analysis</subject><issn>1017-0405</issn><issn>1996-8507</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNotjM1KxDAYAIMouKz7CEJeoPBlky8_x1DSWugmkrZel7YmsIuitHvx7S3oaeYwzB3ZMWNkoRHU_ebAVAEC8JEc1vUyARhApoHvSH2ysW68bWk5xDfbD9F1tAqRVoMv-yb4joaKvtpoT653saONpz74tvHORhpdvfXdlj2Rhzx-rOnwzz0ZKteXL0Ub6qa0bXFlCm9FzvrdmIw6jfMEWrOJ4yiYEiikEmqSMLKcjJxnCcroo0pinidkRmotNCa-J89_3-t6-1rO38vlc1x-zkfBQSJw_guewEAq</recordid><startdate>19980401</startdate><enddate>19980401</enddate><creator>Kang, Gunseog</creator><creator>Rawlings, John O.</creator><general>Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association</general><scope/></search><sort><creationdate>19980401</creationdate><title>MARGINAL CURVATURES FOR FUNCTIONS OF PARAMETERS IN NONLINEAR REGRESSION</title><author>Kang, Gunseog ; Rawlings, John O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-j175t-ff8d99f58eacb0881b35a4174546747b60a1fe96cc6079827e4ccb519688485e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Curvature</topic><topic>Experiment design</topic><topic>Inference</topic><topic>Linear approximation</topic><topic>Mathematical independent variables</topic><topic>Mathematical transformations</topic><topic>Nonlinearity</topic><topic>Parametric models</topic><topic>Point estimators</topic><topic>Regression analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kang, Gunseog</creatorcontrib><creatorcontrib>Rawlings, John O.</creatorcontrib><jtitle>Statistica Sinica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kang, Gunseog</au><au>Rawlings, John O.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>MARGINAL CURVATURES FOR FUNCTIONS OF PARAMETERS IN NONLINEAR REGRESSION</atitle><jtitle>Statistica Sinica</jtitle><date>1998-04-01</date><risdate>1998</risdate><volume>8</volume><issue>2</issue><spage>467</spage><epage>476</epage><pages>467-476</pages><issn>1017-0405</issn><eissn>1996-8507</eissn><abstract>The marginal curvature by Clarke (1987) for individual parameters in nonlinear models not only improves the inference on each parameter but also has been found useful in experimental design for nonlinear models. In this article we develop the marginal curvature for functions of parameters. We show that, for a given reparametrization, the marginal curvatures for the transformed parameters can be computed without determining the inverse transformation. Furthermore, the marginal curvature for a function of parameters depends only on the marginal curvatures of the original parameters and on the derivatives of the function with respect to the parameters involved in that function. We also present a more efficient computing algorithm of Clarke's marginal curvature measure. The resulting expression enables us to compare Clarke's measure with other available measures.</abstract><pub>Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association</pub><tpages>10</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1017-0405
ispartof Statistica Sinica, 1998-04, Vol.8 (2), p.467-476
issn 1017-0405
1996-8507
language eng
recordid cdi_jstor_primary_24306503
source JSTOR
subjects Curvature
Experiment design
Inference
Linear approximation
Mathematical independent variables
Mathematical transformations
Nonlinearity
Parametric models
Point estimators
Regression analysis
title MARGINAL CURVATURES FOR FUNCTIONS OF PARAMETERS IN NONLINEAR REGRESSION
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T08%3A41%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=MARGINAL%20CURVATURES%20FOR%20FUNCTIONS%20OF%20PARAMETERS%20IN%20NONLINEAR%20REGRESSION&rft.jtitle=Statistica%20Sinica&rft.au=Kang,%20Gunseog&rft.date=1998-04-01&rft.volume=8&rft.issue=2&rft.spage=467&rft.epage=476&rft.pages=467-476&rft.issn=1017-0405&rft.eissn=1996-8507&rft_id=info:doi/&rft_dat=%3Cjstor%3E24306503%3C/jstor%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-j175t-ff8d99f58eacb0881b35a4174546747b60a1fe96cc6079827e4ccb519688485e3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=24306503&rfr_iscdi=true