摘要:

For optimality results in sequential analysis which contain explicit description of optimal strategies the assumption of linear costs of observation ct has been of major importance. In this paper we leave this assumption and investigate the question how the shape of nonlinear costs of observation influences the shape of optimal stopping boundaries. We do this for an optimal stopping problem which arises in the derivation of locally most powerful sequential tests for the Wiener process. It is found that costs of observation of the formlead to optimal stopping boundaries which grow in the order ofas t → ∞

ISSN:0747-4946    

DOI:10.1080/07474948708836113

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Three stage sampling procedures have been discussed with the goal of achieving (i) the minimum risk and (ii) the bounded risk separately for point estimation of the mean of a normal population whose variance is completely unknown. The remainder term in the second-order asymptotic expansion of the risk function is shown to have the exact same order as that obtained in the case of the corresponding purely sequential procedure for both these problems. The results obtained for the second problem also form major extensions of the properties derived in Mukhopadhyay (1985, Sequential Analysis, 4, 311-319)

ISSN:0747-4946    

DOI:10.1080/07474948708836114

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

The hazard rate function of the Weibull Exponential lifetime distribution is decreasing over time up to a change point and remains a constant afterward We derive some of the properties of this lifetime distribution and develop a Bayes sequential procedure for estimating the change point. The problem of determining an appropriate burn in time under a certian loss function is also considered. An adaptive Bayesian decision rule for the termination of the burn in procedure is proposed. Results of numerical simulations are given to demonstrate the proposed procedure.

ISSN:0747-4946    

DOI:10.1080/07474948708836115

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Let f be a nonparametric probability density function on the real line. For estimating f(x) at a given point x we consider a recursive estimator fn(x) consisting of kernel functions. For given α (0<α<1) and d>0 we define a certain class of stopping rules Ndand takeas a 2d–width confidence interval for f(x). In this paper we derive the rate at which the probabilityconverges to α as d tends to zero.

ISSN:0747-4946    

DOI:10.1080/07474948708836116

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

The influence of two kinds of contamination on sequential confidence intervals for the mean of a normal population is studied when the contamination probability tends to zero with the length d of the confidence interval. It is shown that if ε/d → a>0 the mean of the asymptotic distribution of the stopping variable (properly normalized) of eachprocedure considered is of special interest.In the case of contamination by a point mass, the asymptotic mean is closely related to the influence function of the measure of spread in the definition of the stopping rule. For the Chow Robbins procedure the influence function of the standard deviation appears and this is unbounded. If the standard deviation in this procedure is replaced by a fractile difference estimator, the influence function, and hence the asymptotic mean, remains bounded. Similar results are obtained for a gross errors contamination model. The asymptotic coverage probability of both procedures is biased under the nonsymmetric point mass contamination model, but not biased under thesymmetric gross errors model. If a = 0 the contamination has no effect on the asymptotic properties of the procedures. Results of a Monte Carlo study indicates agreement between the asymptotic results and the actual behavior of the procedures.

ISSN:0747-4946    

DOI:10.1080/07474948708836117

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474948708836112

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor