Abstract
We investigate a flexible two-component semiparametric mixture of regressions model, in which one of the conditional component distributions of the response given the covariate is unknown but assumed symmetric about a location parameter, while the other is specified up to a scale parameter. The location and scale parameters together with the proportion are allowed to depend nonparametrically on covariates. After settling identifiability, we provide local M-estimators for these parameters which converge in the sup-norm at the optimal rates over Holder-smoothness classes. We also introduce an adaptive version of the estimators based on the Lepski-method. Sup-norm bounds show that the local M-estimator properly estimates the functions globally, and are the first step in the construction of useful inferential tools such as confidence bands. In our analysis we develop general results about rates of convergence in the sup-norm as well as adaptive estimation of local M-estimators which might be of some independent interest, and which can also be applied in various other settings. We investigate the finite-sample behaviour of our method in a simulation study, and give an illustration to a real data set from bioinformatics.
Highlights
Practitioners are frequently interested in modelling the effect of a d-dimensional explanatory vector X on a response random variable Y by using a regression model estimated from a random sample (Xi, Yi)1≤i≤n of (X, Y )
Statistical inference for parametric finite mixtures of regressions (FMRs) models using a moment generating function method was first introduced by Quandt and Ramsey (1978)
In this paper we investigate a two-component FMR model, in which one of the conditional component distributions is unknown but assumed symmetric about a location parameter μ, while the other is specified up to some scale parameter σ
Summary
Practitioners are frequently interested in modelling the effect of a d-dimensional explanatory vector X on a response random variable Y by using a regression model estimated from a random sample (Xi, Yi)1≤i≤n of (X, Y ). To allow varying parameters for different groups of observations, finite mixtures of regressions (FMRs) have been suggested in the literature. Statistical inference for parametric FMR models using a moment generating function method was first introduced by Quandt and Ramsey (1978). Zhu and Zhang (2004) established the asymptotic theory for testing for the number of components in parametric FMR models. Stadler et al (2010) proposed an 1-penalized method based on a Lasso-type estimator for a high-dimensional FMR model with d n
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
