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模型误设下的半参数局部变量选择AI 解读

Summary Local variable selection aims to test for the effect of covariates on an outcome within specific regions. We outline a challenge that arises in the presence of nonlinear effects and model misspecification. Specifically, for common semiparametric methods, even slight model misspecification can result in a high false positive rate, in a manner that is highly sensitive to the chosen basis functions. We propose a method based on orthogonal cut splines that avoids false…

空间混杂下常用空间估计量的一致性AI 解读

Summary This article addresses the asymptotic performance of popular spatial regression estimators of the linear effect of an exposure on an outcome under spatial confounding, the presence of an unmeasured spatially structured variable influencing both the exposure and the outcome. We first show that the estimators from ordinary least squares and restricted spatial regression are asymptotically biased under spatial confounding. We then prove a novel result on the infill…

连续索引图模型AI 解读

Abstract Let X={Xu}u∈U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of X’s covariance kernel, without restricting U to be finite or countable, allowing the modelling of stochastic processes in continuous time/space. Unlike traditional methods, this characterization is not based on zero entries of an…

协变量调整回归函数的去偏推断AI 解读

Abstract In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. Under certain causal conditions, it also corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose–response curve. We propose a debiased local linear estimator of the…

非参数回归中的最优异方差检验AI 解读

Heteroskedasticity testing in nonparametric regression is a classic statistical problem with important practical applications, yet fundamental limits are unknown. Adopting a minimax perspective, this article considers the testing problem in the context of an α-Hölder mean and a β-Hölder variance function. For α>0 and β∈(0,1/2), the sharp minimax separation rate n−4α+n−4β/(4β+1)+n−2β is established. To achieve the minimax separation rate, a kernel-based statistic using…

通过弱条件期望实现随机对象的非线性全局 Fréchet 回归AI 解读

(2019) 691-719) emerges as a special case of our method by choosing a linear kernel. We require that the metric space for the predictor admits a reproducing kernel, while the intrinsic geometry of the metric space for the response is utilized to study the asymptotic properties of the proposed estimates. Numerical studies, including extensive simulations and a real application, are conducted to investigate the finite-sample performance.

含协变量的秩相似分位数断点回归：识别与推断AI 解读

This study investigates the identification and inference of quantile treatment effects (QTEs) in a fuzzy regression discontinuity (RD) design under rank similarity . Unlike Frandsen et al. (2012, Journal of Econometrics 168, 382–395), who focus on QTEs only for the compliant subpopulation, our approach can identify QTEs and average treatment effect for the whole population at the threshold. We derived a new set of moment restrictions for the RD model by imposing a local rank…

时变系数面板模型的设定检验AI 解读

This paper provides nonparametric specification tests for the commonly used homogeneous and stable coefficients structures in panel data models. We first obtain the augmented residuals by estimating the model under the null hypothesis and then run auxiliary time series regressions of augmented residuals on covariates with time-varying coefficients (TVCs) via sieve methods. The test statistic is then constructed by averaging the squared fitted values, which are close to zero…

高维核插值的相图AI 解读

Summary The generalization ability of kernel interpolation in large dimensions, ie, $ n\asymp d^{\gamma} $ for some $ \gamma \gt 0 $, could be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us understand the so-called benign overfitting phenomenon reported in the neural networks literature. Focusing on the inner product kernel on the unit sphere, we fully characterize the exact order of both the variance and the bias of…

信息性观测时点下的函数主成分分析AI 解读

Summary Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serve as important building blocks for forecasting and model building. Decades of research have advanced methods for functional principal component analysis, often assuming independence between the observation times and longitudinal outcomes. Yet such assumptions are fragile in real-world settings where observation times may be driven…

提升核两样本检验的功效AI 解读

Summary The kernel two-sample test based on the maximum mean discrepancy is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power of the kernel test by combining maximum mean discrepancy estimates over multiple kernels using their Mahalanobis distance. We derive the asymptotic null distribution of the proposed test statistic and use a multiplier bootstrap approach…

非参数结构函数与弹性的自适应估计和一致置信带AI 解读

Abstract We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least-squares estimators. When implemented with this choice, estimators of both the structural function h0 and its derivatives (such as elasticities) converge at the fastest possible (i.e. minimax) rates in sup-norm. The second is for constructing…

基于 Hyvärinen 评分的全数据驱动归一化幂化核密度估计AI 解读

Recently, Jewson and Rossell proposed a new approach for kernel density estimation using an exponentiated form of kernel density estimators. The density estimator contained two hyperparameters that flexibly controls the smoothness of the resulting density. We tune them in a data-driven manner by minimizing an objective function based on the Hyvärinen score to avoid the optimization involving the intractable normalizing constant caused by the exponentiation. We show the…

面向多分辨率数据的个体化动态潜因子模型及其移动健康应用AI 解读

Summary Mobile health has emerged as a major success for tracking individual health status, due to the popularity and power of smartphones and wearable devices. This has also brought great challenges in handling heterogeneous, multi-resolution data that arise ubiquitously in mobile health due to irregular multivariate measurements collected from individuals. In this paper, we propose an individualized dynamic latent factor model for irregular multi-resolution time series…

Testing the significance of a variable or group of variables X for predicting a response Y, given additional covariates Z, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for X is nonzero. However, when the model is misspecified, the test may have poor power, for example, when X is involved in complex interactions, or lead to many false rejections. In this work, we study the…

非线性选择模型中的截距估计AI 解读

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then…

用于模型检验的高斯过程方法AI 解读

This paper proposes a Gaussian process (GP) approach for testing conditional moment restrictions. Tests are based on squared Neyman orthogonal function-parametric processes integrated with respect to a GP distribution. This methodology leads to a general unified framework of kernel-based tests having the following properties: (i) bootstrap tests are easy to implement in the presence of nuisance parameters (they are simple quadratic forms, and there is no need to reestimate…

格点数据的多元趋势滤波AI 解读

We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in d dimensions. KTF is a natural extension of univariate trend filtering (Int. J. Comput. Vis. 70 (2006) 214–255; SIAM Rev. 51 (2009) 339–360; Ann. Statist. 42 (2014) 285–323), and is defined by minimizing a penalized least squares problem whose penalty term sums the absolute (higher-order) differences of the parameter to be…

基于概率核嵌入的椭圆分布非参数检验AI 解读

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data dependence structure. Before applying such methods, we need to decide whether the data are elliptically distributed. Currently existing tests either focus exclusively on spherical distributions, or rely on bootstrap to determine the null…

基于核时序差分方法的最优策略评估AI 解读

We study nonparametric methods for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We analyze the kernel-based least-squares temporal difference (LSTD) estimate, which can be understood either as a nonparametric instrumental variables method, or as a projected approximation to the Bellman fixed point equation. Our analysis imposes no assumptions on the transition operator of the Markov chain, but rather only conditions on the…

极值随机森林AI 解读

Classical methods for quantile regression fail in cases where the quantile of interest is extreme and only few or no training data points exceed it. Asymptotic results from extreme value theory can be used to extrapolate beyond the range of the data, and several approaches exist that use linear regression, kernel methods or generalized additive models. Most of these methods break down if the predictor space has more than a few dimensions or if the regression function of…

多个分布之间的核差异度量AI 解读

Given M≥2 distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD)—a parameter that quantifies the difference between the M distributions. The population KMD, which takes values between 0 and 1, is 0 if and only if all the M distributions are the same, and 1 if and only if all the distributions are mutually singular. Moreover, KMD possesses many properties commonly associated with f-divergences…

贝叶斯样条隐马尔可夫模型及其活动与睡眠分析应用AI 解读

B-spline-based hidden Markov models employ B-splines to specify the emission distributions, offering a more flexible modelling approach to data than conventional parametric HMMs. We introduce a Bayesian framework for inference, enabling the simultaneous estimation of all unknown model parameters including the number of states. A parsimonious knot configuration of the B-splines is identified by the use of a trans-dimensional Markov chain sampling algorithm, while model…

Fréchet 回归的充分降维AI 解读

With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fréchet regression model (Petersen and Müller) provides a promising framework for regression analysis with metric space-valued responses. In this article, we introduce a flexible sufficient dimension reduction (SDR) method for Fréchet regression to achieve two purposes: to mitigate the curse of…