Unbiased Estimators and their Applications, V.G. Voinov; M.S. Nikulin

Автор: Saleh
Название: Theory of Ridge Regression Estimators with Applica tions
ISBN: 1118644611 ISBN-13(EAN): 9781118644614
Издательство: Wiley
Рейтинг:
Цена: 16466.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание:

This book discusses current methods of estimation in linearmodels. In particular, the authors address the methodology oflinear multiple regression models that plays an important role inalmost every scientific investigations in various fields, including economics, engineering, and biostatistics. Thestandard estimation method for regression parameters is theordinary least square (OLS) principal where residual squared errorsare minimized. Applied statisticians are often not satisfied withOLS estimators when the design matrix is ill-conditioned, leadingto a multicollinearity problem and large variances that make the"prediction" inaccurate. This book details theridge regression estimator, which was developed to combat themulticollinearity problem. Another estimator, called theLiu-estimator due to Liu Kejian, is also addressed since itprovides a competing resolution to the multicollinearityproblem. The ridge regression estimators are complicatednon-linear functions of the ridge parameter, whereas, theLiu estimators are a linear function of the shrinkage parameter.With a focus on the ridge regression and LIU estimators, this bookprovides expanded coverage beyond the usual preliminary test andStein type estimator. In this case, we propose a class of compositeestimators that are obtained by multiplying the OLS, restrictedOLS, preliminary test OLS, and Stein-type OLS by the "ridgefactor" and "Liu-factor." This research is asignificant step towards the study of dominance properties as wellas the comparison of the extent of LASSO properties. In addition, research materials involving shrinkage and model selection forlinear regression models are provided. Topical coverageincludes: preliminaries; linear regression models; multipleregression models; measurement error models; generalized linearmodels; and autoregressive Gaussian processes.

Автор: James D. Malley
Название: Optimal Unbiased Estimation of Variance Components
ISBN: 0387964495 ISBN-13(EAN): 9780387964492
Издательство: Springer
Рейтинг:
Цена: 14673.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: The clearest way into the Universe is through a forest wilderness. John MuIr As recently as 1970 the problem of obtaining optimal estimates for variance components in a mixed linear model with unbalanced data was considered a miasma of competing, generally weakly motivated estimators, with few firm gUidelines and many simple, compelling but Unanswered questions. Then in 1971 two significant beachheads were secured: the results of Rao 1971a, 1971b] and his MINQUE estimators, and related to these but not originally derived from them, the results of Seely 1971] obtained as part of his introduction of the no ion of quad- ratic subspace into the literature of variance component estimation. These two approaches were ultimately shown to be intimately related by Pukelsheim 1976], who used a linear model for the com- ponents given by Mitra 1970], and in so doing, provided a mathemati- cal framework for estimation which permitted the immediate applica- tion of many of the familiar Gauss-Markov results, methods which had earlier been so successful in the estimation of the parameters in a linear model with only fixed effects. Moreover, this usually enor- mous linear model for the components can be displayed as the starting point for many of the popular variance component estimation tech- niques, thereby unifying the subject in addition to generating answers.