论文检索

广义单指标模型的一种新估计方法AI 解读

The single index and generalized single index models have been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables in the low-dimensional case. In this article, we propose a new estimation approach for generalized single index models E(Y | θ⊤X)=ψ(g(θ⊤X)) with ψ(·) known but g(·) unknown. Specifically, we first obtain a consistent estimator of the regression function by using a local linear smoother, and then estimate the parametric…

面板数据模型中的密度预测：半参数贝叶斯视角AI 解读

This article constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients as well as cross-sectional heteroscedasticity. The panel considered in this article features a large cross-sectional dimension N but short time series T. Due to the short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of…

不交叉的单指标分位数回归曲线估计AI 解读

Copyright © 2022 The Authors. Single-index quantile regression (QR) models can avoid the curse of dimensionality in nonparametric problems by assuming that the response is only related to a single linear combination of the covariates. Like the standard parametric or nonparametric QR whose estimated curves may cross, the single-index QR can also suffer quantile crossing, leading to an invalid distribution for the response. This issue has attracted considerable attention in…

通过经验熵刻画条件密度估计的极小极大速率AI 解读

We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint density estimation, minimax rates have been characterized for general density classes in terms of uniform (metric) entropy, a well-studied notion of statistical capacity. When applying these results to conditional density estimation, the use of…

交互与非交互局部差分隐私估计：二次泛函的两个拐点AI 解读

Local differential privacy has recently received increasing attention from the statistics community as a valuable tool to protect the privacy of individual data owners without the need of a trusted third party. Similar to the classical notion of randomized response, the idea is that data owners randomize their true information locally and only release the perturbed data. Many different protocols for such local perturbation procedures can be designed. In most estimation…

最优应对 RKHS 非参数回归中的协变量偏移AI 解读

We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the source and target distributions. When the likelihood ratios are uniformly bounded, we prove that the kernel ridge regression (KRR) estimator with a carefully chosen regularization parameter is minimax rate-optimal (up to a log factor) for a…

稳健性与局部差分隐私AI 解读

It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners’ privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber’s contamination model and the local differential privacy (LDP) constraints. In this paper, we start with a general minimax lower…

近似流形上的深度非参数回归：具有多项式前因子的非渐近误差界AI 解读

We study the properties of nonparametric least squares regression using deep neural networks. We derive nonasymptotic upper bounds for the excess risk of the empirical risk minimizer of feedforward deep neural regression. Our error bounds achieve minimax optimal rate and improve over the existing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on dimension. We show that the neural regression estimator can circumvent…

招聘来源、企业异质性与工资：来自哪里与就职何处的比较AI 解读

Sequential auction models of labor market competition predict that the wages required to successfully poach a worker from a rival employer will depend on the productivities of both the poached and poaching firms. We develop a theoretically grounded extension of the two-way fixed effects model of Abowd et al. (1999) in which log hiring wages are comprised of a worker fixed effect, a fixed effect for the “destination” firm hiring the worker, and a fixed effect for the “origin”…

具有固定效应的广义变换模型的非参数估计AI 解读

This paper considers a generalized panel data transformation model with fixed effects where the structural function is assumed to be additive. In our model, no parametric assumptions are imposed on the transformation function, the structural function, or the distribution of the idiosyncratic error term. The model is widely applicable and includes many popular panel data models as special cases. We propose a kernel-based nonparametric estimator for the structural function.…

密度、对数密度及相关对象的导数估计AI 解读

We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density function f . The estimator is guaranteed to be non-negative and achieves the same optimal rate of convergence in the interior as on the boundary of the support of f . The estimator is therefore well-suited to applications in which non-negative density estimates are required, such as in semiparametric maximum likelihood estimation. In addition, we show…

条件分位数函数估计与推断的简便非参数方法AI 解读

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared…

适用于相依数据的野生自助法AI 解读

This paper introduces a novel wild bootstrap for dependent data (WBDD) as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The consistency of the bootstrap variance estimator for smooth function of the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the WBDD in distribution approximation is…

危机时期的宏观经济预测AI 解读

Summary We propose a parsimonious semiparametric method for macroeconomic forecasting. Based on ideas of clustering and similarity, we partition the series into blocks, search for the closest blocks to the latest block of observations, and forecast with the matched blocks. In a real‐time forecasting exercise, we show that our approach does especially well for labor market and other key macro variables. Our method outperforms parametric linear, nonlinear, time‐varying, and…

利用稀疏叙事工具识别结构VAR：美国宏观审慎政策的动态效应AI 解读

Summary We study identification in Bayesian proxy VARs for instruments that consist of sparse qualitative observations indicating the signs of shocks in specific periods. We propose the Fisher discriminant regression and a non‐parametric sign concordance criterion as two alternative methods for achieving correct inference in this case. The former represents a minor deviation from a standard proxy VAR, whereas the non‐parametric approach builds on set identification. Our…

通过偏内积进行协方差估计的可分离展开AI 解读

Summary The nonparametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are typically alleviated by assuming separability. However, separability is often questionable, sometimes even demonstrably inadequate. We propose a framework for the analysis of covariance operators of random surfaces that generalizes…

具有有限样本保证的简明通用去偏机器学习定理AI 解读

Summary Debiased machine learning is a meta-algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e., scalar summaries, of machine learning algorithms. For example, an analyst may seek the confidence interval for a treatment effect estimated with a neural network. We present a non-asymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies…

非参数混合模型的一致相合性AI 解读

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to…

无环有向混合图的嵌套马尔可夫性质AI 解读

Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local Markov property. Marginals of DAG models also imply equality constraints that are not conditional independences; the well-known “Verma constraint” is an example. Constraints of this type are used for testing edges, and in a computationally…

稳定算法的条件预测推断AI 解读

We investigate generically applicable and intuitively appealing prediction intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying algorithm used for computing point predictions is sufficiently stable when feature-response…

利用共形 p 值检验异常值AI 解读

This paper studies the construction of p-values for nonparametric outlier detection, from a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a general framework yielding p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact…

基于离散优化的分组变量选择：计算与统计视角AI 解读

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the ℓ0-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodology covers both high-dimensional linear regression and nonparametric sparse additive modeling with…

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…

多重协整系统中的完全修正最小二乘参数估计AI 解读

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The…