Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1）.
In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge. The test statistics are evaluated by some empirical results.
This paper considers variable selection for moment restriction models. We propose a penalized empirical likelihood （PEL） approach that has desirable asymptotic properties comparable to the penalized likelihood approach, which relies on a correct parametric likelihood specification. In addition to being consistent and having the oracle property, PEL admits inference on parameter without having to estimate its estimator＇s covariance. An approximate algorithm, along with a consistent BIC-type criterion for selecting the tuning parameters, is provided for FEL. The proposed algorithm enjoys considerable computational efficiency and overcomes the drawback of the local quadratic approximation of nonconcave penalties. Simulation studies to evaluate and compare the performances of our method with those of the existing ones show that PEL is competitive and robust. The proposed method is illustrated with two real examples.
