Some results for empirical processes of locally dependent time series

In this paper we derive some fundamental properties of locally dependent time series of order m(n), where m(n) is allowed to tend to infinity with the sample size n. More specifically we consider a central limit theorem, an exponential inequality for the local fluctuations of the empirical process, and weak convergence of the empirical process. Locally dependent time series are of independent interest, but they may also serve as useful approximations to other stochastic processes. Some applications are briefly indicated

Tail processes under heavy random censorship with applications

We consider a type of heavy random censoring where the number of uncensored observations still tends to infinity. Under natural conditions the life distribution can be locally analyzed by generalizing tail empirical processes to the heavily censored case. A uniform central limit theorem for the tail product-limit process and the tail empirical cumulative hazard process is established. Statistical applications include a local confidence band for the cumulative life distribution and a test concerning the value of its density at the origin. Key words: heavy censoring, tail product-limit and tail empirical cumulative hazard process, uniform central limit theorem

The order of magnitude of the moments of the modulus of continuity of multiparameter poisson and empirical processes

AbstractIn this note we derive the exact order of magnitude of the moments of the modulus of continuity for multiparameter Poisson and, almost as a corollary, for multivariate empirical processes

Some results for empirical processes of locally dependent time series

In this paper we derive some fundamental properties of locally dependent time series of order m(n), where m(n) is allowed to tend to infinity with the sample size n. More specifically we consider a central limit theorem, an exponential inequality for the local fluctuations of the empirical process, and weak convergence of the empirical process. Locally dependent time series are of independent interest, but they may also serve as useful approximations to other stochastic processes. Some applications are briefly indicated