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线性化最大秩相关估计AI 解读

Summary We propose a linearized maximum rank correlation estimator for the single-index model. Unlike the existing maximum rank correlation and other rank-based methods, the proposed estimator has a closed-form expression, making it appealing in theory and computation. The proposed estimator is robust to outliers in the response and its construction does not need knowledge of the unknown link function or the error distribution. Under mild conditions, it is shown to be…

存在处理习惯化的时序实验中因果效应的极小极大设计AI 解读

Summary In many modern settings, such as an online marketplace, randomized experiments need to be executed over multiple time periods. In such temporal experiments, it has been observed that the effects of an intervention on an experimental unit may be large when the unit is first exposed to it, but then it attenuates after repeated exposures. This is typically due to units’ habituation to the intervention, or some other form of learning, such as when users gradually start…

数据整合：利用外部简化模型的参数估计比值AI 解读

Summary We consider the situation of estimating the parameters in a generalized linear prediction model, from an internal dataset, where the outcome variable $Y$ is binary and there are two sets of covariates, $X$ and $Z$. We have information from an external study that provides parameter estimates for a generalized linear model of $Y$ on $X$. We propose a method that makes limited assumptions about the similarity of the distributions in the two study populations. The method…

含高维干扰参数的广义线性模型检验AI 解读

Summary Generalized linear models often have high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional subvector of the model’s coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and are thus…

用于识别共同极端事件群组的球面聚类AI 解读

Summary There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical $k$-principal-component…

加权最小二乘估计的最优极小极大随机设计AI 解读

Summary This work studies an experimental design problem where the values of a predictor variable, denoted by $x$, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to $m(x)$, but it is not assumed that the model is correctly specified. It follows that the quantity of interest is the best linear approximation of $m(x)$, which is denoted by $\ell(x)$. It is shown that in this framework the ordinary least…

可交换关系数组的回归AI 解读

Summary Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression…

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…

分布函数检验与置信带的新方法AI 解读

We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multiscale methods of testing and based on refined laws of the iterated logarithm for the normalized uniform empirical process Un(t)/ t(1−t) and its natural limiting process, the normalized Brownian bridge process U(t)/ t(1−t). The new tests and confidence bands refine the procedures of Berk and Jones (1979) and Owen (1995). Roughly speaking, the high…

含测量误差的高维泊松模型：非线性非凸优化中的假设检验AI 解读

We study estimation and testing in the Poisson regression model with noisy high-dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a nonconvex target function to minimize. Treating the high-dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target…

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…

刻画 SLOPE 的权衡：变分视角与 Donoho–Tanner 极限AI 解读

Sorted ℓ1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this paper, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I error and power. Assuming a…

ScreeNOT：相关噪声下精确 MSE 最优的奇异值阈值化AI 解读

We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nominally involves unobservables, we show how to apply it even where the noise covariance structure is not a priori known or is not independently estimable. The proposed method, which we call ScreeNOT, is a mathematically solid alternative to Cattell’s ever-popular but vague scree plot heuristic from 1966. ScreeNOT has a surprising…

聚类稳健推断：实证实践指南AI 解读

Methods for cluster-robust inference are routinely used in economics and many other disciplines. However, it is only recently that theoretical foundations for the use of these methods in many empirically relevant situations have been developed. In this paper, we use these theoretical results to provide a guide to empirical practice. We do not attempt to present a comprehensive survey of the (very large) literature. Instead, we bridge theory and practice by providing a…

矩阵值观测相关结构的检验与支持集恢复：股票市场应用AI 解读

Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore imperative to make rigorous statistical inference on correlation matrix equality between the two groups of countries. However, if the traditional vector-valued approach is undertaken, such inference is either infeasible due to limited…

完整多元随机波动率模型的可扩展推断AI 解读

We introduce a multivariate stochastic volatility model that imposes no restrictions on the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. Inference is achieved via a carefully designed feasible and scalable MCMC that has quadratic, rather than cubic, computational complexity for evaluating the multivariate normal densities required. We illustrate how our model can be applied on macroeconomic applications through a…

放宽内生二元反应模型中的条件独立性AI 解读

For binary response models, the literature primarily addresses endogeneity by a control function approach assuming conditional independence (CF-CI). However, as the literature also notes, CF-CI implies conditions like homoskedasticity (of the latent error with respect to the instruments) that fail in many empirical settings. I propose an alternative approach that allows for heteroskedasticity, achieving identification with a conditional mean restriction. These identification…

当偏差也贡献方差：函数系数协整回归的正确极限理论AI 解读

Limit distribution theory in the econometric literature for functional coefficient cointegrating regression is incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. The correct limit theory reveals that components from both bias and variance terms contribute to variability in the asymptotics. The errors in the literature arise because random variability in the bias term has been neglected in earlier research. In…

组合预测方差的估计：基于 Bootstrap 的方法AI 解读

This paper considers bootstrap inference in model averaging for predictive regressions. We first show that the standard pairwise bootstrap is not valid in the context of model averaging. This common bootstrap approach induces a bias-related term in the bootstrap variance of averaging estimators. We then propose and justify a fixed-design residual-based bootstrap resampling approach for model averaging. In a local asymptotic framework, we show the validity of the bootstrap in…

平滑分位数回归与大规模推断AI 解读

Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. This paper focuses on statistical inference for quantile regression in the “increasing dimension” regime. We provide a comprehensive analysis of a convolution smoothed approach that achieves adequate approximation to computation and inference for quantile regression. This method, which we refer to as conquer,…

多工具变量下 t 统计量的二阶修正AI 解读

This paper studies second-order properties of the many instruments robust t-ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models with homoskedastic errors under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n, and proposes second-order refinements to the t-ratios to improve the size and power properties. Based on asymptotic expansions…

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…