Maximum Likelihood Estimation for Binomially Distributed Signals in Discrete Noise
研究了当观测变量X是二项分布变量Y与独立噪声Z之和时，如何利用正则条件和概率比单调性来估计二项参数p，适用于已知噪声分布或可从辅助实验估计噪声的模型。
Abstract Let X be the sum of independent variables Y and Z, where Y is binomially distributed and Z is a nonnegative integer-valued variable whose distribution does not depend on the binomial parameter p. Convoluted binomial distributions describing variables like X are characterized by regularity conditions and equations of the form ∂/∂p P(X = x)=c[P(X = x − 1) − P(X = x)]. The characterization, together with a monotonicity property for probability ratios, is shown to facilitate maximum likelihood estimation of p. Results are applicable to models for binomial signals in noise in which the noise distribution is known or can be estimated from an auxiliary experiment.