STRONG IDENTIFIABILITY AND OPTIMAL MINIMAX RATES FOR FINITE MIXTURE ESTIMATION By
نویسندگان
چکیده
Abstract We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with m0 components, the optimal local minimax rate of estimation of a mixing distribution with m components is n−1/(4(m−m0)+2). This corrects a previous paper by Chen (1995). By contrast, it turns out that there are estimators with a (nonuniform) pointwise rate of estimation of n−1/2 for all mixing distributions with a finite number of components.
منابع مشابه
On strong identifiability and optimal rates of parameter estimation in finite mixtures
Abstract: This paper studies identifiability and convergence behaviors for parameters of multiple types, including matrix-variate ones, that arise in finite mixtures, and the effects of model fitting with extra mixing components. We consider several notions of strong identifiability in a matrix-variate setting, and use them to establish sharp inequalities relating the distance of mixture densit...
متن کاملRate - Optimal Graphon Estimation
Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with k clu...
متن کاملNumerical Parameter Identifiability and Estimability: Integrating Identifiability, Estimability, and Optimal Sampling Design
We define two levels of parameters. The basic parameters are associated with the model and experiment(s). However, the observations define a set of identifiable observational parameters that are functions of the basic parameters. Starting with this formulation, we show that an implicit function approach provides a common basis for examining local identifiability and estimability and gives a lea...
متن کاملKullback – Leibler Aggregation and Misspecified Generalized Linear Models
In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is show...
متن کاملA moment-based method for estimating the proportion of true null hypotheses and its application to microarray gene expression data.
Due to advances in experimental technologies, it is feasible to collect measurements for a large number of variables. When these variables are simultaneously screened by a statistical test, it is necessary to consider the adjustment for multiple hypothesis testing. The false discovery rate has been proposed and widely used to address this issue. A related problem is the estimation of the propor...
متن کامل