Estimation of location parameters from two linear models under normality

Khatri, C. G.; Shah, Kirti R.

doi:10.1080/03610927408827165

Cited by 79 publications

(34 citation statements)

References 5 publications

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“…As shown by Khatri and Shah (1974), Brown and Cohen (1974) and Swamy and Mehta (1979), the estimator ; DS (,, ) is unbiased. Using the Integral-Expression-of-Risk-Difference (IERD) method given by Takeuchi (1991), Kubokawa (1994), and Kubokawa et al ( , 1996, we can establish the following theorem concerning the superiority of the single shrinkage estimators.…”

Section: Inadmissibility Of the Fgls Estimatorsmentioning

confidence: 94%

“…Before stating the main results, it is noted that the estimation of common regression coefficients in our model is related to the problem of recovery of interblock information in balanced incomplete block designs, treated by Khatri and Shah (1974), Brown and Cohen (1974) and Bhattacharya (1980), and the problem of estimating the common mean of two different populations, studied by Cohen and Sackrowitz (1974) and Kubokawa (1987) among others. In general, the problem of estimation of common regression coefficients appears in various applicable models such as heteroscedastic linear models and mixed linear (or variance components) models in biostatistics and econometrics, and FGLS estimators are heavily and widely exploited.…”

Section: Introductionmentioning

confidence: 99%

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Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

Kubokawa

1998

Journal of Multivariate Analysis

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The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, nevertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as possible candidates of improved procedures. Academic PressAMS 1991 subject classifications: primary 62C15; secondary 62F11, 62H12, 62J05.

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Section: Inadmissibility Of the Fgls Estimatorsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

Kubokawa

1998

Journal of Multivariate Analysis

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“…Note that Meier [23] proposed an approximate unbiased estimator of the variance of the GD estimator, which has bias of order [24] gave an exact expression of the variance of this estimator in the form of an infinite series, which is given as.…”

Section: Analysis For Category II Adaptive Designsmentioning

confidence: 99%

Analysis of Two-Stage Adaptive Seamless Trial Design

M¹

2015

Pharm Anal Acta

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In the past decade, adaptive design methods in clinical research have attracted much attention because it offers the principal investigators (1) potential flexibility for identifying clinical benefit of a test treatment under investigation, but efficiency for speeding up the development process. One of the most commonly considered adaptive designs is probably a two-stage seamless (e.g., phase I/II or phase II/III) adaptive design. The two-stage seamless adaptive designs can be classified into four categories depending upon study objectives and study endpoints at different stages. These categories include (I) design with same study objectives and study endpoints at different stages, (II) designs with same study objectives but different study endpoints at different stages, (III) designs with different study objectives but same study endpoints at different stages, and (IV) designs with different study objectives and different study endpoints at different stages. In this article, an overview of statistical methods for analysis of these different types of two-stage designs is provided. In addition, a case study concerning the evaluation of a test treatment for treating hepatitis C infected patients utilizing type (IV) trial design is presented.

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“…Later, many authors, including Brown and Cohen (1974), Khatri and Shah (1974) and Bhattacharya et al (1980) have given a class of improved estimators of the form…”

Section: Introductionmentioning

confidence: 99%

Estimation of Order Restricted Normal Means when the Variances Are Unknown and Unequal

Pedram

Bazyari

2017

AJS

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In the present paper, two normal distributions with parameters µ i and σ 2 i where there is an order restriction on the means when the variances are unknown and unequal are considered. Under the squared error loss function, a necessary and sufficient condition for the plug-in estimators to improve upon the unrestricted maximum likelihood estimators uniformly is given. Also under the modified Pitman nearness criterion; a class of estimators is considered that reduce to the estimators of a common mean when the unbiased estimators violate the order restriction. It is shown that the most critical case for uniform improvement with regard to the unbiased estimators is the one when two means are equal. To illustrate the results, two numerical examples are presented.

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Estimation of location parameters from two linear models under normality

Cited by 79 publications

References 5 publications

Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

Analysis of Two-Stage Adaptive Seamless Trial Design

Estimation of Order Restricted Normal Means when the Variances Are Unknown and Unequal

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