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高维半参数矩约束模型AI 解读

We consider nonlinear moment restriction semiparametric models where both the dimension of the parameter vector and the number of restrictions are divergent with sample size and an unknown smooth function is involved. We propose an estimation method based on the sieve generalized method of moments (sieve-GMM). We establish consistency and asymptotic normality for the estimated quantities when the number of parameters increases modestly with sample size. We also consider the…

线性样条模型中的结点估计AI 解读

The linear spline model is able to accommodate nonlinear effects while allowing for an easy interpretation. It has significant applications in studying threshold effects and change-points. However, its application in practice has been limited by the lack of both rigorously studied and computationally convenient method for estimating knots. A key difficulty in estimating knots lies in the nondifferentiability. In this article, we study influence functions of regular and…

动态交互半参数函数对标量回归模型AI 解读

Motivated by recent work studying massive functional data, such as the COVID-19 data, we propose a new dynamic interaction semiparametric function-on-scalar (DISeF) model. The proposed model is useful to explore the dynamic interaction among a set of covariates and their effects on the functional response. The proposed model includes many important models investigated recently as special cases. By tensor product B-spline approximating the unknown bivariate coefficient…

核平均估计量AI 解读

The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation…

倾向得分估计中的最优协变量平衡条件AI 解读

Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pretreatment covariates. While these methods appear to empirically perform well, little is known about how the…

无限维与维度增长时间序列回归的稳健推断AI 解读

We develop a class of tests for time‐series models such as multiple regression with growing dimension, infinite‐order autoregression, and nonparametric sieve regression. Examples include the Chow test and general linear restriction tests of growing rank p . Employing such increasing p asymptotics, we introduce a new scale correction to conventional test statistics, which accounts for a high‐order long‐run variance (HLV), which emerges as p grows with sample size. We also…

动态模型的筛模拟矩估计量AI 解读

This paper proposes a Sieve Simulated Method of Moments (Sieve‐SMM) estimator for the parameters and the distribution of the shocks in nonlinear dynamic models where the likelihood and the moments are not tractable. An important concern with SMM, which matches sample with simulated moments, is that a parametric distribution is required. However, economic quantities that depend on this distribution, such as welfare and asset prices, can be sensitive to misspecification. The…

横截面依赖下的自助法推断AI 解读

In this paper, we introduce a method of generating bootstrap samples with unknown patterns of cross‐ sectional/spatial dependence, which we call the spatial dependent wild bootstrap. This method is a spatial counterpart to the wild dependent bootstrap of Shao (2010) and generates data by multiplying a vector of independently and identically distributed external variables by the eigendecomposition of a bootstrap kernel. We prove the validity of our method for studentized and…

多元非可逆扩散的上确界范数自适应漂移估计AI 解读

We consider the question of estimating the drift for a large class of ergodic multivariate and possibly nonreversible diffusion processes, based on continuous observations, in sup-norm loss. Nonparametric classes of smooth functions of unknown order are considered, and we suggest an adaptive approach which allows to construct drift estimators attaining optimal sup-norm rates of convergence. Reversibility structures and related functional inequalities are known to be key…

协方差核的补全AI 解读

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Ω of a rectangular domain I×I to a covariance kernel on the entire domain I×I. For a broad class of domains Ω called serrated domains, we are able to present a complete theory. Namely, we demonstrate that a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of…

随机对象的 Fréchet 充分降维AI 解读

Summary We consider Fréchet sufficient dimension reduction with responses being complex random objects in a metric space and high-dimensional Euclidean predictors. We propose a novel approach, called the weighted inverse regression ensemble method, for linear Fréchet sufficient dimension reduction. The method is further generalized as a new operator defined on reproducing kernel Hilbert spaces for nonlinear Fréchet sufficient dimension reduction. We provide theoretical…

广义贝叶斯损失函数选择与非正规化模型的使用AI 解读

Abstract Statisticians often face the choice between using probability models or a paradigm defined by minimising a loss function. Both approaches are useful and, if the loss can be re-cast into a proper probability model, there are many tools to decide which model or loss is more appropriate for the observed data, in the sense of explaining the data's nature. However, when the loss leads to an improper model, there are no principled ways to guide this choice. We address…

核常微分方程AI 解读

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for…

断点回归中的局部复合分位数回归AI 解读

We introduce the local composite quantile regression (LCQR) to causal inference in regression discontinuity (RD) designs. Kai, Li and Zou study the efficiency property of LCQR, while we show that its nice boundary performance translates to accurate estimation of treatment effects in RD under a variety of data generating processes. Moreover, we propose a bias-corrected and standard error-adjusted t-test for inference, which leads to confidence intervals with good coverage…

含固定效应与时变系数的半参数空间自回归面板模型AI 解读

This article considers a semiparametric spatial autoregressive (SAR) panel data model with fixed effects and time-varying coefficients. The time-varying coefficients are allowed to follow unknown functions of time, while the other parameters are assumed to be unknown constants. We propose a local linear quasi-maximum likelihood estimation method to obtain consistent estimators for the SAR coefficient, the variance of the error term, and the nonparametric time-varying…

变系数中介模型及其在行为经济学数据分析中的应用AI 解读

This paper is concerned with causal mediation analysis with varying indirect and direct effects. We propose a varying coefficient mediation model, which can also be viewed as an extension of moderation analysis on a causal diagram. We develop a new estimation procedure for the direct and indirect effects based on B-splines. Under mild conditions, rates of convergence and asymptotic distributions of the resulting estimates are established. We further propose a F-type test for…

可能存在多次周期结构变化的非平稳时间序列稳健推断AI 解读

Motivated by two examples concerning global warming and monthly total import and export by China, we study time series that contain a nonparametric periodic component with an unknown period, a nonparametric trending behavior and also additive covariate effects. Further, as the amplitude function may change at some known or unknown change-point(s), we extend our model to take this dynamical periodicity into account and introduce two change-point estimators. To the best of…

空间相关稀疏与稠密函数型数据的统一主成分分析AI 解读

We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially independent functional nugget effect. Observations on each function are made on discrete time points and contaminated with measurement errors. Under the assumption of spatial stationarity and isotropy, we propose a tensor product spline…

Sobolev 椭球中在线非参数回归的筛随机梯度下降估计AI 解读

The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. in nonparametric regression, one assumes that the regression function belongs to a pre-specified infinite-dimensional function space (the hypothesis space). in the online setting, when the observations come in a stream, it is computationally-preferable to iteratively update an estimate rather than refitting an entire model repeatedly.…

近似核主成分分析：计算与统计之间的权衡AI 解读

Kernel methods are powerful learning methodologies that allow to perform nonlinear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistical consistency of most of these approximate kernel methods is not well understood except for kernel ridge regression wherein it has been shown that the random…

跳跃扩散模型中跳跃成分的存在性检验AI 解读

In this paper we propose a nonparametric test to determine whether an underlying jump diffusion process indeed contains jump component, or equivalently, is indeed a diffusion. Our test is based upon a robust threshold estimation of diffusive volatility and the kernel estimation of the conditional moment function of the squared instantaneous increments of the underlying process. We show that our test statistic has asymptotic standard normal distribution under the null…

含平稳协变量的分位数协整非参数推断AI 解读

This paper considers the inference problems in nonlinear quantile regressions with both stationary and nonstationary covariates. The nonparametric local constant quantile estimator is proposed to estimate the unknown quantile regression function, whose asymptotic properties are established under quite general conditions. Specification testing of the quantile regression function is further considered through a statistic constructed based on the integrated squared distance…

存在测量误差的变系数模型估计AI 解读

We propose a semiparametric estimator for varying coefficient models when the regressors in the nonparametric components are measured with error. Varying coefficient models are an extension of other popular semiparametric models , including partially linear and nonparametric additive models, and deliver an attractive solution to the curse-of-dimensionality. We use deconvolution kernel estimation in a two-step procedure and show that the estimator is consistent and…

MCMC 输出的最优抽稀AI 解读

Abstract The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to ‘burn in’ and removed, while the remainder of the chain is ‘thinned’ if compression is also required. In this paper, we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path…