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Autoregressive (AR) models with finite variance errors have been well studied. This paper is concerned with AR models with heavy-tailed errors, which is useful in various scientific research areas. Statistical estimation for AR models with infinite variance errors is very different from those for AR models with finite variance errors. In this paper, we consider a weighted quantile regression for AR models to deal with infinite variance errors. We further propose an induced smoothing method to deal with computational challenges in weighted quantile regression. We show that the difference between weighted quantile regression estimate and its smoothed version is negligible. We further propose a test for linear hypothesis on the regression coefficients. We conduct Monte Carlo simulation study to assess the finite sample performance of the proposed procedures. We illustrate the proposed methodology by an empirical analysis of a real-life data set. [ABSTRACT FROM AUTHOR]

Abstract: Based on measures and minimum estimators , we present three families of test statistics for testing nonadditivity in loglinear models. The minimum estimator can be seen to be a generalization of the maximum likelihood estimator. In the process of testing nonadditivity, the two-stage tests procedure is usually used as the standard method. The unknown parameters are first estimated by some method (here ) and then these estimators which are treated as known constants are applied in the second-stage of this procedure. These three families of statistics which generalize the conclusions in Pardo and Pardo (2005) are asymptotically chi-squared. In the last section, we apply our method to a practical example and do a simulation study. [Copyright &y& Elsevier]