Shrinkage Estimation of Linear Regression Models with ARIMA Errors and Applications to Canadian Crime Rates Data
DOI:
https://doi.org/10.6092/issn.1973-2201/19747Keywords:
Linear regression model, ARIMA, Monte Carlo simulation, Shrinkage estimators, Asymptotic biases and risksAbstract
Shrinkage methods for estimating the parameters of a regression model with autoregressive integrated moving average (ARIMA) errors are presented when some of the regression parameters are restricted to a subspace. The estimates are defined by the maximization of the likelihood function with and without restriction which makes the unrestricted and restricted estimators, respectively. The shrinkage estimators combine these two estimators optimally. To demonstrate the optimality of these estimators, we rely on metrics like asymptotic distributional bias (ADB) or asymptotic distributional risk (ADR), which aim to minimize these two quantities. We show that the relative efficiency of the shrinkage estimator is superior to that of the unrestricted estimator when the dimension of shrinkage exceeds two. Our large sample theory and simulation study demonstrate that shrinkage estimators dominate the unrestricted estimator in the entire parameter space. An empirical example of Canadian crime rates data is also provided.
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