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高维控制变量选择后的处理效应推断AI 解读

We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances. Our analysis allows the number of controls to be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be…

近似因子模型中的高维协方差矩阵估计AI 解读

The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By…

分数阶时间序列模型的高斯伪极大似然估计AI 解读

We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible regions. In these circumstances, a proof of consistency (which is a prerequisite for proving asymptotic normality) can be difficult owing to nonuniform convergence of the objective function over a large admissible parameter space. In particular,…

大样本下基于 MCMC 的估计方法的计算复杂度AI 解读

In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using the conditions required for the central limit theorem to hold, we establish polynomial bounds…

高维稀疏计量经济模型的统计推断AI 解读

This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the regression function is well-approximated by a parsimonious, yet unknown set of regressors. The latter condition makes it possible to estimate the entire regression function effectively by searching for approximately the right set of…

平方根 LASSO：通过锥规划实现稀疏信号的枢轴恢复AI 解读

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors $p$ is large, possibly much larger than $n$, but only $s$ regressors are significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation $σ$ or nor does it need to pre-estimate $σ$. Moreover, the method does not rely on normality or…

任意协方差依赖下的错误发现比例估计AI 解读

Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any SNPs are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In the current paper, we propose a novel method based…

高维分类中的正则化最优仿射判别方法 ROADAI 解读

For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules to mitigate the issue of noise accumulation. However, in biological applications, there are often a group of correlated genes responsible for clinical outcomes, and the use of the…

高维稀疏计量经济模型导论AI 解读

In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using L1-penalization and post-L1-penalization methods. Focusing on linear and nonparametric regression frameworks, we discuss various econometric examples, present basic theoretical results, and illustrate the concepts and methods with Monte Carlo simulations and an empirical application. In the application, we examine and confirm the empirical validity…

变系数函数型线性回归AI 解读

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression models is a regression parameter function in one or two arguments. If, in addition, one has scalar predictors, as is often the case in applications to longitudinal studies, the question arises how to incorporate these into a functional…

高斯工具变量模型中的 LASSO 方法AI 解读

In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when the number of instruments is much larger than the sample size. We derive asymptotic distributions for the resulting IV estimators and provide conditions under which these…

筛选观测数据下的非参数回归AI 解读

We present a general principle for estimating a regression function nonparametrically, allowing for a wide variety of data filtering, for example, repeated left truncation and right censoring. Both the mean and the median regression cases are considered. The method works by first estimating the conditional hazard function or conditional survivor function and then integrating. We also investigate improved methods that take account of model structure such as independent errors…

稀疏超高维加性模型中的非参数独立筛选AI 解读

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening is called NIS, a specific member of the sure independence screening. Several closely related…

超高维回归中基于重拟合交叉验证的方差估计AI 解读

Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable. Recent advances on variable selection in ultrahigh dimensional linear regressions make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved realized noise…

任意协方差依赖下的错误发现率控制AI 解读

Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any genes are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In the current paper, we propose a new methodology…

连续时间模型中马尔可夫假设的非参数检验AI 解读

We propose several statistics to test the Markov hypothesis for $β$-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman--Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks's phenomenon holds. We compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process,…

微阵列数据中基因方差的非参数估计AI 解读

Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman--Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is…

高度相关及非高度相关协变量下的加性模型估计AI 解读

Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are…

用于超高维变量选择的惩罚复合准似然AI 解读

In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a data-driven weighted linear combination of convex loss functions, together with weighted $L_1$-penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted $L_1$-penalty is used both to…

GARCH 模型的非高斯准最大似然估计AI 解读

The non-Gaussian quasi maximum likelihood estimator is frequently used in GARCH models with intension to improve the efficiency of the GARCH parameters. However, unless the quasi-likelihood happens to be the true one, non-Gaussian QMLE methods suffers inconsistency even if shape parameters in the quasi-likelihood are estimated. To correct this bias, we identify an unknown scale parameter that is critical to the consistent estimation of non-Gaussian QMLE, and propose a…

用于组合选择的高频大规模波动率矩阵估计AI 解读

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al (2008). The required high-dimensional volatility matrix can be estimated by using high frequency financial data. This enables us to better adapt to the local volatilities and local correlations among vast number of assets and to increase significantly the sample size for estimating…

极端条件分位数模型的推断：市场与出生体重风险应用AI 解读

Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applications, such as conditional value-at-risk, production efficiency, and adjustment bands in (S,s) models. In this paper we provide feasible inference tools for…

基于 Copula 的半参数马尔可夫模型的有效估计AI 解读

This paper considers the efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications.…

大规模协方差矩阵估计的稀疏一致性与收敛速度AI 解读

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three…