Search

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]

Summary: In nonlinear growth models, we considered the parameter estimation under subspace information for low‐dimensional and high‐dimensional data. We proposed novel estimators based on pretest and shrinkage strategies to improve the estimation efficiency and to establish asymptotic properties. We used simulation studies and a real data example to confirm the theoretical results. We also applied two well‐known penalised methods—least absolute shrinkage and selection operator (LASSO) and adaptive LASSO (aLASSO)—for the dimensional reduction of the predictor variables. The results demonstrated that the pretest and shrinkage estimation strategies performed well in parameter estimations when the subspace information was incorrect for both low‐ and high‐dimensional regimes. [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]

We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators. We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes. [ABSTRACT FROM AUTHOR]

This study aims to introduce four modified linear estimators for the right-censored high-dimensional data. Obviously, data of interest involves two important problems to be solved that are censorship and high dimensionality. This paper can be distinguished from other studies in the literature with that it achieves to handle these two problems simultaneously. The main contribution of the paper is merging weightedridge method with the imputation techniques to obtain more efficient estimators than its alternatives. To solve the censorship problem, four imputation techniques are considered based on machine learning algorithms kNN, sliding-windows, regression and support vector machines. The high-dimensionality problem is handled by the weighted ridge approach which provides estimator with less risk than its alternatives because it detects the covariates with a weak contribution via the post-selection procedure. To show the empirical performance of the introduced estimators, a simulation study is made and comparative results are presented. Results show that kNN and regression imputation basis WR esitmators show satisfying performances on estimation of the high-dimensional right-censored model. [ABSTRACT FROM AUTHOR]

Summary: In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high‐dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real‐data analysis. We show that the suggested methods can be accounted as good competitors to regularisation techniques, by means of a mean squared error of estimation and prediction error. A thorough comparison of pretest and shrinkage estimators based on the maximum likelihood method to the penalty methods. In this paper, we extend the comparison outlined in his work using the least squares method for the generalised ridge regression. [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]

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]