OPTIMAL SIMILAR TESTS FOR STRUCTURAL CHANGE FOR THE LINEAR REGRESSION MODEL

2002 ◽  
Vol 18 (4) ◽  
pp. 853-867 ◽  
Author(s):  
G. Forchini
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
American Mathematical Society ◽  
Error Variance ◽  
Optimal Test ◽  
Finite Samples ◽  
Power Comparisons

This paper analyzes similar tests for structural change for the normal linear regression model in finite samples. Using the approach of Wald (1943, American Mathematical Society Transactions 54, 426–482), Hillier (1987, Econometric Theory 3, 1–44), Andrews and Ploberger (1994, Econometrica 62, 1382–1414), and Andrews, Lee, and Ploberger (1996, Journal of Econometrics 70, 9–36), we characterize a class of optimal similar tests for the existence of (possibly multiple) changepoints at unknown times. We extend the analysis of Andrews et al. (1996) by deriving weighted optimal similar tests for the case where the error variance is not known. We also show that when the sample size is large, the tests of Andrews et al. constructed by replacing the error variance with an estimate are equivalent to the optimal test derived in this paper. Power comparisons are provided by a small simulation study.

scholarly journals WEIGHTED AVERAGE POWER SIMILAR TESTS FOR STRUCTURAL CHANGE IN THE GAUSSIAN LINEAR REGRESSION MODEL

2008 ◽  
Vol 24 (5) ◽  
pp. 1277-1290
Author(s):  
Giovanni Forchini
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Quadratic Forms ◽  
Average Power ◽  
Numerical Algorithms ◽  
Weighted Average ◽  
Test Statistics ◽  
Weighting Functions

Average exponential F tests for structural change in a Gaussian linear regression model and modifications thereof maximize a weighted average power that incorporates specific weighting functions to make the resulting test statistics simple. Generalizations of these tests involve the numerical evaluation of (potentially) complicated integrals. In this paper, we suggest a uniform Laplace approximation to evaluate weighted average power test statistics for which a simple closed form does not exist. We also show that a modification of the avg-F test is optimal under a very large class of weighting functions and can be written as a ratio of quadratic forms so that both its p-values and critical values are easy to calculate using numerical algorithms.

scholarly journals POWER AND SIZE OF NORMAL DISTRIBUTION AND ITS APPLICATIONS

2017 ◽  
Vol 9 (2) ◽  
pp. 111
Author(s):  
Budi Pratikno ◽  
Jajang Jajang ◽  
Setianingsih Setianingsih ◽  
Raden Sudarwo
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Regression Model ◽  
Normal Distribution ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Graphical Analysis ◽  
Maximum Power ◽  
Minimum Size ◽  
Large Standard Deviation

. The research studied power and size of normal distribution and its applications on linear regression model. The power and size formulas are derived, and the unrestricted test (UT), restrcited test (RT) and pre-test test (PTT) are used. The recommendation of the test is given by choosing maximum power and minimum size, and also graphical analysis. The result showed that the power and size for large standard deviation () tend to be identical and flat. In simulation study, the graphs of the UT, RT, and PTT are still similar to the previous research (Pratikno, 2012), where the PTT  tend to lie between UT and RT.

scholarly journals The Performance of Some Restricted Estimators In Restricted Linear Regression Model

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Bader Aboud ◽  
Mustafa Ismaeel Naif
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Regression Estimator ◽  
Mean Square ◽  
Ridge Regression Estimator ◽  
The Mean ◽  
Biased Estimators ◽  
Better Than

In the linear regression model, the restricted biased estimation as one of important  methods to addressing the high variance and the  multicollinearity problems. In this paper, we make the simulation study of the some restricted biased estimators. The mean square error (MME) criteria are used to make a comparison  among them. According to the simulation study we observe that, the performance of the restricted modified unbiased  ridge regression estimator (RMUR) was proposed by  Bader and Alheety (2020)  is better than  of these estimators. Numerical example have been considered to illustrate the performance of the estimators.

scholarly journals Distributional consistency of the lasso by perturbation bootstrap

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 957-964
Author(s):  
Debraj Das ◽  
S N Lahiri
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Multiple Linear Regression ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Bootstrap Method ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Lasso Estimator

Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the proposed bootstrap method in a moderately large simulation study.

A Point Optimal Test for Moving Average Regression Disturbances

1985 ◽  
Vol 1 (2) ◽  
pp. 211-222 ◽  
Author(s):  
Maxwell L. King
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Sample Size ◽  
Linear Regression Model ◽  
Alternative Hypothesis ◽  
Moving Average ◽  
Test Procedure ◽  
Empirical Comparison ◽  
Optimal Test ◽  
First Order

This paper reconsiders King's [12] locally optimal test procedure for first-order moving average disturbances in the linear regression model. It recommends two tests, one for problems involving positively correlated disturbances and one for negatively correlated disturbances. Both tests are most powerful invariant at a point in the alternative hypothesis parameter space that is determined by a function involving the sample size and the number of regressors. Selected bounds for the tests' significance points are tabulated and an empirical comparison of powers demonstrates the overall superiority of the new test for positively correlated moving average disturbances.

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