摘要:

The robustness of sequential confidence intervals is studied by considering contamination with probability ε of the basic underlying distribution in a so-called gross errors model. Asymptotic theory is considered when d → 0, where the prescribed length of the interval is 2d, and simultaneously ε ≏ ε(d) → 0. A general theorem, in a distribution free setting, is given which provides expressions for the asymptotic coverage probability and the asymptotic distribution of the stopping variable. The results depend on the rate of ε(d)/d as d → 0 and on the contaminating distribution. If the latter distribution is degenerate, it turns out that the influence functions of the above mentioned two estimators used in the construction of the procedure, appear in the expressions for the asymptotic coverage probability and the asymptotic distribution of the stopping variable respectively. This shows how the sequential procedure inherits the robustness properties of the estimators concerned and how this is quantified. The general theorem is specialized to two procedures for the estimation of the mean of a symmetric distribution. Results of Monte Carlo studies indicate agreement between the asymptotic theory and the actual behavior of the procedures.

ISSN:0747-4946    

DOI:10.1080/07474949608836361

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

In the theory of asymptotically risk-efficient sequential estimation, one encounters uniform integrability of both positive and negative powers of stopping rules and moment convergence of randomly stopped statistics. We describe a simple approach to obtain these uniform integrability and moment convergence results, not only in the classical setting of i.i.d. observations but also for much more general stochastic sequences. We also use this approach to establish asymptotic risk efficiency of sequential estimators of means of stochastic sequences and to derive asymptotic approximations for the mean squared errors of ratio estimators.

ISSN:0747-4946    

DOI:10.1080/07474949608836362

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

A new type of accelerated sequential procedure is developed and its associated second-order characteristics are investigated. In the case of a few known sequential estimation problems, it is shown that the new methodology (i) is flexible in terms of what one plugs in as the estimator of the nuisance parameter in the boundary condition, and (ii) can economize at the same time on the starting sample size condition to provide second-order properties similar to those already available for the existing methodologies. The power and novelty of the newly constructed sampling techniques are also substantiated by the simplicity of derivation of the second-order expansions for the regret function associated with the estimator of the scale parameter of an exponential distribution, as well as in the context of one-sample and two-sample problems for estimating means when the distributions are unspecified.

ISSN:0747-4946    

DOI:10.1080/07474949608836363

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

In this paper, we consider one-truncation parameter family of distribution of the form f(x;θ)=q(θ)h(x),c<x<θ) We look at the theoretical properties of the stopping rule and the sequential estimation of q(θ) of this family under the assumptions that the sample is type II censored so that one observes only X1:n,X2:n,…Xr:n,1<r<n.

ISSN:0747-4946    

DOI:10.1080/07474949608836364

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

The Wolfowitz lower bound is extended to the multiparameter case. Efficient or admissible sequential estimation procedures based on the sequence of multinomial trials for a parametric function are obtained. It is also shown that the results become a natural extension of DeGroot (1959) and Wasan (1964) for the binomial case and Bhat and Kulkarni (1966) for the multinomial case.

ISSN:0747-4946    

DOI:10.1080/07474949608836365

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

The relationships between some standard multidimensional test statistics and their corresponding one-dimensional versions in a sequential setup are investigated. One conclusion is that sequential log-likelihood ratio tests are in general not very suitable;in a typical case no one-dimensional (marginal) null hypothesis can be rejected even though the multidimensional null hypothesis is. An alternative method based on the maximum modulus test is proposed. Furthermore, sequential log-likelihood ratio tests are compared to sequential tests based on ad-hoc statistics. We focus on the normal case, although most results are valid in more general setups.

ISSN:0747-4946    

DOI:10.1080/07474949608836366

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

A generalized CUSUM procedure is constructed for sequential detection of a specified amount of change within a multi-parameter family of distributions when the initial value of the parameter is unknown. The stopping time of the procedure is defined on a doubly-indexed stochastic process whose asymptotics are studied in terms of its weak convergence properties when there is no change and when there is a contiguous change. Analogous results are also obtained for the Page-CUSUM procedure with known initial parameter. To account for misspecification of models, the results are derived for the case when the procedures are based on a form of distribution which is different from the true one. It is seen how the drift term which sets in after a change occurs, and drives the underlying stochastic process towards the decision boundary, slows down under model misspecification for both the Page-CUSUM and the generalized CUSUM procedures.

ISSN:0747-4946    

DOI:10.1080/07474949608836367

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949608836368

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0747-4946    

DOI:10.1080/07474949608836360

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor