Mean Integrated Squared Error of Nonlinear Wavelet-based Estimators with Long Memory Data
نویسندگان
چکیده
We consider the nonparametric regression model with long memory data that are not necessarily Gaussian and provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators. We show this MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators. However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent. Short title: Wavelet estimator with long memory data 2000 Mathematics Subject Classification: Primary: 62G07; Secondary: 62C20
منابع مشابه
Wavelet-based estimators of scaling behavior
Various wavelet-based estimators of self-similarity or long-range dependence scaling exponent are studied extensively. These estimators mainly include the (bi)orthogonal wavelet estimators and the Wavelet Transform Modulus Maxima (WTMM) estimator. This study focuses both on short and long time-series. In the framework of Fractional Auto-Regressive Integrated Moving Average (FARIMA) processes, w...
متن کاملUsing Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter
We develop an ordinary least squares estimator of the long memory parameter from a fractionally integrated process that is an alternative to the Geweke Porter-Hudak estimator. Using the wavelet transform from a fractionally integrated process, we establish a log-linear relationship between the wavelet coe cients' variance and the scaling parameter equal to the long memory parameter. This log-li...
متن کاملWavelet threshold estimators for data
Wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level-dependent soft threshold to the coeecients in the wavelet transform. A variety of threshold choices are proposed, including one based on an unbiased estimate of mean squared error. The practical performance of the method is demonstrated on examples, including data from a neurophysiological...
متن کاملEstimation of Hurst exponent revisited
In order to estimate the Hurst exponent of long-range dependent time series numerous estimators such as based e.g. on rescaled 9 range statistic (R/S) or detrended fluctuation analysis (DFA) are traditionally employed. Motivated by empirical behaviour of the bias of R/S estimator, its bias-corrected version is proposed. It has smaller mean squared error than DFA and behaves comparably 11 to wav...
متن کاملMemory-Universal Prediction of Stationary Random Processes
We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process fXig1i= 1. The best mean-square predictor of X0 is its conditional mean given the entire infinite past fXig 1 i= 1. Given a sequence of observations X1 X2 XN , we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasi...
متن کامل