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Sequential analysis (SA) as a sampling technique has notable advantages like smaller average sample size and reduced value of risk compared to similarly comparable fixed-sample techniques. In this study, we first propose a few models for the estimation of the regression parameters or functions of parameters under the multiple linear regression (MLR) setup using a balanced loss function (BLF). Thereafter, we obtain the expressions of risk functions and optimal fixed sample sizes for the proposed models based on the bounded risk criteria. We establish that no fixed-sample procedures can tackle these estimation problems. Hence, we propose different multistage sampling methodologies, viz. (i) two-stage sampling, (ii) three-stage sampling, (iii) purely sequential sampling, and (iv) batch sequential sampling, and corroborate the same with the detailed simulation and real data analyses. [ABSTRACT FROM AUTHOR]

In this article, we develop a general class of purely sequential procedures and obtain the associated first- and second-order asymptotics for the expected sample size and regret. We establish that many estimation and ranking and selection problems can be handled with the help of the proposed class of sequential procedures. A brief simulation analysis is carried out in support of the accuracy of our proposed sequential methodology and a real data set from environment study is included to demonstrate the practical utility. [ABSTRACT FROM AUTHOR]

For the family of distributions considered by Chaturvedi and Alam, the problems of minimum risk point estimation and bounded risk point estimation of the parameter are handled. Consideration is given to squared-error loss function. The failure of fixed sample size procedure is established. Sequential procedures are proposed to deal with the situation. For both the estimation problems,the uniformly minimum variance unbiased estimator/maximum likelihood estimator and minimum mean square estimator are utilized to develop the fixed sample size procedures. Second-order approximations are derived for the sequential procedures and 'improved' estimators are proposed. First-order properties are also discussed. The negative 'regret' [see Starr and Woodroofe] is achieved. [ABSTRACT FROM AUTHOR]

In this article, we have proposed a three-stage procedure for the estimation of the difference of the means of two multivariate normal populations having unknown and unequal variances. Point as well as confidence region estimation is done for the same. Here, we have used the concept of classical Behrens-Fisher problem. Second-order approximations are obtained in both the cases, i.e., point estimation and confidence region estimation. [ABSTRACT FROM AUTHOR]

In this article, we have estimated the mean vector of a multivariate normal population by using a k-stage sequential estimation procedure. Point estimation as well as confidence region estimation is done. Second-order approximations are obtained in both the cases. In case of minimum risk point estimation of , negative regret is achieved. [ABSTRACT FROM AUTHOR]

In this paper, we develop purely sequential, two-stage, three-stage, and "accelerated" sequential procedures for the point estimation of the location of negative exponential distribution having an unknown scale parameter. We do minimum risk point estimation by using all four sequential procedures mentioned above. In addition, we do bounded risk point estimation by using three-stage and "accelerated" sequential procedures. Consideration is given to a modified LINEX loss function. We aim at controlling the associated risk functions for all the procedures. Second-order approximations are obtained for the proposed procedures. We also discuss first-order properties for purely sequential procedure. [ABSTRACT FROM AUTHOR]