We propose an empirical likelihood method to test whether the coefficients in a possibly high-dimensional linear model are equal to given values. The asymptotic distribution of the test statistic is independent of the number of covariates in the linear model.

Intermediate quantiles play an important role in the statistics of extremes with particular applications in risk management. For interval estimation of quantiles, Chen and Hall (1993) proposed the so-called smoothed empirical likelihood method. In this paper, we apply the method in Chen and Hall...

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ...

In this paper, a Chover-type law of the iterated logarithm is established for the weighted sums of independent and identically distributed random variables with a distribution in the domain of attraction of a stable law.

Suppose our data {Xn} come from the model Xt=[summation operator]j=0[infinity]cjZt-j, where {Zn} are i.i.d. with a symmetric distribution function which lies in the domain of normal attraction of a stable law with index [alpha][set membership, variant](1,2). Further we assume that cj=jd-1L(j),...

For the estimation of the mean of a heavy tailed distribution with tail index -[alpha]<-1, the asymptotic distribution of the sample mean is not normal as [alpha]<2. In this paper we propose an alternative estimator whose limiting distribution, under a second order condition, is normal for any [alpha]>1.

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second-order regular variation is needed. In this paper we first supplement earlier results on...

Asymptotic expansions of densities of the normalized sums of random vectors with at least finite third moment have been studied extensively (Normal Approximation and Asymptotic expansions. Wiley, New York.). In this note, we obtain the asymptotic expansions of densities of the normalized sums of...

Modeling and estimating a tail copula play an important role in forecasting rare events. Due to their easy simulation, elliptical copulas have been employed in risk management. Recently, Klppelberg, [Klppelber, C., Kuhn, G., Peng, L., 2007. Estimating the tail dependence function of an...