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非参数加性回归中交互效应的识别与估计AI 解读

Abstract A new formulation of the additive interaction model is introduced. In contrast to existing approaches, the new formulation separates well the joint effects of covariates that cannot be accounted for by individual main effects. The new approach enables correct interpretation of interaction effects by making them orthogonal to the associated main effects in the $ L^{2} $ sense. A new method is developed to estimate the resulting main and interaction effects.…

高维加性回归的高效函数型 Lasso 核平滑AI 解读

Smooth backfitting has been proposed and proved as a powerful nonparametric estimation technique for additive regression models in various settings. Existing studies are restricted to cases with a moderate number of covariates and are not directly applicable to high dimensional settings. In this paper, we develop new kernel estimators based on the idea of smooth backfitting for high dimensional additive models. We introduce a novel penalization scheme, combining the idea of…

动态交互事件网络中的全局协变量效应检验AI 解读

In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the observation horizon. In addition, covariates are observed and the goal is to model the impact of the covariates on the interactions. We distinguish two types of covariates: global, system-wide covariates (i.e., covariates taking the same…

变量选择、单调似然比与组稀疏性AI 解读

In the pivotal variable selection problem, we derive the exact nonasymptotic minimax selector over the class of all s-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in general, not realizable in polynomial time, we show that its tractable counterpart (the scan selector) attains the minimax expected Hamming risk to within factor 2, and is also exact minimax with respect to the probability of wrong recovery.…

具有乘法分量的比例风险模型的光滑回代估计AI 解读

Smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression. By projecting the data down onto the structured space of interest smooth backfitting provides a direct link between data and estimator. This article introduces the ideas of smooth backfitting to survival analysis in a proportional hazard model, where we assume an underlying conditional hazard with multiplicative components. We develop asymptotic theory for the…

稀疏高维加性模型中的统计推断AI 解读

In this paper, we discuss the estimation of a nonparametric component f1 of a nonparametric additive model Y=f1(X1)+⋯+fq(Xq)+ϵ. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f1 in the oracle model Z=f1(X1)+ϵ, for which the additive components f2,…,fq are known. We construct a two-step presmoothing-and-resmoothing…

泊松降秩模型及其在政治文本数据中的应用AI 解读

Summary We discuss Poisson reduced-rank models for low-dimensional summaries of high-dimensional Poisson vectors that allow inference on the location of individuals in a low-dimensional space. We show that under weak dependence conditions, which allow for certain correlations between the Poisson random variables, the locations can be consistently estimated using Poisson maximum likelihood estimation. Moreover, we develop consistent rules for determining the dimension of the…

标记变量依赖风险率模型推断的一般半参数方法AI 解读

We examine a new general class of hazard rate models for duration data, containing a parametric and a nonparametric component. Both can be a mix of a time effect and possibly time-dependent covariate effects. A number of well-known models are special cases. In a counting process framework, a general profile likelihood estimator is developed and the parametric component of the model is shown to be asymptotically normal and efficient. Finite sample properties are investigated…

高维工具变量模型中的不适定估计AI 解读

This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector β0 which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included and excluded covariates, denoted by M, to shrink to zero as the sample size increases. We propose a novel estimator based on desparsification of an instrumental variable Lasso estimator, which is a regularized version of 2SLS with an additional…

We develop an instrumental variable approach for identification of dynamic treatment effects on survival outcomes in the presence of dynamic selection, noncompliance, and right-censoring. The approach is nonparametric and does not require independence of observed and unobserved characteristics or separability assumptions. We propose estimation procedures and derive asymptotic properties. We apply our approach to evaluate a policy reform in which the pathway of unemployment…

内生样本选择下的非参数估计AI 解读

This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed for. In the exogenous and endogenous case, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Pointwise asymptotic distribution of the…

操作时间与样本内密度预测AI 解读

In this paper, we consider a new structural model for in-sample density forecasting. In-sample density forecasting is to estimate a structured density on a region where data are observed and then reuse the estimated structured density on some region where data are not observed. Our structural assumption is that the density is a product of one-dimensional functions with one function sitting on the scale of a transformed space of observations. The transformation involves…

参数化 GARCH-in-Mean 模型的渐近理论AI 解读

In this paper we develop an asymptotic theory for the Quasi-Maximum Likelihood Estimator (QMLE) of the parametric GARCH-in-Mean model. The asymptotics is based on a study of the volatility as a process of the model parameters. The proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem. Our results show why the asymptotics for this specification is quite complex although it is a rather standard…

含生成协变量的半参数估计AI 解读

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem…

局部线性风险率估计的双重单侧交叉验证AI 解读

Summary The paper brings together the theory and practice of local linear kernel hazard estimation. Bandwidth selection is fully analysed, including double one-sided cross-validation that is shown to have good practical and theoretical properties. Insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability. A new semiparametric hazard estimator transforming the…

样本内密度预测的渐近理论AI 解读

This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed. Identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation. In this paper, the structural assumption is made that the density is a product of one-dimensional functions. The…

In this paper, we study ordinary backfitting and smooth backfitting as methods of fitting varying coefficient quantile models. We do this in a unified framework that accommodates various types of varying coefficient models. Our framework also covers the additive quantile model as a special case. Under a set of weak conditions, we derive the asymptotic distributions of the backfitting estimators. We also briefly report on the results of a simulation study.

非参数工具变量回归中含噪非线性算子方程的迭代估计AI 解读

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach…

摘要暂缺

灵活的广义变系数回归模型AI 解读

This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model accommodates both continuous and discrete random variables for the response and covariates. It is quite flexible to cover the generalized varying coefficient models and the generalized additive models as special cases. Under a weak condition…

含非参数生成协变量的非参数回归AI 解读

We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator’s statistical…

核密度估计的双侧验证带宽选择AI 解读

Bandwidth selection in kernel density estimation is one of the fundamental model selection problems of mathematical statistics. The study of this problem took major steps forward with the articles of Hall and Marron (1987) and Hall and Johnstone (1992). Since then, the focus seems to have been on various versions of implementing the so-called plug-in method aimed at estimating the minimum mean integrated squared error (MISE). The most successful of these efforts still seems…

未知连接函数加性模型的 Oracle 有效非参数估计AI 解读

This paper describes an estimator of the additive components of a nonparametric additive model with an unknown link function. When the additive components and link function are twice differentiable with sufficiently smooth second derivatives, the estimator is asymptotically normally distributed with a rate of convergence in probability of n −2/5 . This is true regardless of the (finite) dimension of the explanatory variable. Thus, the estimator has no curse of…

加性分位数模型的回拟合与平滑回拟合AI 解读

In this paper, we study the ordinary backfitting and smooth backfitting as methods of fitting additive quantile models. We show that these backfitting quantile estimators are asymptotically equivalent to the corresponding backfitting estimators of the additive components in a specially-designed additive mean regression model. This implies that the theoretical properties of the backfitting quantile estimators are not unlike those of backfitting mean regression estimators. We…