论文检索

高维纵向数据的显著性检验AI 解读

This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic…

高维混杂效应模型中目标系数的简便估计AI 解读

Often an investigator is interested in a single parameter or low-dimensional parameter vector (e.g. a treatment effect) in a regression model, rather than in the full set of regression coefficients. There may also be a relatively high-dimensional set of potential explanatory variables other than the effect of interest which, if omitted, could bias the estimate of the parameter of interest. However there may be too many such variables to include all of them without…

利用连续统矩条件检验分布假设AI 解读

We propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test, which takes into account the correlation between influence functions for different argument values. We derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size. We show its…

高维线性混合模型中的固定效应检验AI 解读

Many scientific and engineering challenges—ranging from pharmacokinetic drug dosage allocation and personalized medicine to marketing mix (4Ps) recommendations—require an understanding of the unobserved heterogeneity to develop the best decision making-processes. In this article, we develop a hypothesis test and the corresponding p-value for testing for the significance of the homogeneous structure in linear mixed models. A robust matching moment construction is used for…

IPAD：结合 Knockoffs 推断的稳定可解释预测AI 解读

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in statistics, economics, and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped. To this end, in this paper we exploit the general framework of…

资产定价中哪些因子是风险因子？模型扫描框架AI 解读

A key question for understanding the cross-section of expected returns of equities is the following: which factors, from a given collection of factors, are risk factors, equivalently, which factors are in the stochastic discount factor (SDF)? Though the SDF is unobserved, assumptions about which factors (from the available set of factors) are in the SDF restricts the joint distribution of factors in specific ways, as a consequence of the economic theory of asset pricing. A…

高维多样本比较问题的非参数方法AI 解读

Summary High-dimensional $k$-sample comparison is a common task in applications. We construct a class of easy-to-implement distribution-free tests based on new nonparametric tools and unexplored connections with spectral graph theory. The test is shown to have various desirable properties and a characteristic exploratory flavour that has practical consequences for statistical modelling. Numerical examples show that the proposed method works surprisingly well across a broad…

通过高维协变量平衡倾向得分稳健估计因果效应AI 解读

Summary We propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. Our method consists of three steps. We first use a class of penalized $M$-estimators for the propensity score and outcome models. We then calibrate the initial estimate of the propensity score by balancing a carefully selected subset of covariates that are predictive of the outcome.…

无限分解的贝叶斯累积收缩AI 解读

Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing…

高维线性中介模型中间接效应的估计与推断AI 解读

Summary Mediation analysis is difficult when the number of potential mediators is larger than the sample size. In this paper we propose new inference procedures for the indirect effect in the presence of high-dimensional mediators for linear mediation models. We develop methods for both incomplete mediation, where a direct effect may exist, and complete mediation, where the direct effect is known to be absent. We prove consistency and asymptotic normality of our indirect…

混合类型数据的稀疏半参数典型相关分析AI 解读

Summary Canonical correlation analysis investigates linear relationships between two sets of variables, but it often works poorly on modern datasets because of high dimensionality and mixed data types such as continuous, binary and zero-inflated. To overcome these challenges, we propose a semiparametric approach to sparse canonical correlation analysis based on the Gaussian copula. The main result of this paper is a truncated latent Gaussian copula model for data with excess…

高维均值向量的经验似然检验AI 解读

Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension $p$ and the sample size $n$ satisfy $p/n\rightarrow c\in [1,\infty)$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p/n>1/2$ because the convex hull of the $n$ observations in $\mathbb{R}^p$ becomes too small to cover the true mean value. Moreover, when $p> n$, the sample covariance matrix becomes singular, and this…

低秩估计中的错误发现及其控制AI 解读

Summary Models specified by low rank matrices are ubiquitous in contemporary applications. In many of these problem domains, the row–column space structure of a low rank matrix carries information about some underlying phenomenon, and it is of interest in inferential settings to evaluate the extent to which the row–column spaces of an estimated low rank matrix signify discoveries about the phenomenon. However, in contrast with variable selection, we lack a formal framework…

通过近似留一交叉验证高效估计样本外预测误差AI 解读

Summary The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as K-fold cross-validation suffer from large biases. Motivated by the low bias of the leave-one-out cross-validation method, we propose a computationally efficient closed form approximate leave-one-out formula ALO for a large class of regularized estimators. Given the regularized estimate, calculating ALO requires a minor computational…

高维变点检测的统一数据自适应框架AI 解读

Summary In recent years, change point detection for a high dimensional data sequence has become increasingly important in many scientific fields such as biology and finance. The existing literature develops a variety of methods designed for either a specified parameter (e.g. the mean or covariance) or a particular alternative pattern (sparse or dense), but not for both scenarios simultaneously. To overcome this limitation, we provide a general framework for developing tests…

可视化黑箱监督学习模型中预测变量的效应AI 解读

Summary In many supervised learning applications, understanding and visualizing the effects of the predictor variables on the predicted response is of paramount importance. A shortcoming of black box supervised learning models (e.g. complex trees, neural networks, boosted trees, random forests, nearest neighbours, local kernel-weighted methods and support vector regression) in this regard is their lack of interpretability or transparency. Partial dependence plots, which are…

深度神经网络与计量方法预测气候变化对农业产量影响的比较AI 解读

Summary Predicting the impact of climate change on crop yield is difficult, in part because the production function mapping weather to yield is high dimensional and nonlinear. We compare three approaches to predicting yields: (a) deep neural networks (DNNs), (b) traditional panel-data models, and (c) a new panel-data model that allows for unit and time fixed effects in both intercepts and slopes in the agricultural production function—made feasible by a new estimator called…

基于投影的条件依赖度量及其在高维无向图模型中的应用AI 解读

Measuring conditional dependence is an important topic in econometrics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic type I error and can be…

大型时变参数 VAR 的状态空间降维AI 解读

This paper proposes a new approach to estimating high dimensional time varying parameter structural vector autoregressive models (TVP-SVARs) by taking advantage of an empirical feature of TVP-(S)VARs. TVP-(S)VAR models are rarely used with more than 4–5 variables. However recent work has shown the advantages of modelling VARs with large numbers of variables and interest has naturally increased in modelling large dimensional TVP-VARs. A feature that has not yet been utilized…

潜在资产定价因子的估计AI 解读

We develop an estimator for latent factors in a large-dimensional panel of financial data that can explain expected excess returns. Statistical factor analysis based on Principal Component Analysis (PCA) has problems identifying factors with a small variance that are important for asset pricing. We generalize PCA with a penalty term accounting for the pricing error in expected returns. Our estimator searches for factors that can explain both the expected return and…

摘要暂缺

关于“使用 ReLU 深度神经网络进行非参数回归”的讨论AI 解读

First we would like to congratulate Professor Johannes Schmidt-Hieber for his excellent paper, which shows the surprising result that deep neural networks can achieve good rates of convergence even in case of nonsmooth activation functions.In the following we divide our discussion into three parts:1.The importance of compository assumptions.2. The necessity of the sparsity of the networks.3. The theoretical difference between ReLU and sigmoidal functions.

关于“使用 ReLU 深度神经网络进行非参数回归”的讨论AI 解读

I would like to congratulate Johannes Schmidt–Hieber on a very interesting paper in which he considers regression functions belonging to the class of so-called compositional functions and analyzes the ability of estimators based on the multivariate nonparametric regression model of deep neural networks to achieve minimax rates of convergence. In my discussion, I will first regard such a type of result from the general viewpoint of the theoretical foundations of deep neural…

关于“使用 ReLU 深度神经网络进行非参数回归”的讨论AI 解读

We congratulate Johannes Schmidt-Hieber for his elegant and thought-provoking results.His article uses deep-learning-inspired methods in the context of nonparametric regression.Schmidt-Hieber defines a rich class of composition-based functions G(q, d, t, β, K) and a class of sparse multilayer neural networks F(L, p, s, F ).He proves that least squares estimation over the class of sparse neural networks (with suitably chosen architecture (L, p, s, F )) achieves nearly minimax…