# SFB 303 Discussion Paper No. A-544

**Author**: Zhu-Yu Li , Zu-Di Lu, Gen-Xiang Chai

**Title**: Nonparametric Estimation of Density Function for a Sample Process under Mixing Condition

**Abstract**: Nonparametric density estimation is a useful tool for examining the
structure of data, in particular, for the stationary time series,
since usually it is really difficult to find the real marginal density
of the series. Some papers contributed to this aspect for alpha-mixing stationary sequence can be found in the literature, e.g., Robinson (1983), Tran (1989, 1990). However, just as Tran et al (1996) stressed, yet there are a great number of processes which may not be alpha-mixing. In this paper, we will adopt a nonparametrical method to estimate unknown density function of a sample data process which is based on relaxing phi-mixing assumptions (see Billingsley (1968) and Bierens (1983)). Uniformly weak and strong consistency and the convergence rates of the estimator we adopted will be discussed, and some
numerical examples will be given.

**Keywords**: Relaxing phi-Mixing Sample, Stationary Sample Process, Non-
parametric Statistics, Kernel Density Estimators, Asymptotic Consistency,
Rate of Convergence.

**JEL-Classification-Number**: C13, C14, C22.

**Creation-Date**: 1997

**URL**: ../1997/a/bonnsfa544.pdf"
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