The Asymptotic Mean Squared Error of Multistep Prediction from the Regression Model with Autoregressive Errors

1979 ◽  
Vol 74 (365) ◽  
pp. 175-184 ◽  
Author(s):  
Richard T. Baillie
Keyword(s):  
Regression Model ◽  
Mean Squared Error ◽  
Squared Error ◽  
Autoregressive Errors ◽  
Asymptotic Mean Squared Error

scholarly journals Dynamic Regression and Filtered Data Series: A Laplace Approximation to the Effects of Filtering in Small Samples

1996 ◽  
Vol 12 (3) ◽  
pp. 432-457 ◽  
Author(s):  
Eric Ghysels ◽  
Offer Lieberman
Keyword(s):  
Regression Model ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
Small Sample ◽  
Data Series ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Lagged Dependent Variable ◽  
Dynamic Regression Model

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample bias and mean squared error. In general, these results entail a numerical integration of derivatives of the joint moment generating function of two quadratic forms in normal variables. The computation of these integrals is quite involved. However, we take advantage of the Laplace approximations to the bias and mean squared error, which substantially reduce the computational burden, as they yield relatively simple analytic expressions. We obtain analytic formulae for approximating the effect of filtering on the finite sample bias and mean squared error. We evaluate the adequacy of the approximations by comparison with Monte Carlo simulations, using the Census X-11 filter as a specific example

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals A New Ridge-Type Estimator for the Gamma Regression Model

Scientifica ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Adewale F. Lukman ◽  
Issam Dawoud ◽  
B. M. Golam Kibria ◽  
Zakariya Y. Algamal ◽  
Benedicta Aladeitan
Keyword(s):  
Biological Activity ◽  
Regression Model ◽  
Mean Squared Error ◽  
Real Life ◽  
Regression Parameter ◽  
Likelihood Estimator ◽  
Response Variable ◽  
Explanatory Variables ◽  
Squared Error ◽  
The Mean

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered 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 A Novel S-Regression Model on an Auto Price

2018 ◽  
Vol 7 (2.29) ◽  
pp. 912
Author(s):  
Fadzilah Salim ◽  
Nur Azman Abu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Mean Squared Error ◽  
Squared Error ◽  
Curve Model ◽  
Used Car ◽  
Independent Variable ◽  
The Mean ◽  
Used Cars ◽  
The Relationship

A simple linear regression model is useful in a prediction model. A general linear regression beyond a single independent variable is still not popular. A nonlinear regression can be easily produced a better predictive model but it is difficult to construct. The objective of this paper is to propose a technique for predicting the price of used cars in Malaysia using S-shaped curve model. In this paper, the S-shaped Membership Function [SMF] is used as the basis to develop a novel S-Regression model. Comparisons between linear regression, cubic regression and S-Regression have been made on the used car prices. The mean squared error of S-Regression model is found to be closer to cubic regression than the linear regression. S-Regression model is found to be quite suitable to represent the relationship between the price of a used car and the make year of a car. The result demonstrates that the S-Regression model gives better and practical estimate of the price of a used car in Malaysia.  

Rates of Expansions for Functional Estimators

2021 ◽  
Author(s):  
Yulia Kotlyarova ◽  
Marcia M. A. Schafgans ◽  
Victoria Zinde-Walsh
Keyword(s):  
Convergence Rates ◽  
Mean Squared Error ◽  
Model Averaging ◽  
Finite Sample ◽  
Squared Error ◽  
Semiparametric Estimators ◽  
Asymptotic Mean Squared Error ◽  
The Impact ◽  
Nonconvex Model

AbstractIn this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness.

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