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A new stochastic restricted biased estimator under heteroscedastic or correlated error

Mustafa Ismaeel Alheety (2011)

ESAIM: Probability and Statistics

In this paper, under the linear regression model with heteroscedastic and/or correlated errors when the stochastic linear restrictions on the parameter vector are assumed to be held, a generalization of the ordinary mixed estimator (GOME), ordinary ridge regression estimator (GORR) and Generalized least squares estimator (GLSE) is proposed. The performance of this new estimator against GOME, GORR, GLS and the stochastic restricted Liu estimator (SRLE) [Yang and Xu, Statist. Papers 50 (2007) 639–647]...

A new stochastic restricted biased estimator under heteroscedastic or correlated error

Mustafa Ismaeel Alheety (2011)

ESAIM: Probability and Statistics

In this paper, under the linear regression model with heteroscedastic and/or correlated errors when the stochastic linear restrictions on the parameter vector are assumed to be held, a generalization of the ordinary mixed estimator (GOME), ordinary ridge regression estimator (GORR) and Generalized least squares estimator (GLSE) is proposed. The performance of this new estimator against GOME, GORR, GLS and the stochastic restricted Liu estimator (SRLE) [Yang and Xu, Statist. Papers50 (2007) 639–647]...

A review of the results on the Stein approach for estimators improvement.

Vassiliy G. Voinov, Mikhail S. Nikulin (1995)

Qüestiió

Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.

An alternative analysis of variance.

Nicholas T. Longford (2008)

SORT

The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.

Estimator selection in the gaussian setting

Yannick Baraud, Christophe Giraud, Sylvie Huet (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider the problem of estimating the mean f of a Gaussian vector Y with independent components of common unknown variance σ 2 . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection 𝔽 of estimators of f based on Y and, with the same data Y , aim at selecting an estimator among 𝔽 with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to Y may be unknown. We establish...

Improving both domain and total area estimation by composition.

Alex Costa, Albert Satorra, Eva Ventura (2004)

SORT

In this article we propose small area estimators for both the small and large area parameters. When the objective is to estimate parameters at both levels, optimality is achieved by a sample design that combines fixed and proportional allocation. In such a design, one fraction of the sample is distributed proportionally among the small areas and the rest is evenly distributed. Simulation is used to assess the performance of the direct estimator and two composite small area estimators, for a range...

Improving small area estimation by combining surveys: new perspectives in regional statistics.

Alex Costa, Albert Satorra, Eva Ventura (2006)

SORT

A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey...

L 1 -penalization in functional linear regression with subgaussian design

Vladimir Koltchinskii, Stanislav Minsker (2014)

Journal de l’École polytechnique — Mathématiques

We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being “sparse” in the sense that it can be represented as a sum of a small number of well separated “spikes”. This can be viewed as an extension of now classical sparse estimation problems to the case of infinite dictionaries. We study an estimator of the regression function...

L 2 -type contraction for systems of conservation laws

Denis Serre, Alexis F. Vasseur (2014)

Journal de l’École polytechnique — Mathématiques

The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in L 1 . However it is not a contraction in L p for any p > 1 . Leger showed in [20] that for a convex flux, it is however a contraction in L 2 up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

A. K. Md. Ehsanes Saleh, Radim Navrátil (2018)

Kybernetika

In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary test and Stein-type...

Ridge estimation of covariance matrix from data in two classes

Yi Zhou, Bin Zhang (2024)

Applications of Mathematics

This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether...

Ridge Estimator Revisited

Lubomír Kubáček (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Bad conditioned matrix of normal equations in connection with small values of model parameters is a source of problems in parameter estimation. One solution gives the ridge estimator. Some modification of it is the aim of the paper. The behaviour of it in models with constraints is investigated as well.

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