On Weighted U -statistics for Stationary Processes by Tailen Hsing
نویسنده
چکیده
A weighted U -statistic based on a random sample X1, . . . ,Xn has the form Un = ∑1≤i,j≤n wi−jK(Xi,Xj ), where K is a fixed symmetric measurable function and the wi are symmetric weights. A large class of statistics can be expressed as weighted U -statistics or variations thereof. This paper establishes the asymptotic normality of Un when the sample observations come from a nonlinear time series and linear processes.
منابع مشابه
On weighted U-statistics for stationary processes
A weighted U -statistic based on a random sample X1, . . . , Xn has the form Un = ∑ 1≤i,j≤n wi−jK(Xi, Xj) where K is fixed symmetric measurable function and the wi are symmetric weights. A large class of statistics can be expressed as weighted U -statistics or variations thereof. This paper establishes the asymptotic normality of Un when the sample observations come from a non-linear time serie...
متن کاملConfidence Interval Estimation of the Mean of Stationary Stochastic Processes: a Comparison of Batch Means and Weighted Batch Means Approach (TECHNICAL NOTE)
Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...
متن کاملSpectral density estimation through a regularized inverse problem
In the study of stationary stochastic processes on the real line, the covariance function and the spectral density function are parameters of considerable interest. They are equivalent ways of expressing the temporal dependence in the process. In this article, we consider the spectral density function and propose a new estimator that is not based on the periodogram; the estimator is derived thr...
متن کاملSome New Methods for Prediction of Time Series by Wavelets
Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...
متن کاملEfficient Prediction for Linear and Nonlinear Autoregressive Models
Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better...
متن کامل