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使用δ序列估计多元密度函数AI 解读

This paper studies some asymptotic properties of density estimates $\hat{f}$ of $f$ based on $d$-variate delta sequences. The mean-square consistency, almost sure consistency, and asymptotic normality of $\hat{f}$ have been obtained as corollaries to the $L_1$ convergence properties of these delta sequences. Estimators based on kernel functions, orthogonal series, and some histogram methods can be obtained as special cases of $\hat{f}$.

利用δ序列进行概率密度估计AI 解读

Let $X_1, X_2, \cdots, X_n$ be i.i.d. random variables with common density function $f$. A method of density estimation based on "delta sequences" is studied and mean square rates established. This method generalizes certain others including kernel estimators, orthogonal series estimators, Fourier transform estimators, and the histogram. Rates are obtained for densities in Sobolev spaces and for densities satisfying Lipschitz conditions. The former generalizes some results…