A NOTE ON LEAST ABSOLUTE DEVIATION ESTIMATION OF A THRESHOLD MODEL

2002 ◽  
Vol 18 (3) ◽  
pp. 800-814 ◽  
Author(s):  
Mehmet Caner
Keyword(s):  
Least Squares ◽  
Threshold Model ◽  
Ratio Test ◽  
Threshold Models ◽  
Least Absolute Deviation ◽  
Threshold Parameter ◽  
Absolute Deviation ◽  
Least Absolute Deviation Estimation ◽  
Heavy Tailed ◽  
First Time

This paper develops the limit law for the least absolute deviation estimator of the threshold parameter in linear regression. In this respect, we extend the literature of threshold models. The existing literature considers only the least squares estimation of the threshold parameter (see Chan, 1993, Annals of Statistics 21, 520–533; Hansen, 2000, Econometrica 68, 575–605). This result is useful because in the case of heavy-tailed errors there is an efficiency loss resulting from the use of least squares. Also, for the first time in the literature, we derive the limit law for the likelihood ratio test for the threshold parameter using the least absolute deviation technique.

scholarly journals LEAST ABSOLUTE DEVIATION ESTIMATION FOR UNIT ROOT PROCESSES WITH GARCH ERRORS

2009 ◽  
Vol 25 (5) ◽  
pp. 1208-1227 ◽  
Author(s):  
Guodong Li ◽  
Wai Keung Li
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Maximum Likelihood Estimators ◽  
Unit Root Tests ◽  
Order Moment ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Least Absolute Deviation Estimation ◽  
Heavy Tailed ◽  
Quasi Maximum Likelihood

This paper considers a local least absolute deviation estimation for unit root processes with generalized autoregressive conditional heteroskedastic (GARCH) errors and derives its asymptotic properties under only finite second-order moment for both errors and innovations. When the innovations are symmetrically distributed, the asymptotic distribution of the estimated unit root is shown to be a functional of a bivariate Brownian motion, and then two unit root tests are derived. The simulation results demonstrate that the tests outperform those based on the Gaussian quasi maximum likelihood estimators with heavy-tailed innovations and those based on the simple least absolute deviation estimators.

scholarly journals Statistical Inference for Least Absolute Deviation Regression with Autocorrelated Errors

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Gorgees Shaheed Mohammad
Keyword(s):  
Least Squares ◽  
Serial Correlation ◽  
Significance Test ◽  
Least Absolute Deviation ◽  
Test Procedures ◽  
Absolute Deviation ◽  
Least Absolute Deviation Estimation ◽  
Significance Levels ◽  
Least Absolute Deviation Regression ◽  
Autocorrelated Errors

The method of least absolute deviation provides a robust alternative to least squares, particularly when the data follow distributions that are non-normal and subject to outliers. While inference in least squares estimation is well understood, inferential procedures in the situation of least absolute deviation estimation have not been studied as extensively, particularly in the presence of autocorrelation. In this search, we study two alternative significance test procedures in least absolute deviation regression, along with two approaches used to correct for serial correlation. The study is based on a Monte Carlo simulation, and comparisons are made based on observed significance levels.

Least absolute deviation estimates in autoregression with infinite variance

1979 ◽  
Vol 16 (1) ◽  
pp. 104-116 ◽  
Author(s):  
S. Gross ◽  
W. L. Steiger
Keyword(s):  
Monte Carlo ◽  
Convergence Rate ◽  
Least Squares ◽  
Finite Order ◽  
Monte Carlo Study ◽  
Least Squares Estimator ◽  
Infinite Variance ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Strongly Consistent

We consider an L1 analogue of the least squares estimator for the parameters of stationary, finite-order autoregressions. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. The striking feature is that the conditions are so mild as to include processes with infinite variance, notably the stationary, finite autoregressions driven by stable increments in Lα, α > 1. Finally, sampling properties of LAD are compared to those of least squares. Together with a known convergence rate result for least squares, the Monte Carlo study provides evidence for a conjecture on the convergence rate of LAD.

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