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一个非参数最大似然估计问题的简单解法
Three approaches to a nonparametric maximum likelihood problem are considered. One, based on the method of "sieves", is shown to include the other two. The sieve considered is a double exponential convolution sieve. A closed form solution is given for certain values of the sieve parameter.
概率密度的 Hermite 级数估计性质
An unknown density function $f(x)$, its derivatives, and its characteristic function are estimated by means of Hermite functions $\{h_j\}$. The estimates use the partial sums of series of Hermite functions with coefficients $\hat{a}_{jn} = (1/n) \sum^n_{i=1} h_j(X_i)$ where $X_1\cdots X_n$ represent a sequence of i.i.d. random variables with the unknown density function $f$. The integrated mean square rate of convergence of the $p$th derivative of the estimate is $O(n^{(p/r) + (5/6r)-1})$…