JSM 2005 Online Program

Abstract #303716

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Activity Number:	452
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor:	IMS
Abstract - #303716
Title:	Optimal Designs for Calibrations in Multiresponse-univariate Linear Regression Models
Author(s):	Chun-Sui Lin*+ and Mong-Na L. Huang
Companies:	National Sun Yat-sen University and National Sun Yat-sen University
Address:	3F No 19 Lane 598 Sec 2 Ching Nien Rd, Fong Shan City Kaohsiung, 830, Taiwan
Keywords:	c-criterion ; locally optimal design ; multivariate calibration ; prediction
Abstract:	Consider a linear regression model with a one-dimensional control variable $x$ and an $m$-dimensional response variable ${\bf y}=(y_1,\cdots,y_m)$. The calibration problem discussed here is that based on the assumed regression model. It is of interest to obtain a suitable estimation of the corresponding $x$ for a given target ${\bf T}=(T_1,\cdots,T_m)$ on the expected responses. As there is more than one target value to be achieved in the multiresponse case, the $m$ expected responses may meet their target values at different control values respectively. We define the optimal value of calibration point $x_0$ to be the one that minimizes the weighted sum of squares of deviations of the expected response from its corresponding target value for each component within the range of $x$. The objective of this study is to find a locally optimal design for estimating $x_0$, which minimizes the mean square error on the difference between $x_0$ and its estimator.

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