每日简报

含噪矩阵补全的推断与不确定性量化AI 解读

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained estimates and how to perform statistical inference on the unknown matrix (e.g.~constructing a valid and short confidence interval for an unseen entry). This paper takes a step towards inference and uncertainty quantification for…

断点回归设计AI 解读

This handbook chapter gives an introduction to the sharp regression discontinuity design, covering identification, estimation, inference, and falsification methods.

跨多产品类别消费者选择的反事实推断AI 解读

This paper proposes a method for estimating consumer preferences among discrete choices, where the consumer chooses at most one product in a category, but selects from multiple categories in parallel. The consumer's utility is additive in the different categories. Her preferences about product attributes as well as her price sensitivity vary across products and are in general correlated across products. We build on techniques from the machine learning literature on…

协变量辅助的经验贝叶斯估计AI 解读

We study methods for simultaneous analysis of many noisy experiments in the presence of rich covariate information. The goal of the analyst is to optimally estimate the true effect underlying each experiment. Both the noisy experimental results and the auxiliary covariates are useful for this purpose, but neither data source on its own captures all the information available to the analyst. In this paper, we propose a flexible plug-in empirical Bayes estimator that…

nprobust：非参数核估计与稳健偏差校正推断AI 解读

Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as a preliminary ingredient entering some other estimation or inference procedure. This article describes the main methodological and numerical features of the software package nprobust, which offers an array of estimation and inference…

lspartition：基于分区的最小二乘回归AI 解读

Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and numerical features of the R software package lspartition, which implements modern estimation and inference results for partitioning-based least squares (series) regression estimation. This article discusses the main methodological and…

Kronecker 协方差模型的二次型估计AI 解读

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension $n$ is large relative to the sample size $T$). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided $\log^3n/T\to 0$. We obtain the limiting distributions of Lagrange multiplier (LM) and Wald tests…

关于 Wald 统计量发散的技术说明AI 解读

The Wald test statistic has been shown to diverge (Dufour et al, 2013, 2017) under some conditions. This note links the divergence to eigenvalues of a polynomial matrix and establishes the divergence rate.

lpdensity：局部多项式密度估计与推断AI 解读

Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their well-known boundary bias. Alternative smoothing methods are available to handle boundary points in density estimation, but they all require additional tuning parameter choices or other typically ad hoc modifications depending on the…

通信高效且准确的统计估计AI 解读

When the data are stored in a distributed manner, direct application of traditional statistical inference procedures is often prohibitive due to communication cost and privacy concerns. This paper develops and investigates two Communication-Efficient Accurate Statistical Estimators (CEASE), implemented through iterative algorithms for distributed optimization. In each iteration, node machines carry out computation in parallel and communicate with the central processor, which…

简便的局部多项式密度估计量AI 解读

This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel…

回归分析中的抽样不确定性与设计不确定性AI 解读

Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it…

基于分区的级数估计量的大样本性质AI 解读

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and propose feasible tuning parameter selection. Third, we develop pointwise inference methods…

SHOPPER：含替代与互补关系的消费者选择概率模型AI 解读

We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimate these forces from large-scale data, and we analyze a large dataset from a major chain grocery store. We are interested in answering counterfactual queries…