An Adaptive Orthogonal-Series Estimator for Probability Density Functions
概率密度的自适应正交级数估计
Given a sample set $X_1, \cdots, X_N$ of independent identically distributed real-valued random variables, each with the unknown probability density function $f(\cdot)$, the problem considered is to estimate $f$ from the sample set. The function $f$ is assumed to be in $L_2(a, b); f$ is not assumed to be in any parametric family. This paper constructs an adaptive "two-pass" solution to the problem: in a preprocessing step (the first pass), a preliminary rough estimate of $f$…