Estimation of the Last Mean of a Monotone Sequence

Cohen, Arthur; Sackrowitz, Harold

doi:10.1214/aoms/1177696702

Cited by 51 publications

(20 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…He showed in the paper that the criterion of universal domination is equivalent to the criterion of stochastic domination which has attracted broad attention among statistians (see also Cohen and Sackrowitz, 1970;Ali and Ponnapalli, 1990;Hwang and Peddada, 1994). In order to compare estimators of %, we consider, for an estimator %*, its concentration probability P(%*&% # C) for some prespecified set C, where the set C is usually taken as a convex set containing the origin as an inner point.…”

Section: â2mentioning

confidence: 99%

Universal Inadmissibility of Least Squares Estimator

Shi

2000

Journal of Multivariate Analysis

View full text Add to dashboard Cite

For a p-dimensional normal distribution with mean vector % and covariance matrix I p , it is known that the maximum likelihood estimator % of % with p 3 is inadmissible under the squared loss. The present paper considers possible extensions of the result to the case where the loss is a member of a general class of losses of the form L( |$&%| Q ), where L is nondecreasing and |$&%| Q denotes the1Â2 with respect to a given positive definite matrix Q, which, without loss of generality, may be assumed to be diagonal, i.e., Q=diag(q 1 , ..., q p ), q 1 >q 2 q 3 } } } q p >0. For the case where q 1 >q 2 =q 3 = } } } =q p >0, L. D. Brown and J. T. Hwang (1989, Ann. Statist. 17, 252 267) showed that there exists an estimate of % universally dominates % if and only if p 4. This paper further extends Brown and Hwang's result to the case in which q 1 >q 2 and at least there are two equal elements among q 2 , } } } , q p&1 ; namely, we show that, for this case, there exists an estimate of % which universally dominates % if and only if p 4. For a general Q, we gives a lower bound on p that implies the least squares estimators is universally inadmissible. Academic PressAMS 1991 subject classifications: 62C05, 62H12, 62J07.

show abstract

Section: â2mentioning

confidence: 99%

Universal Inadmissibility of Least Squares Estimator

Shi

2000

Journal of Multivariate Analysis

View full text Add to dashboard Cite

show abstract

“…(This circumstance, however, is not always the case, even in nice situations with convex losses, as seen in Cohen and Sackrowitz (1970 Extending the work of Brown, Brewster and Zidek selected, for fixed r as above, r 1 , with 0 < r 1 < r and considered the estimator ¢(Z 2 )S 2 , where…”

Section: Figure 1 About Here Imentioning

confidence: 99%

Developments in Decision-Theoretic Variance Estimation

Maatta¹,

Casella²

1990

Statist. Sci.

View full text Add to dashboard Cite

This article traces the history of the problem of estimating the variance, 0" 2 , based on a random sample from a normal distribution with mean J-l unknown. Considered are both the point estimation and confidence interval cases. We see that improvement over both usual estimators follows a remarkably parallel development and stemmed from the innovative ideas presented in Stein (1964). We examine developments through the most recent dealing with improved confidence intervals and conditional evaluations of interval estimators.-2-

show abstract

“…Such restrictions may enable us to improve on usual estimation procedures. Methods for improving have been investigated by Cohen and Sackrowiz (1970), Brewster and Zidek (1974), Kushary and Cohen (1989), and Kubokawa and Saleh (1994) and Kubokawa (1994). The relevant estimation problems with restricted parameters have been treated by Kubokawa (2004) and Machand and Strawderman (2005).…”

Section: Introductionmentioning

confidence: 99%