Estimator Wavelet Untuk Fungsi Hazard = Wavelet Estimator for the Hazard Function

ABSTRACT The works of Aalen (1978) showed that the hazard function (h) estimation for censored life test data can be described in the context of inference for a counting process (N) multiplicative intensity model given by X(t) = h(t)Y(t) where Y(t) is a nonnegative observed process. Based on a Nelson-Aalen estimator for cumulative hazard function ft Ramlau-Hansen (1983) defined a kernel estimator for the hazard function as 1 g(t) = (1/b) 5 K((t-s)/b)dA (s) 0 Furthermore by showing that wavelet estimator analogies of some familiar kernel and orthogonal series estimators on the use of standard non-parametric regresion function r estimation along with use the same assumption for h as well as use of r, Antoniadis et al. (1994) defined the wavelet estimator for the hazard function as 1g(t) - 5 Em(t,�)dA (s)0 where Em(t,�) = E4)k(t)k,k(s) is the kernel wavelet as defined by Mayer (19%)k eZ From the result of further analysis it is known that the wavelet estimator for the hazard function has some properties : asymptotically unbiased, consitent, and -jn2 -1" (hd (t) � h(t)) be asymptotically normal with zero mean and variance h(t)w02h(t). Key words : kernel estimator, wavelet estimator, hazard function