53 research outputs found
On estimation of Poisson intensity functions
Under the presence of only one realization, we consider a computationally simple algorithm for estimating the intensity function of a Poisson process with exponential quadratic and cyclic of fixed frequency trends. We argue that the algorithm can successfully be used to estimate any Poisson intensity function provided that it has a parametric form
Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences
We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized L - statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodic sequences of random variables. Most of the previous results were obtained under the additional assumption that the sequences are weakly Bernoullian or, in other words, absolutely regular. We also argue that the latter assumption can be undesirable from the applications point of vie
On the M fewer than N bootstrap approximation to the trimmed mean
We show that the M fewer than N (N is the real data sample size, M denotes the size of the bootstrap resample; M=N ! 0, as M ! 1) bootstrap approximation to the distribution of the trimmed mean is consistent without any conditions on the
population distribution F, whereas Efron's naive (i.e. M = N) bootstrap as well as the normal approximation fails to be consistent if the population distribution F has gaps at the two quantiles where the trimming occurs
Bootstrapping multivariate -quantiles and related statistics
AbstractThe asymptotic consistency of the bootstrap approximation of the vector of the marginal generalized quantiles of U-statistic structure (multivariate U-quantiles for short) is established. The asymptotic accuracy of the bootstrap approximation is also obtained. Extensions to smooth functions of marginal generalized quantiles are given and some specific examples, such as the vector of marginal sample quantiles and the vector of marginal Hodges-Lehmann location estimators, are discussed
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