Stochastic Restricted Biased Estimators in misspecified regression model with incomplete prior information

In this article, the analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCR), Stochastic Restricted r-k class estimator (SRrk) and Stochastic Restricted r-d class estimator (SRrd) were examined in the misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings.Comment: 35 Pages, 6 Figure

MODELING ADVERTISING CARRYOVER IN FLUID MILK: COMPARISON OF ALTERNATIVE LAG SPECIFICATIONS

The performance of restricted estimators such as Almon and Shiller in modeling advertising carryover is tested and compared to the unrestricted OLS estimator, using 1971-1988 monthly New York City fluid milk market data. Results indicate that in the absence of autocorrelation and multicollinearity among the lagged advertising variables, the unrestricted OLS estimator is still the preferred estimator, based on Mean Square Error and Root Mean Square Percent Error criteria. In this case, the Almon and Shiller estimators perform equally well, although next only to the OLS estimator. In the presence of autocorrelation or multicollinearity however, the restricted estimators may outperform the OLS estimator, in a MSE sense, with the flexible Shiller estimator (which subsumes the Almon) being more desirable.Marketing,

Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

New Versions of Liu-type Estimator in Weighted and non-weighted Mixed Regression Model

            هذا البحث يصف ويقترح مقدرين جديدين بالاعتماد على معلومات العينة وكذلك المعلومات الاولية في حالة كانت هذه المعلومات متساوية من ناحية الاهمية في بناء النموذج ام غير متساوية. لقد كانت المعلومات الاولية موصوفة كقيود تصادفية خطية.  سنقوم بدراسة خواص واداء هذه المقدرات المقترحة مقارنة مع مقدرات اخرى معروفة وذلك من خلال استخدام متوسط مربعات الخطأ كمعيار لجودة التقدير. مثال عددي وكذلك دراسة محاكاة تم اقتراحهما لتوضيح سلوك واداء المقدرات المقترحة في هذا البحث.This paper considers and proposes new estimators that depend on the sample and on prior information in the case that they either are equally or are not equally important in the model. The prior information is described as linear stochastic restrictions. We study the properties and the performances of these estimators compared to other common estimators using the mean squared error as a criterion for the goodness of fit. A numerical example and a simulation study are proposed to explain the performance of the estimators

Difference based Ridge and Liu type Estimators in Semiparametric Regression Models

We consider a difference based ridge regression estimator and a Liu type estimator of the regression parameters in the partial linear semiparametric regression model, y = Xβ + f + ε. Both estimators are analysed and compared in the sense of mean-squared error. We consider the case of independent errors with equal variance and give conditions under which the proposed estimators are superior to the unbiased difference based estimation technique. We extend the results to account for heteroscedasticity and autocovariance in the error terms. Finally, we illustrate the performance of these estimators with an application to the determinants of electricity consumption in Germany.Difference based estimator; Differencing estimator, Differencing matrix, Liu estimator, Liu type estimator, Multicollinearity, Ridge regression estimator, Semiparametric model