Practical Small Sample Inference for Single Lag Subset Autoregressive Models
Editor(s)
DasGupta, A. and Dette, H. and Loh, W. -L.
Abstract
We propose a method for saddlepoint approximating the distribution of estimators in single lag subset autoregressive models of order one. By viewing the estimator as the root of an appropriate estimating equation, the approach circumvents the difficulty inherent in more standard methods that require an explicit expression for the estimator to be available. Plots of the densities reveal that the distributions of the Burg and maximum likelihood estimators are nearly identical. We show that one possible reason for this is the fact that Burg enjoys the property of estimation equation optimality among a class of estimators expressible as a ratio of quadratic forms in normal random variables, which includes Yule-Walker and least squares. By inverting a two-sided hypothesis test, we show how small sample confidence intervals for the parameters can be constructed from the saddlepoint approximations. Simulation studies reveal that the resulting intervals generally outperform traditional ones based on asymptotics and have good robustness properties with respect to heavy-tailed and skewed innovations. The applicability of the models is illustrated by analyzing a longitudinal data set in a novel manner.
Recommended Citation
R. Paige and A. A. Trindade, "Practical Small Sample Inference for Single Lag Subset Autoregressive Models," Journal of Statistical Planning and Inference, Elsevier, Jan 2008.
The definitive version is available at https://doi.org/10.1016/j.jspi.2007.07.006
Department(s)
Mathematics and Statistics
Keywords and Phrases
Yule-Walker; Burg; maximum likelihood; estimating equation; saddlepoint approximation; confidence interval; longitudinal data
International Standard Serial Number (ISSN)
0378-3758
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2008 Elsevier, All rights reserved.
Publication Date
01 Jan 2008
