Mean squared error matrix comparisons between biased estimators — An overview of recent results

1990 ◽  
Vol 31 (1) ◽  
pp. 165-179 ◽  
Author(s):  
G. Trenkler ◽  
H. Toutenburg
Keyword(s):  
Mean Squared Error ◽  
Error Matrix ◽  
Mean Squared Error Matrix ◽  
Squared Error ◽  
Biased Estimators

scholarly journals Modifying Two-Parameter Ridge Liu Estimator Based on Ridge Estimation

2019 ◽  
pp. 881-890
Author(s):  
Tarek Mahmoud Omara
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Error Matrix ◽  
Liu Estimator ◽  
Mean Squared Error Matrix ◽  
Ridge Estimation ◽  
Squared Error ◽  
The Mean ◽  
Two Parameter

In this paper, we introduce the new biased estimator to deal with the problem of multicollinearity. This estimator is considered a modification of Two-Parameter Ridge-Liu estimator based on ridge estimation. Furthermore, the superiority of the new estimator than Ridge, Liu and Two-Parameter Ridge-Liu estimator were discussed. We used the mean squared error matrix (MSEM) criterion to verify the superiority of the new estimate.  In addition to, we illustrated the performance of the new estimator at several factors through the simulation study.

scholarly journals Stochastic Restricted Liu Type estimator for SUR model

2018 ◽  
pp. 903-911
Author(s):  
Tarek Mahmoud Omara
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Error Matrix ◽  
Mean Squared Error Matrix ◽  
Squared Error ◽  
Restricted Estimator

In this paper, we introduce new Stochastic Restricted Estimator for SUR model, defined by Stochastic  Restricted Liu Type  SUR estimator (SRLTSE) . The propose estimator has deal with multicollinearity in SUR model if there is a degree of uncertainty in the parameters restriction. Moreover, the superiority of (SRLTSE) estimator  was derived with respect to mean squared error matrix (MSEM) criteria. Finally, a simulation study was conducted. This simulation used standard mean squares error  (MSE) criterion to illustrate the advantage between Stochastic  Restricted SUR estimator (SRSE), Stochastic  Restricted Ridge SUR estimator (SRRSE), and Stochastic  Restricted Liu Type  SUR estimator (SRLTSE) at several factors. 

scholarly journals Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Lorcán O. Conlon ◽  
Jun Suzuki ◽  
Ping Koy Lam ◽  
Syed M. Assad
Keyword(s):  
Finite Number ◽  
Mean Squared Error ◽  
Efficient Computation ◽  
Error Matrix ◽  
Mean Squared Error Matrix ◽  
Multiple Parameters ◽  
Squared Error ◽  
The Mean ◽  
Cramer Rao Bound ◽  
Physical Quantities

AbstractFinding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound.

Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable

1993 ◽  
Vol 9 (1) ◽  
pp. 62-80 ◽  
Author(s):  
Jan F. Kiviet ◽  
Garry D.A. Phillips
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Small Sample ◽  
Large Sample ◽  
Squared Error ◽  
Coefficient Vector ◽  
Lagged Dependent Variable ◽  
Biased Estimators ◽  
The One

The small sample bias of the least-squares coefficient estimator is examined in the dynamic multiple linear regression model with normally distributed whitenoise disturbances and an arbitrary number of regressors which are all exogenous except for the one-period lagged-dependent variable. We employ large sample (T → ∞) and small disturbance (σ → 0) asymptotic theory and derive and compare expressions to O(T−1) and to O(σ2), respectively, for the bias in the least-squares coefficient vector. In some simulations and for an empirical example, we examine the mean (squared) error of these expressions and of corrected estimation procedures that yield estimates that are unbiased to O(T−l) and to O(σ2), respectively. The large sample approach proves to be superior, easily applicable, and capable of generating more efficient and less biased estimators.

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