| Nonparametric density estimation is a kind of important density estimation,it has widely used in real life.In nature,Most general still unknown distribution and the sample is not necessarily independent,so the nonparametric density function estimation has attracted much attention in the research of mathematical statistics.From the initial histogram density estimation,nonparamet-ric density function through constantly exploring gradually has some density estimation,such as Rosenblatt density estimation,Parzen kernel estimation,kernel density estimation,nearest neigh-bor density estimates,moving average histogram density estimation and frequency interpolation density estimation.In 1985,Scott[5]proposed the frequency interpolation density estimation based on the histogram estimation.He pointed out that the optimal window width is chosen so that themean square error is the smallest,the convergence rate of n-2/3 andn-4/5 respectively,at the same time,?-mixing sequence in time series model,the reliability theory,ecological system,and other fields have a wide range of application,so the statisticians to hybrid ? sequence has a wide attention and interest.Scott(1985)frequency interpolation density estimation is put forward,many scholars have made in-depth study.However,there is no literature on the estimated ?-mixing random domain properties for more research.Therefore,under the ?-mixing random field density estimation of frequency interpolation asymptotic properties of the research is meaningful.?-mixing random field is presented in this paper,the main is to estimate the frequency in-terpolation density asymptotic properties research.First of all,introduce ?-mixing,frequency interpolation density estimation.Secondly,mixing coefficient ? meet,where 0<?<1.Prove out the With the help of Carbona(2010)on ?-random field frequency polygon by adopting the idea of "block size",for?-mixing random field size block,to prove the ?-under the mixed sample frequency interpolation asymptotic normality. |
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