*J. Japan Statist. Soc.,* Vol. 34 (No. 1), pp. 1-17, 2004

## Nonparametric Regression In Proportional Hazards Models

Toshio Honda

**Abstract. **
Fan *et al*. (1997) considered two kinds of nonparametric estimators of the effects of the covariates in proportional hazards models. One of them has no parametric assumption on the baseline hazard function and is based on the integration of the estimated first order derivative of the regression function. We study the asymptotic properties of the estimator and consider another nonparametric estimator of the effects of the covariates in proportional hazards models. We show both of the estimators have very similar asymptotic properties. The latter is closely related to estimation in two-sample problems and is much easier to calculate.

*Key words and phrases*:
Asymptotic distribution, censoring time, estimation of the first order derivative, failure time, integration, local partial likelihood, local polynomial fitting, nonparametric regression, proportional hazards models, two-sample problem.

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