scholarly journals Transformations for an Exact Goodness-of-Fit Test of Structural Change in the Linear Regression Model

1989 ◽  
pp. 49-57
Author(s):  
Maxwell L. King ◽  
Phillip M. Edwards
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Goodness Of Fit ◽  
Goodness Of Fit Test

scholarly journals Significant non-linearity in nitrous oxide chamber data and its effect on calculated annual emissions

2009 ◽  
Vol 6 (1) ◽  
pp. 115-141 ◽  
Author(s):  
P. C. Stolk ◽  
C. M. J. Jacobs ◽  
E. J. Moors ◽  
A. Hensen ◽  
G. L. Velthof ◽  
...  
Keyword(s):  
Nitrous Oxide ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Surface Fluxes ◽  
Linear Regression Models ◽  
Open Questions ◽  
Non Linear

Abstract. Chambers are widely used to measure surface fluxes of nitrous oxide (N2O). Usually linear regression is used to calculate the fluxes from the chamber data. Non-linearity in the chamber data can result in an underestimation of the flux. Non-linear regression models are available for these data, but are not commonly used. In this study we compared the fit of linear and non-linear regression models to determine significant non-linearity in the chamber data. We assessed the influence of this significant non-linearity on the annual fluxes. For a two year dataset from an automatic chamber we calculated the fluxes with linear and non-linear regression methods. Based on the fit of the methods 32% of the data was defined significant non-linear. Significant non-linearity was not recognized by the goodness of fit of the linear regression alone. Using non-linear regression for these data and linear regression for the rest, increases the annual flux with 21% to 53% compared to the flux determined from linear regression alone. We suggest that differences this large are due to leakage through the soil. Macropores or a coarse textured soil can add to fast leakage from the chamber. Yet, also for chambers without leakage non-linearity in the chamber data is unavoidable, due to feedback from the increasing concentration in the chamber. To prevent a possibly small, but systematic underestimation of the flux, we recommend comparing the fit of a linear regression model with a non-linear regression model. The non-linear regression model should be used if the fit is significantly better. Open questions are how macropores affect chamber measurements and how optimization of chamber design can prevent this.

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.

The Local Power of the CUSUM and CUSUM of Squares Tests

1990 ◽  
Vol 6 (3) ◽  
pp. 335-347 ◽  
Author(s):  
Werner Ploberger ◽  
Walter Krämer;
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Regression Model ◽  
Wide Class ◽  
Linear Regression Model ◽  
Structural Changes ◽  
Local Power ◽  
Cusum Test

We consider the local power of the cusum and cusum of squares tests for structural change in the linear regression model. We show that the local power of the cusum of squares test equals its size for a wide class of structural changes, as compared to a nontrivial local power for the cusum test. The conventional ranking of these procedures is thus reversed.

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