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如何利用经济理论改进估计：向理论约束收缩AI 解读

Abstract We propose to use economic theories to construct shrinkage estimators that perform well when the theories' empirical implications are approximately correct but perform no worse than unrestricted estimators when the theories' implications do not hold. We implement this construction in various settings, including labor demand and wage inequality, and estimation of consumer demand. We provide asymptotic and finite sample characterizations of the behavior of the…

利用大量矩不等式对因果参数与结构参数进行推断AI 解读

Abstract This article considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters; a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly…

高维向量独立性的检验AI 解读

In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we…

对数凹密度众数的统计推断AI 解读

We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the constrained maximum likelihood estimator where the constraint is that the mode of the density is fixed, say at $m$. The constrained estimation problem is studied in detail in Doss and Wellner (2018). Here, the results of that paper are…

高维相关矩阵检验AI 解读

Testing correlation structures has attracted extensive attention in the literature due to both its importance in real applications and several major theoretical challenges. The aim of this paper is to develop a general framework of testing correlation structures for the one-, two-, and multiple sample testing problems under a high-dimensional setting when both the sample size and data dimension go to infinity. Our test statistics are designed to deal with both the dense and…

高维随机效应模型中方差分量估计量的特征值分布AI 解读

We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well-approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a…

不可知 PAC 机器学习模型的精确下界AI 解读

We provide an exact nonasymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-approximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized “voting” procedures. Based on this result, an exact asymptotic lower bound on the minimax EER is provided. This bound is of the simple form $c_{\infty}/\sqrt{\nu}$ as $\nu\to\infty$, where $c_{\infty}=0.16997\dots$…

利用 p-filter 统一处理含先验知识的多重检验AI 解读

There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null, modeled by nonuniform prior weights; (b) differing importances of hypotheses, modeled by differing penalties for false discoveries; (c) multiple arbitrary partitions of the hypotheses into (possibly overlapping) groups and (d) knowledge of…

Rademacher 先验尖峰随机张量中的相变AI 解读

We consider the problem of detecting a deformation from a symmetric Gaussian random $p$-tensor $(p\geq3)$ with a rank-one spike sampled from the Rademacher prior. Recently, in Lesieur et al. (Barbier, Krzakala, Macris, Miolane and Zdeborová (2017)), it was proved that there exists a critical threshold $\beta_{p}$ so that when the signal-to-noise ratio exceeds $\beta_{p}$, one can distinguish the spiked and unspiked tensors and weakly recover the prior via the minimal…

高维广义线性模型的线性假设检验AI 解读

This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test…

单位根的半参数点最优混合秩检验AI 解读

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size,…

半监督推断：一般理论与总体均值估计AI 解读

We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of covariate vectors along with real-valued responses (“labels”). Otherwise, the formulation is “assumption-lean” in that no major conditions are imposed on the statistical or functional form of the data. We consider both the ideal semi-supervised…

高维 Ising 模型中的图性质检验AI 解读

This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom…

距离多重方差：随机向量的新依赖度量AI 解读

We introduce two new measures for the dependence of $n\ge2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^{2}$-distance of quantities related to the characteristic functions of the underlying random variables. These extend distance covariance (introduced by Székely, Rizzo and Bakirov) from pairs of random variables to $n$-tuplets of random variables. We show that total distance multivariance can be used…

用于高维选择后推断的knockoff过滤器AI 解读

This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units. In this framework, the observations are split into two groups, where the first group is used to screen for a set of potentially relevant variables, whereas the second is used for inference over this reduced set of variables; we also develop strategies for leveraging information from…

二到无穷范数与奇异子空间几何及其高维统计应用AI 解读

The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors. This paper provides a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two-to-infinity norm. Motivated by preliminary…

高维数据下的非可分模型AI 解读

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and numerical…

非光滑准则函数下的间接推断AI 解读

Indirect inference requires simulating realizations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function is discontinuous and does not permit the use of derivative-based optimization routines. Using a change of variables technique, we propose a novel simulation algorithm that alleviates the discontinuities inherent in such indirect inference…

含交互固定效应的半参数单指标面板模型：理论与实践AI 解读

In this paper, we propose a single-index panel data model with unobserved multiple interactive fixed effects. This model has the advantages of being flexible and of being able to allow for common shocks and their heterogeneous impacts on cross sections, thus making it suitable for the investigation of many economic issues. The asymptotic theories are established accordingly. Our Monte Carlo simulations show that our methodology works well for large N and T cases. In our…

随机方差的已实现经验分布函数及其拟合优度检验AI 解读

We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) – inferred from noisy high-frequency data – is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it…

工具变量与平均处理效应的符号AI 解读

This paper considers identification and inference about the sign of the average effect of a binary endogenous regressor (or treatment) on a binary outcome of interest when a binary instrument is available. In this setting, the average effect of the endogenous regressor on the outcome is sometimes referred to as the average treatment effect (ATE). We consider four different sets of assumptions: instrument exogeneity, instrument exogeneity and monotonicity on the outcome…

不连续与折点激励分配机制下加权平均处理效应的识别及小波估计AI 解读

This paper studies identification, estimation, and inference of a weighted average treatment effect (W-ATE) parameter in a class of switching regime models, where the agent’s selection of treatment is affected by either a discontinuous or kink incentive assignment mechanism and some unobservable characteristic. For each assignment mechanism, we (i) establish identification and propose a local wavelet estimator of the W-ATE; (ii) establish asymptotic properties of the local…

具有异质动态结构的面板数据分析AI 解读

This paper proposes a model-free approach to analyze panel data with heterogeneous dynamic structures across observational units. We first compute the sample mean, autocovariances, and autocorrelations for each unit, and then estimate the parameters of interest based on their empirical distributions. We then investigate the asymptotic properties of our estimators using double asymptotics and propose split-panel jackknife bias correction and inference based on the…

随机系数Logit模型中的渐近检验尺寸失真AI 解读

We show that, in the random coefficients logit model, standard inference procedures can suffer from asymptotic size distortions. The problem arises due to boundary issues and is aggravated by the standard parameterization of the model, in terms of standard deviations. For example, in case of a single random coefficient, the asymptotic size of the nominal 95% confidence interval obtained by inverting the two-sided t-test for the standard deviation equals 83.65%. In seeming…