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Optimal convex M-estimation via score matching

通过得分匹配实现最优凸 M 估计

In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the population level, the negative derivative of the optimal convex loss is the best decreasing approximation of the derivative of the log-density of the noise distribution. This motivates a fitting process via a nonparametric extension of score…

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Semiparametric Bernstein–von Mises phenomenon via Isotonized Posterior in Wicksell’s problem

Wicksell 问题中经保序化后验的半参数 Bernstein–von Mises 现象

In this paper, we propose a novel Bayesian approach for nonparametric estimation in Wicksell’s problem. This has important applications in astronomy for estimating the distribution of the positions of the stars in a galaxy given projected stellar positions and in materials science to determine the 3D microstructure of a material, using its 2D cross-sections. We deviate from the classical Bayesian nonparametric approach, which would place a Dirichlet Process (DP) prior on the…

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Inference in Semiparametric Formation Models for Directed Networks

有向网络半参数形成模型的推断

We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that reflects the homophily effect resulting from the nodal attributes or pairwise covariates associated with edges, and a set of latent random noises with unknown distributions. Our interest lies in inferring the unknown degree parameters and…

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Quantile approach to intertemporal consumption with multiple assets

多资产跨期消费的分位数方法

This paper develops a novel economic model and econometric methods to jointly identify and estimate parameters related to intertemporal preference and risk attitude. We begin by formulating an intertemporal consumption model with multiple assets based on dynamic quantile preferences that account for elasticity of intertemporal substitution, risk attitude, and discount factor. We establish the properties of the model and obtain interesting explicit expressions for the value…

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Difference-in-Differences with compositional changes

存在样本构成变化的双重差分

This paper studies Difference-in-Differences (DiD) setups with repeated cross-sectional data and potential compositional changes across time periods. We begin our analysis by deriving the efficient influence function and the semiparametric efficiency bound for the average treatment effect on the treated (ATT). We introduce nonparametric estimators that attain the semiparametric efficiency bound under mild rate conditions on the estimators of the nuisance functions,…

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Functional semiparametric modeling for nonstationary and periodic time series data

非平稳与周期时间序列的函数型半参数建模

Inspired by a real data example illustrating the periodicity in hog price data, this study aims to analyze time series that exhibit an unknown period alongside complex covariate effects. To address these complexities and effectively handle the data structures, we incorporate the partial functional varying-coefficient single-index model into the classical time series decomposition model. We propose a two-stage estimation procedure designed to accurately estimate the unknown…

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Locally Robust Semiparametrically Efficient Bayesian Inference

局部稳健且半参数有效的贝叶斯推断

We propose a framework for making Bayesian parametric models robust to local misspecification. Suppose in a baseline parametric model, a parameter of interest has an interpretation in an encompassing semiparametric model. Bayesian and maximum likelihood estimators are generally biased under local misspecification. We propose to augment the baseline likelihood by a multiplicative factor that involves scores for the baseline model, the efficient scores for the encompassing…

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Causal Inference With Noisy Covariates: Heteroscedastic Measurement Error and Differential Privacy

含噪协变量的因果推断:异方差测量误差与差分隐私

We study causal inference with high‐dimensional covariates, observed with various types of heteroscedastic noise. Our main assumption is that the true covariates are low rank, which we empirically evaluate with plots and interpret as approximate repeated measurements. This assumption delivers semiparametric inference on the causal parameter, as precisely as if the true covariates were available. A methodological contribution is to introduce an error‐in‐variable balancing…

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Distribution Regression with Sample Selection and UK Wage Decomposition

样本选择下的分布回归与英国工资分解

We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model, which accommodates much richer patterns of heterogeneity in the effect of covariates and selection process and allows for departures from Gaussian errors while maintaining the same level of tractability. The model applies to continuous, discrete, and mixed outcomes. We provide identification, estimation, and inference…

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EFFICIENCY IN ESTIMATION UNDER MONOTONIC ATTRITION

单调样本流失下的有效估计

Attrition is monotonic when agents leaving multi-period studies do not return. Under a general missing at random (MAR) assumption, we study efficiency in estimation of parameters defined by moment restrictions on the distributions of the counterfactuals that were unrealized due to monotonic attrition. We discuss novel issues related to overidentification, usability of sample units, and the information content of various MAR assumptions for estimation of such parameters. We…

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Semiparametric localized principal stratification analysis with continuous strata

连续主层的半参数局部化主分层分析

Abstract Principal stratification is essential for revealing causal mechanisms involving post-treatment intermediate variables, in real-world applications like surrogate marker evaluation. Principal stratification analysis with continuous intermediate variables is increasingly common but challenging due to the infinite principal strata and the nonidentifiability and nonregularity of principal causal effects (PCEs). Inspired by recent research, we resolve these challenges by…

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A statistical view of column subset selection

列子集选择的统计视角

Abstract We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as column subset selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of principal variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum-likelihood…

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Finite Sample Inference for the Maximum Score Estimand

最大得分目标参数的有限样本推断

Abstract We provide a finite sample inference method for the structural parameters of Manski's semiparametric binary response model under a conditional median restriction. This is achieved by exploiting distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on the size n sequence of exogenous covariates are constructed, and the proposed test statistic is a monotone function of violations…

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Addressing endogeneity issues in a spatial autoregressive model using copulas

利用 Copula 处理空间自回归模型中的内生性

This paper develops a novel, instrument-free semiparametric copula framework for a spatial autoregressive (SAR) model to address endogeneity arising from an endogenous spatial weights matrix, endogenous regressors, or both. Moving beyond conventional Gaussian copulas, we develop a flexible estimator based on the Student’s t copula with an unknown degrees-of-freedom (df) parameter, which nests the Gaussian case and allows the data to determine the presence of tail dependence.…

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Inference on model parameters with many L-moments

使用大量 L 矩的模型参数推断

This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains ad-hoc, though: researchers typically set the number of L-moments equal to the number of parameters, which is…

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Estimating high dimensional monotone index models by iterative convex optimization

通过迭代凸优化估计高维单调指标模型

In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric transformation, and duration models. A main advantage of our approach is computational. For instance, rank estimation procedures such as those proposed in [13] and [7] that optimize a nonsmooth, nonconvex objective function are difficult to use…

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Identification and estimation of partial effects in nonlinear semiparametric panel models

非线性半参数面板模型中偏效应的识别与估计

Average partial effects (APEs) are often not point identified in panel models with unrestricted unobserved individual heterogeneity, such as a binary response panel model with fixed effects and logistic errors as a special case. This lack of point identification occurs despite the identification of these models' common coefficients. We provide a unified framework to establish the point identification of various partial effects in a wide class of nonlinear semiparametric…

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Improved estimation of semiparametric dynamic copula models with filtered nonstationarity

过滤非平稳成分后的半参数动态 Copula 模型改进估计

This paper considers estimation of short-run dynamics in time series that contain a nonstationary component. We assume that appropriate preliminary methods can be applied to the observed time series to separate short-run elements from long-run slowly evolving secular components, and focus on estimation of the short-run dynamics based on the filtered data. We use a flexible copula-generated Markov model to capture the nonlinear temporal dependence in the short-run component…

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Estimation of wage inequality in the UK by quantile regression with censored selection

利用删失选择分位数回归估计英国工资不平等

Arellano and Bonhomme (2017) proposed a quantile selection model to study the evolution of wage inequality in the UK, which specifies a binary selection equation and requires an exclusion restriction. In this paper we propose a quantile selection model with a more informative censored selection equation. Following Heckman (1974, 1979), Heckman and Sedlacek (1990), and Blundell et al. (2003), among others, the employment selection equation could be equivalently modeled by an…

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Identification of time-varying counterfactual parameters in nonlinear panel models

非线性面板模型中时变反事实参数的识别

We develop a general framework for the identification of counterfactual parameters in a class of nonlinear semiparametric panel models with fixed effects and time effects. Our method applies to models for discrete outcomes (e.g., two-way fixed effects binary choice) or continuous outcomes (e.g., censored regression), with discrete or continuous regressors. Our results do not require parametric assumptions on the error terms or time-homogeneity on the outcome equation. Our…

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Loss aversion and the welfare ranking of policy interventions

损失厌恶与政策干预的福利排序

This paper develops theoretical criteria and econometric methods to rank policy interventions in terms of welfare when individuals are loss-averse. Our new criterion for “loss aversion-sensitive dominance” defines a weak partial ordering of the distributions of policy-induced gains and losses. It applies to the class of welfare functions which model individual preferences with non-decreasing and loss-averse attitudes towards changes in outcomes. We also develop new…

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A semiparametric instrumented difference-in-differences approach to policy learning

用于政策学习的半参数工具变量双重差分方法

Summary Recently, there has been a surge in methodological development for the difference-in-differences approach to evaluate causal effects. Standard methods in the literature rely on the parallel-trend assumption to identify the average treatment effect on the treated. However, the parallel-trend assumption may be violated in the presence of unmeasured confounding, and the average treatment effect on the treated may not be useful in learning a treatment assignment policy…

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Mixture Models: Parametric, Semiparametric, and New Directions

混合模型:参数、半参数与新方向

Weixin Yao and Sijia Xiang. Boca Raton, FL: Chapman & Hall/CRC Press, 2024, xvii + 379 pp., $130.00(H), ISBN: 978-0-367-48182-7.The mixture modeling framework has become a mainstay in the toolkit o...

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Inference in Generalized Linear Models with Robustness to Misspecified Variances

对方差误设稳健的广义线性模型推断

Generalized linear models usually assume a common dispersion parameter, an assumption that is seldom true in practice. Consequently, standard parametric methods may suffer appreciable loss of type I error control. As an alternative, we present a semi-parametric group-invariance method based on sign flipping of score contributions. Our method requires only the correct specification of the mean model, but is robust against any misspecification of the variance. We present tests…

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