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Statistical Learning from a Regression Perspective

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article

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Least squares estimators in measurement error models under the balanced loss function

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Balanced loss function, direct and reverse regression, ineasurement errors, ultrastructural model, 62J05

Balanced loss function, direct and reverse regression, ineasurement errors, ultrastructural model, 62J05 Minimize

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Prediction of values of variables in linear measurement error model

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This article presents the framework of a linear measurement error model for analysing the data in environmental studies where observations on variables are subjected to measurement errors. The problem of predicting the average and actual values of such variables separately as well as simultaneously are discussed. The methods of ordinary least sq...

This article presents the framework of a linear measurement error model for analysing the data in environmental studies where observations on variables are subjected to measurement errors. The problem of predicting the average and actual values of such variables separately as well as simultaneously are discussed. The methods of ordinary least squares, joint least squares and generalized least squares are employed to construct the predictors. Efficiency properties of these predictors are derived and their comparative study is made. These predictors are exposed to a data set and their performance properties are analysed. Minimize

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Consistent estimation of coefficients in measurement error models with replicated observations

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For the estimation of coefficients in a measurement error model, the least squares method utilizing original observations and averaged observations over replications provides inconsistent estimators. Based on these, consistent estimators are formulated and asymptotic properties are analyzed. ; Ultrastructural model Measurement errors Replicated ...

For the estimation of coefficients in a measurement error model, the least squares method utilizing original observations and averaged observations over replications provides inconsistent estimators. Based on these, consistent estimators are formulated and asymptotic properties are analyzed. ; Ultrastructural model Measurement errors Replicated observations Minimize

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Improved Estimation in Measurement Error Models Through Stein Rule Procedure

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This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression c...

This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression coefficients. A further application may improve the efficiency properties of the estimators of regression coefficients. It is observed that the proposed family of estimators under some constraint on the characterizing scalar dominates the conventional consistent estimator with respect to the criterion of asymptotic risk under a specific quadratic loss function. Then the problem of prediction of the values of the study variable within the sample is considered, and it is found that the predictors based on the proposed family of estimators are always more efficient than the predictors based on the conventional estimator according to asymptotic predictive mean squared error criterion, although both are biased. ; Measurement errors ultrastructural model Stein rule estimators predictions mean squared error matrix criterion Minimize

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Meta-analysis of Binary Data using Profile Likelihood

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Simultaneous Prediction of Actual and Average Values of Study Variable Using Stein-rule Estimators

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The simultaneous prediction of average and actual values of study variable in a linear regression model is considered in this paper. Generally, either of the ordinary least squares estimator or Stein-rule estimators are employed for the construction of predictors for the simultaneous prediction. A linear combination of ordinary least squares and...

The simultaneous prediction of average and actual values of study variable in a linear regression model is considered in this paper. Generally, either of the ordinary least squares estimator or Stein-rule estimators are employed for the construction of predictors for the simultaneous prediction. A linear combination of ordinary least squares and Stein-rule predictors are utilized in this paper to construct an improved predictors. Their efficiency properties are derived using the small disturbance asymptotic theory and dominance conditions for the superiority of predictors over each other are analyzed. Minimize

Year of Publication:

2011-02-11

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Language:

eng

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Technische Reports ; ddc:310

Technische Reports ; ddc:310 Minimize

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http://epub.ub.uni-muenchen.de/12184/1/tr104.pdf ; Shalabh, Shalabh und Heumann, Christian (2011): Simultaneous Prediction of Actual and Average Values of Study Variable Using Stein-rule Estimators. Department of Statistics: Technical Reports, Nr. 104

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