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现代高斯—马尔可夫定理AI 解读

This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares…

平滑性与稀疏性下离散—连续分布的自适应贝叶斯估计AI 解读

We consider nonparametric estimation of a mixed discrete‐continuous distribution under anisotropic smoothness conditions and a possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at…

部分有序备选项的离散选择模型AI 解读

In this paper, we analyze a discrete choice model for partially ordered alternatives. The alternatives are differentiated along two dimensions: the first an unordered “horizontal” dimension, and the second an ordered “vertical” dimension. The model can be used in circumstances in which individuals choose among products of different brands, wherein each brand offers an ordered choice menu, for example, by offering products of varying quality. The unordered–ordered nature of…

市场反事实与多产品需求设定：非参数方法AI 解读

Demand estimates are essential for addressing a wide range of positive and normative questions in economics that are known to depend on the shape—and notably the curvature—of the true demand functions. The existing frontier approaches, while allowing flexible substitution patterns, typically require the researcher to commit to a parametric specification. An open question is whether these a priori restrictions are likely to significantly affect the results. To address this, I…

升价拍卖的识别及其数字版权管理应用AI 解读

This study provides new identification and estimation results for ascending (traditional English or online) auctions with unobserved auction‐level heterogeneity and an unknown number of bidders. When the seller's reserve price and two order statistics of bids are observed, we derive conditions under which the distributions of buyer valuations, unobserved heterogeneity, and number of participants are point identified. We also derive conditions for point identification in…

半参数估计量的影响函数AI 解读

There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, and constructing debiased machine learning…

非线性半参数模型的正则化正交机器学习AI 解读

Summary This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally,…

具有乘法结构的非平稳非参数回归模型估计AI 解读

Summary This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially…

具有参数化截面依赖的非参数面板回归AI 解读

Summary In this paper, we consider efficiency improvement in a nonparametric panel data model with cross-sectional dependence. A generalised least squares (GLS)-type estimator is proposed by taking into account this dependence structure. Parameterising the cross-sectional dependence, a local linear estimator is shown to be dominated by this type of GLS estimator. Also, possible gains in terms of rate of convergence are studied. Asymptotically optimal bandwidth choice is…

渐变均值的偏离是否具有实质意义？基于上确界范数估计量的检验AI 解读

Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly nonstationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be nonrelevant (i.e., small), or relevant for a specific problem at hand, and the present paper presents statistical methodology…

多尺度贝叶斯生存分析AI 解读

We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for ‘many’ functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein–von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these…

度量空间值数据的总变差正则化 Fréchet 回归AI 解读

Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for new methodology in this area, we develop a total variation regularization technique for nonparametric Fréchet regression, which refers to a regression setting where a response residing in a metric space is paired with a scalar predictor…

非光滑非凸统计学习中的广义 Bregman 替代算法分析AI 解读

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for…

凹扩展线性模型中惩罚样条估计量的渐近性质：收敛速率AI 解读

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the…

弱依赖数据半参数回归的 Wilks 定理AI 解读

The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the present and past values of a vector of covariates. A parametric model for the conditional variance of the series is added to capture further nonlinear effects. We propose suitable moment equations which characterize the mean and variance…

协变量偏移中的边际奇异性与标签收益AI 解读

Transfer Learning addresses common situations in Machine Leaning where little or no labeled data is available for a target prediction problem—corresponding to a distribution Q, but much labeled data is available from some related but different data distribution P. This work is concerned with the fundamental limits of transfer, that is, the limits in target performance in terms of (1) sample sizes from P and Q, and (2) differences in data distributions P, Q. In particular, we…

动态处理效应非参数模型中的识别AI 解读

This paper develops a nonparametric model that represents how sequences of outcomes and treatment choices influence one another in a dynamic manner. In this setting, we are interested in identifying the average outcome for individuals in each period, had a particular treatment sequence been assigned. The identification of this quantity allows us to identify the average treatment effects (ATE’s) and the ATE’s on transitions, as well as the optimal treatment regimes, namely,…

基于非参数似然的相对误差精确统计量AI 解读

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p -value of the TET statistic can provide an accurate approximation to the p -value of an…

大规模数据的时变协方差矩阵估计AI 解读

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible…

具有不限定分布的相关随机效应的非线性面板模型AI 解读

Under a Mundlak-type correlated random effect (CRE) specification, we first show that the average likelihood of a parametric nonlinear panel data model is the convolution of the conditional distribution of the model and the distribution of the unobserved heterogeneity. Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a…

多重相互依赖持续时间模型AI 解读

We propose a multiplex interdependent durations model and study its empirical content. The model considers an empirical stopping game of multiple agents making optimal timing decisions with incomplete information. We characterize the unique Bayesian Nash equilibrium of the stopping game in a system of simultaneous equations involving the conditional distribution of each duration with a moderate strategic interaction condition. The system of nonlinear simultaneous equations…

面板计数数据半参数回归模型的最大似然估计AI 解读

Summary Panel count data, in which the observation for each study subject consists of the number of recurrent events between successive examinations, are commonly encountered in industrial reliability testing, medical research and other scientific investigations. We formulate the effects of potentially time-dependent covariates on one or more types of recurrent events through nonhomogeneous Poisson processes with random effects. We employ nonparametric maximum likelihood…

依赖删失生存数据的半参数建模、估计与推断AI 解读

Summary When modelling survival data, it is common to assume that the survival time $T$ is conditionally independent of the censoring time $C$ given a set of covariates. However, there are numerous situations in which this assumption is not realistic. The goal of this paper is therefore to develop a semiparametric normal transformation model which assumes that, after a proper nonparametric monotone transformation, the vector $(T, C)$ follows a linear model, and the vector of…

交叉验证带宽的袋装聚合及其大数据应用AI 解读

Summary Hall & Robinson (2009) proposed and analysed the use of bagged cross-validation to choose the bandwidth of a kernel density estimator. They established that bagging greatly reduces the noise inherent in ordinary cross-validation, and hence leads to a more efficient bandwidth selector. The asymptotic theory of Hall & Robinson (2009) assumes that $N$, the number of bagged subsamples, is $\infty$. We expand upon their theoretical results by allowing $N$ to be finite, as…