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This article focuses on the estimation of the cross-product ratio ρ = p 1 (1 − p 2) p 2 (1 − p 1) under so-called special case of the direct-inverse sampling scheme, where the number of successes in the direct sampling scheme is used in the second sampling scheme of the inverse binomial scheme. Asymptotic confidence intervals are constructed. Our goal is to investigate the cases when the normal approximations for estimators of the cross-product ratio are reliable for the construction of confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals. We present estimations of the coverage probability and interval width in tables. In the last section, Cytochrome Psychotropic Genotyping Under Investigation for Decision Support case study is discussed where the standard and genetically guided therapy is compared and estimates for the cross-product ratio are presented and interpreted when the participants are enrolled according to the special case of the direct-inverse sampling scheme. [ABSTRACT FROM AUTHOR]

In this article, we have developed asymptotic theory for the simultaneous estimation of thekmeans of arbitrary populations under the common mean hypothesis and further assuming that corresponding population variances are unknown and unequal. The unrestricted estimator, the Graybill-Deal-type restricted estimator, the preliminary test, and the Stein-type shrinkage estimators are suggested. A large sample test statistic is also proposed as a pretest for testing the common mean hypothesis. Under the sequence of local alternatives and squared error loss, we have compared the asymptotic properties of the estimators by means of asymptotic distributional quadratic bias and risk. Comprehensive Monte-Carlo simulation experiments were conducted to study the relative risk performance of the estimators with reference to the unrestricted estimator in finite samples. Two real-data examples are also furnished to illustrate the application of the suggested estimation strategies. [ABSTRACT FROM AUTHOR]

In this paper, we consider estimation techniques based on ridge regression when the matrixappears to be ill-conditioned in the partially linear model using kernel smoothing. Furthermore, we consider that the coefficientscan be partitioned aswhereis the coefficient vector for main effects, andis the vector for ‘nuisance’ effects. We are essentially interested in the estimation ofwhen it is reasonable to suspect thatis close to zero. We suggest ridge pretest, ridge shrinkage and ridge positive shrinkage estimators for the above semi-parametric model, and compare its performance with some penalty estimators. In particular, suitability of estimating the nonparametric component based on the kernel smoothing basis function is also explored. Monte Carlo simulation study is used to compare the relative efficiency of proposed estimators, and a real data example is presented to illustrate the usefulness of the suggested methods. Moreover, the asymptotic properties of the proposed estimators are obtained. [ABSTRACT FROM AUTHOR]

This article addresses the problem of parameter estimation of the logistic regression model under subspace information via linear shrinkage, pretest, and shrinkage pretest estimators along with the traditional unrestricted maximum likelihood estimator and restricted estimator. We developed an asymptotic theory for the linear shrinkage and pretest estimators and compared their relative performance using the notion of asymptotic distributional bias and asymptotic quadratic risk. The analytical results demonstrated that the proposed estimation strategies outperformed the classical estimation strategies in a meaningful parameter space. Detailed Monte-Carlo simulation studies were conducted for different combinations and the performance of each estimation method was evaluated in terms of simulated relative efficiency. The results of the simulation study were in strong agreement with the asymptotic analytical findings. Two real-data examples are also given to appraise the performance of the estimators. [ABSTRACT FROM AUTHOR]