Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..

Almost unbiased ratio-cum-product estimators for the finite population mean

Almost unbiased ratio-cum-product estimator, Finite population mean, Optimum estimator, Jackknife,

Bandwidth selection in local polynomial regression using eigenvalues

Local polynomial regression is commonly used for estimating regression functions. In practice, however, with rough functions or sparse data, a poor choice of bandwidth can lead to unstable estimates of the function or its derivatives. We derive a new expression for the leading term of the bias by using the eigenvalues of the weighted design matrix where the bias depends on the arrangement of the "X"-values in the bandwidth window. We then use this result to determine a local data-driven bandwidth selection method and to provide a diagnostic for poor bandwidths that are chosen by using other methods. We show that our data-driven bandwidth is asymptotically equivalent to the optimal local bandwidth and that it performs well for relatively small samples when compared with other methods. In addition, we provide simulation results for first-derivative estimation. We illustrate its performance with data from Mars Global Surveyor. Copyright 2006 Royal Statistical Society.