scholarly journals Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 52
Author(s):  
Abdenour Hamdaoui ◽  
Waleed Almutiry ◽  
Mekki Terbeche ◽  
Abdelkader Benkhaled
Keyword(s):  
Asymptotic Behavior ◽  
Performance Evaluation ◽  
Maximum Likelihood ◽  
Parameter Space ◽  
Shrinkage Estimators ◽  
High Dimensions ◽  
Likelihood Estimator ◽  
Positive Part ◽  
Stein Estimator ◽  
Risk Ratios

In this paper, we analyze the risk ratios of several shrinkage estimators using a balanced loss function. The James–Stein estimator is one of a group of shrinkage estimators that has been proposed in the existing literature. For these estimators, sufficient criteria for minimaxity have been established, and the James–Stein estimator’s minimaxity has been derived. We demonstrate that the James–Stein estimator’s minimaxity is still valid even when the parameter space has infinite dimension. It is shown that the positive-part version of the James–Stein estimator is substantially superior to the James–Stein estimator, and we address the asymptotic behavior of their risk ratios to the maximum likelihood estimator (MLE) when the dimensions of the parameter space are infinite. Finally, a simulation study is carried out to verify the performance evaluation of the considered estimators.

scholarly journals On shrinkage estimators improving the James-Stein estimator under balanced loss function

2021 ◽  
pp. 711-727
Author(s):  
Abdenour Hamdaoui ◽  
Mekki Terbeche ◽  
Abdelkader Benkhaled
Keyword(s):  
Maximum Likelihood ◽  
Loss Function ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Balanced Loss Function ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stein Estimator ◽  
Class Of Estimators

In this paper, we are interested in estimating a multivariate normal mean under the balanced loss function using the shrinkage estimators deduced from the Maximum Likelihood Estimator (MLE). First, we consider a class of estimators containing the James-Stein estimator, we then show that any estimator of this class dominates the MLE, consequently it is minimax. Secondly, we deal with shrinkage estimators which are not only minimax but also dominate the James- Stein estimator.

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

OPTIMAL INVARIANT INFERENCE WHEN THE NUMBER OF INSTRUMENTS IS LARGE

2009 ◽  
Vol 25 (3) ◽  
pp. 793-805 ◽  
Author(s):  
Laura Chioda ◽  
Michael Jansson
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Instrumental Variables ◽  
Asymptotic Efficiency ◽  
Rotation Invariance ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Rotation Invariant

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance restriction.

scholarly journals Limits of Risks Ratios of Shrinkage Estimators under the Balanced Loss Function

2021 ◽  
pp. 301-312
Author(s):  
Mekki Terbeche
Keyword(s):  
Maximum Likelihood ◽  
Loss Function ◽  
Sufficient Conditions ◽  
Maximum Likelihood Estimators ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Balanced Loss Function ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stein Estimator

In this paper we study the estimation of a multivariate normal mean under the balanced loss function. We present here a class of shrinkage estimators which generalizes the James-Stein estimator and we are interested to establish the asymptotic behaviour of risks ratios of these estimators to the maximum likelihood estimators (MLE). Thus, in the case where the dimension of the parameter space and the sample size are large, we determine the sufficient conditions for that the estimators cited previously are minimax

scholarly journals ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES

1999 ◽  
Vol 15 (2) ◽  
pp. 184-217 ◽  
Author(s):  
Tjacco van der Meer ◽  
Gyula Pap ◽  
Martien C.A. van Zuijlen
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Limit Distribution ◽  
Continuous Time ◽  
Convergence Result ◽  
Likelihood Estimator ◽  
Characteristic Roots ◽  
Least Squares Estimators ◽  
General Complex ◽  
Complex Valued

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes.

Estimation for diffusion processes under misspecified models

1984 ◽  
Vol 21 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Ian W. McKeague
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Diffusion Processes ◽  
Parametric Model ◽  
Likelihood Estimator ◽  
Ergodic Diffusion Process ◽  
Misspecified Models ◽  
Drift Term ◽  
Noise Function ◽  
Ergodic Diffusion

The asymptotic behavior of the maximum likelihood estimator of a parameter in the drift term of a stationary ergodic diffusion process is studied under conditions in which the true drift function and true noise function do not coincide with those specified by the parametric model.

scholarly journals On shrinkage estimators improving the positive part of James-Stein estimator

2021 ◽  
Vol 54 (1) ◽  
pp. 462-473
Author(s):  
Abdenour Hamdaoui
Keyword(s):  
Loss Function ◽  
Quadratic Loss ◽  
Shrinkage Estimators ◽  
Multivariate Normal ◽  
Positive Part ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stein Estimator ◽  
Class Of Estimators ◽  
The One

Abstract In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein estimator. Then, we treat estimators of polynomial form and prove if we increase the degree of the polynomial we can build a better estimator from the one previously constructed. Furthermore, we discuss the minimaxity property of the considered estimators.

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