Sensitivity analysis in linear models

Shuangzhe LIU, Tiefeng Ma, Yonghui Liu

Research output: A Conference proceeding or a Chapter in BookConference contribution

3 Downloads (Pure)

Abstract

In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators' sensitivity results. We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

Original languageEnglish
Title of host publicationSpecial Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics
EditorsJeffrey J Hunter, Simo Puntanen, Dietrich van Rosen
Place of PublicationWarsaw Poland
PublisherWalter de Gruyter
Pages225-232
Number of pages8
Volume4
Edition1
DOIs
Publication statusPublished - 2016
Event24th Internatiopnal Workshop on Matrices and Statistics - Haikou, Haikou, China
Duration: 25 May 201528 May 2015
http://iwms2015.csp.escience.cn/dct/page/1 (Conference website)

Publication series

NameSpecial Matrices
PublisherDe Gruyter Open Ltd.
ISSN (Print)2300-7451

Conference

Conference24th Internatiopnal Workshop on Matrices and Statistics
Abbreviated titleIWMS
CountryChina
CityHaikou
Period25/05/1528/05/15
Internet address

Fingerprint

Sensitivity Analysis
Linear Model
Regression Coefficient
Estimator
Local Influence
Generalized Least Squares
Ordinary Least Squares
Least Squares Estimator

Cite this

LIU, S., Ma, T., & Liu, Y. (2016). Sensitivity analysis in linear models. In J. J. Hunter, S. Puntanen, & D. V. Rosen (Eds.), Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics (1 ed., Vol. 4, pp. 225-232). (Special Matrices). Warsaw Poland: Walter de Gruyter. https://doi.org/10.1515/spma-2016-0021
LIU, Shuangzhe ; Ma, Tiefeng ; Liu, Yonghui. / Sensitivity analysis in linear models. Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics. editor / Jeffrey J Hunter ; Simo Puntanen ; Dietrich van Rosen. Vol. 4 1. ed. Warsaw Poland : Walter de Gruyter, 2016. pp. 225-232 (Special Matrices).
@inproceedings{576fd6c356a744a5ab8d15c6fe4f6e5d,
title = "Sensitivity analysis in linear models",
abstract = "In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators' sensitivity results. We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.",
keywords = "least-squares, maximum-likelihood, sensitivity-matrix, Least squares, Maximum likelihood, Mixed estimation, sensitivity matrix, Elliptical distribution",
author = "Shuangzhe LIU and Tiefeng Ma and Yonghui Liu",
year = "2016",
doi = "10.1515/spma-2016-0021",
language = "English",
volume = "4",
series = "Special Matrices",
publisher = "Walter de Gruyter",
pages = "225--232",
editor = "Hunter, {Jeffrey J} and Simo Puntanen and Rosen, {Dietrich van}",
booktitle = "Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics",
address = "Germany",
edition = "1",

}

LIU, S, Ma, T & Liu, Y 2016, Sensitivity analysis in linear models. in JJ Hunter, S Puntanen & DV Rosen (eds), Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics. 1 edn, vol. 4, Special Matrices, Walter de Gruyter, Warsaw Poland, pp. 225-232, 24th Internatiopnal Workshop on Matrices and Statistics, Haikou, China, 25/05/15. https://doi.org/10.1515/spma-2016-0021

Sensitivity analysis in linear models. / LIU, Shuangzhe; Ma, Tiefeng; Liu, Yonghui.

Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics. ed. / Jeffrey J Hunter; Simo Puntanen; Dietrich van Rosen. Vol. 4 1. ed. Warsaw Poland : Walter de Gruyter, 2016. p. 225-232 (Special Matrices).

Research output: A Conference proceeding or a Chapter in BookConference contribution

TY - GEN

T1 - Sensitivity analysis in linear models

AU - LIU, Shuangzhe

AU - Ma, Tiefeng

AU - Liu, Yonghui

PY - 2016

Y1 - 2016

N2 - In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators' sensitivity results. We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

AB - In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators' sensitivity results. We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

KW - least-squares

KW - maximum-likelihood

KW - sensitivity-matrix

KW - Least squares

KW - Maximum likelihood

KW - Mixed estimation, sensitivity matrix

KW - Elliptical distribution

UR - http://www.scopus.com/inward/record.url?scp=85011961562&partnerID=8YFLogxK

U2 - 10.1515/spma-2016-0021

DO - 10.1515/spma-2016-0021

M3 - Conference contribution

VL - 4

T3 - Special Matrices

SP - 225

EP - 232

BT - Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics

A2 - Hunter, Jeffrey J

A2 - Puntanen, Simo

A2 - Rosen, Dietrich van

PB - Walter de Gruyter

CY - Warsaw Poland

ER -

LIU S, Ma T, Liu Y. Sensitivity analysis in linear models. In Hunter JJ, Puntanen S, Rosen DV, editors, Special Matrices Topical Issue on Proceedings of the 24th International Workshop on Matrices and Statistics. 1 ed. Vol. 4. Warsaw Poland: Walter de Gruyter. 2016. p. 225-232. (Special Matrices). https://doi.org/10.1515/spma-2016-0021