| Summary: | 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.
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