Posterior Inference in Single-Index Models

Title & Authors
Posterior Inference in Single-Index Models
Park, Chun-Gun; Yang, Wan-Yeon; Kim, Yeong-Hwa;

Abstract
A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\small{\beta}$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\small{\theta}$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.
Keywords
Single-index model;Wavelet series;Daubechies wavelet;Posterior inference;Hierarchical distribution;Metropolis-Hastings algorithm;
Language
English
Cited by
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