Segmentation of the mean of heteroscedastic data via cross-validation

Asymptotic inference in some heteroscedastic regression models with long memory design and errors

This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple linear regression model, the first-order asymptotic distribution of the least square estimator of the slope parameter is observed to be degenerate. However, in the second order, this estimator is $n^{1/2}$-consistent and asymptotically normal for $h+H<3/2$; nonnormal otherwise, where $h$ and $H$ are LM parameters of design and error processes, respectively. The f…

基于多元依赖权重的加权最小二乘估计用于线性回归模型

Weighted least squares estimation by multivariate-dependent weights for linear regression models

本文提出一种基于多元依赖权重的加权最小二乘估计方法，用于改善多元线性回归模型中异方差性问题的估计精度和预测性能。

Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases

We investigate the optimality for model selection of the so-called slope heuristics, $V$-fold cross-validation and $V$-fold penalization in a heteroscedastic with random design regression context. We consider a new class of linear models that we call strongly localized bases and that generalize histograms, piecewise polynomials and compactly supported wavelets. We derive sharp oracle inequalities that prove the asymptotic optimality of the slope heuristics---when the optimal penalty shape is known---and $V$ -fold penalization. Furthermore, $V$-fold cross-validation seems to be suboptimal for a…

K折交叉验证在Lasso中的渐近理论及Bootstrap的有效性

Asymptotic Theory of $K$-fold Cross-validation in Lasso and the validity of Bootstrap

本文研究了K折交叉验证在Lasso中的渐近性质，证明在特定条件下Lasso估计量具有n^{1/2}一致性，但不具有变量选择一致性，并验证了Bootstrap在近似K折交叉验证Lasso估计量分布的有效性。

高维异方差数据的变点推断

Change-point Inference for High-dimensional Heteroscedastic Data

本文提出一种基于野自助法的检验方法，用于检测高维异方差数据中的均值变点，该方法无需调参且能适应时变异方差，并扩展到多变点检验与估计。

Double Cross Validation for the Number of Factors in Approximate Factor Models

Determining the number of factors is essential to factor analysis. In this paper, we propose {an efficient cross validation (CV)} method to determine the number of factors in approximate factor models. The method applies CV twice, first along the directions of observations and then variables, and hence is referred to hereafter as double cross-validation (DCV). Unlike most CV methods, which are prone to overfitting, the DCV is statistically consistent in determining the number of factors when both dimension of variables and sample size are sufficiently large. Simulation studies show that DCV ha…