scholarly journals A Note on the Performance of Biased Estimators with Autocorrelated Errors

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Gargi Tyagi ◽  
Shalini Chandra
Keyword(s):  
Regression Analysis ◽  
Relative Efficiency ◽  
Mean Squared Error ◽  
Numerical Examples ◽  
Squared Error ◽  
Special Cases ◽  
Established Fact ◽  
Biased Estimators ◽  
Autocorrelated Errors ◽  
Percentage Relative Efficiency

It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the r-(k,d) class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the r-(k,d) class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators.

scholarly journals Adapted Factor-Type Imputation Strategies

2016 ◽  
Vol 8 (3) ◽  
pp. 321-339
Author(s):  
R. Pandey ◽  
K. Yadav ◽  
N. S. Thakur
Keyword(s):  
Relative Efficiency ◽  
Mean Squared Error ◽  
Data Sets ◽  
Optimum Conditions ◽  
Population Mean ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
The Mean ◽  
Factor Type ◽  
Percentage Relative Efficiency

The present paper provides alternative improved Factor-Type (F-T) estimators of population mean in presence of item non-response for the practitioners. The proposed estimators have been shown to be more efficient than the four existing estimators which are more efficient than the usual ratio and the mean estimators. Optimum conditions for minimum mean squared error are obtained for the new estimators. Empirical comparisons based on three different data sets establish that the proposed estimators record least mean squared error and hence a substantial gain in Percentage Relative Efficiency (P.R.E.), over these five contemporary estimators.

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.

scholarly journals A new modified ridge-type estimator for the beta regression model: simulation and application

2021 ◽  
Vol 7 (1) ◽  
pp. 1035-1057
Author(s):  
Muhammad Nauman Akram ◽  
◽  
Muhammad Amin ◽  
Ahmed Elhassanein ◽  
Muhammad Aman Ullah ◽  
...  
Keyword(s):  
Regression Model ◽  
Mean Squared Error ◽  
Model Simulation ◽  
Beta Regression ◽  
Explanatory Variables ◽  
Squared Error ◽  
The Matrix ◽  
Biased Estimators ◽  
Highly Correlated ◽  
Beta Regression Model

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

scholarly journals Pre-Test Single and Double Stage Shrunken Estimators for the Mean of Normal Distribution with Known Variance

2010 ◽  
Vol 7 (4) ◽  
pp. 1432-1441
Author(s):  
Baghdad Science Journal
Keyword(s):  
Sample Size ◽  
Normal Distribution ◽  
Relative Efficiency ◽  
Mean Squared Error ◽  
Numerical Results ◽  
Squared Error ◽  
Expected Sample Size ◽  
Test Region ◽  
Prior Estimate ◽  
The Mean

This paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.

Minimax Shrunken Technique for Estimate Burr X Distribution Shape Parameter

2018 ◽  
pp. 484
Author(s):  
Abbas Najim Salman ◽  
Maymona M. Ameen ◽  
A. E. Abdul-Nabi
Keyword(s):  
Relative Efficiency ◽  
Prior Information ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
The Real ◽  
Squared Error ◽  
Distribution Shape ◽  
Original Estimate ◽  
Bias Ratio

      The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.  Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.  Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.  

An Improved Estimation of Parameter of Morgenstern-Type Bivariate Exponential Distribution Using Ranked Set Sampling

2022 ◽  
pp. 1-25
Author(s):  
Vishal Mehta
Keyword(s):  
Exponential Distribution ◽  
Mean Squared Error ◽  
Ranked Set Sampling ◽  
Error Estimator ◽  
Bivariate Exponential Distribution ◽  
Ranked Set Sample ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Bivariate Exponential ◽  
Special Cases

In this chapter, the authors suggest some improved versions of estimators of Morgenstern type bivariate exponential distribution (MTBED) based on the observations made on the units of ranked set sampling (RSS) regarding the study variable Y, which is correlated with the auxiliary variable X, where (X,Y) follows a MTBED. In this chapter, they firstly suggested minimum mean squared error estimator for estimation of 𝜃2 based on censored ranked set sample and their special case; further, they have suggested minimum mean squared error estimator for best linear unbiased estimator of 𝜃2 based on censored ranked set sample and their special cases; they also suggested minimum mean squared error estimator for estimation of 𝜃2 based on unbalanced multistage ranked set sampling and their special cases. Efficiency comparisons are also made in this work.

scholarly journals PMSE PERFORMANCE OF THE BIASED ESTIMATORS IN A LINEAR REGRESSION MODEL WHEN RELEVANT REGRESSORS ARE OMITTED

2002 ◽  
Vol 18 (5) ◽  
pp. 1086-1098 ◽  
Author(s):  
Akio Namba
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Positive Part ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Explicit Formulae ◽  
Biased Estimators

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.

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