An Asymptotic Lower Bound for the Local Minimax Regret in Sequential Point Estimation

Tahir, Mohamed

doi:10.1214/aos/1176347273

Cited by 7 publications

(3 citation statements)

References 17 publications

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“…Martinsek (1983) extended Woodroofe's result to the nonparametric case. Tahir (1989) proposed a class of bias-reduction estimators of the mean of the oneparameter exponential family and provided an asymptotic second-order lower bound for the regret. Kim and Han (2009) considered estimation of the scale parameter of the Rayleigh distribution under general progressive censoring.…”

Section: Jmssmentioning

confidence: 99%

Sequential Estimation of the Square of the Rayleigh Parameter

Tahir¹

2014

Journal of Mathematics and Statistics

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Section: Jmssmentioning

confidence: 99%

Sequential Estimation of the Square of the Rayleigh Parameter

Tahir¹

2014

Journal of Mathematics and Statistics

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“…, X,. hen, we estimate p by the bias-reduction estimator as in Tahir (1989), where bk, k l l , is a sequence of bounded, continuous functions on p ( 8 ) The proof of this theorem is presented in Section 3.…”

Section: Asymptotically Negative Regretmentioning

confidence: 99%

Bias reduction and negative regret in sequential point extimation

Tahir¹,

Rekab

2001

Journal of Nonparametric Statistics

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Let XI, X2,. . . be independent random variables with common distribution Fo for which the mean, p = p(B), is a one-to-one function of the parameter 19 E 0 c (-oo. w ).Suppose that XI. X2,. . . a n to be taken one at a time up to stage f. Iff is chosen before observing X I , . ..,XI, then one may estimate p by the sample mean XI, which is an unbiased estimator of p . However, if f is determined according to a stopping rule, then may be biased for, p . Lctting r be a stopping time of the type proposed by Robbins (1959) and estimating p by a bias-reduction estimator, fi,, subject to the loss function L,, =&fit -p)' + f , a >O, we show that the asymptotic regret (as a + w ) of the sequential procedure (t,ji,) can be negative if the bias-reduction function is chosen properly.

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“…Bayesian sequential estimation problems were studied by Bickel and Yahav (1969), Alvo (1977), Rasmussen (1980), Shapiro and Wardrop (1980), Woodroofe (1981Woodroofe ( , 1985, Tahir (1989), Woodroofe and Hardwick (1990), among others.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Sequential Estimation of the Inverse of the Pareto Shape Parameter

Tahir¹

2016

IJSP

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The problem addressed is that of developing a sequential procedure for estimating the inverse of the shape parameter of the Pareto distribution under the squared loss, assuming that the shape parameter is the value of a random variable having a density function with compact support and that the cost per observation is one unit. A stopping time is proposed and a second-order asymptotic expansion is obtained for the Bayes regret incurred by the proposed procedure.

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An Asymptotic Lower Bound for the Local Minimax Regret in Sequential Point Estimation

Cited by 7 publications

References 17 publications

Sequential Estimation of the Square of the Rayleigh Parameter

Sequential Estimation of the Square of the Rayleigh Parameter

Bias reduction and negative regret in sequential point extimation

Bayesian Sequential Estimation of the Inverse of the Pareto Shape Parameter

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