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半参数部分线性变系数众数回归AI 解读

We in this paper propose a semiparametric partially linear varying coefficient (SPLVC) modal regression, in which the conditional mode function of the response variable given covariates admits a partially linear varying coefficient structure. In comparison to existing regressions, the newly developed SPLVC modal regression captures the “most likely” effect and provides superior prediction performance when the data distribution is skewed. The consistency and asymptotic…

用于充分降维的协变量信息矩阵AI 解读

Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or…

高斯过程混合模型的核平滑估计AI 解读

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed…

纵向数据非参数回归函数的新局部估计方法AI 解读

Summary The paper develops a new estimation of non-parametric regression functions for clustered or longitudinal data. We propose to use Cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously. We further prove that the estimator proposed is as asymptotically efficient as if the covariance matrix were known. A Monte Carlo simulation study is conducted to examine the finite sample performance of…

混合比例可变的回归混合模型：半参数方法AI 解读

In this article, we study a class of semiparametric mixtures of regression models, in which the regression functions are linear functions of the predictors, but the mixing proportions are smoothing functions of a covariate. We propose a one-step backfitting estimation procedure to achieve the optimal convergence rates for both regression parameters and the nonparametric functions of mixing proportions. We derive the asymptotic bias and variance of the one-step estimate, and…

基于最高后验密度的贝叶斯混合模型标签确定AI 解读

A fundamental problem for Bayesian mixture model analysis is label switching, which occurs as a result of the nonidentifiability of the mixture components under symmetric priors. We propose two labeling methods to solve this problem. The first method, denoted by PM(ALG), is based on the posterior modes and an ascending algorithm generically denoted ALG. We use each Markov chain Monte Carlo sample as the starting point in an ascending algorithm, and label the sample based on…