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高维广义潜因子模型中的因子数确定AI 解读

Summary As a generalization of the classical linear factor model, generalized latent factor models are useful for analysing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting, where both the sample size and the number of manifest…

广义极值分布最大似然估计的唯一性与全局最优性AI 解读

Summary The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit…

量化回归风险与公平性权衡的极小极大框架AI 解读

We propose a theoretical framework for the problem of learning a real-valued function which meets fairness requirements. This framework is built upon the notion of α-relative (fairness) improvement of the regression function which we introduce using the theory of optimal transport. Setting α=0 corresponds to the regression problem under the Demographic Parity constraint, while α=1 corresponds to the classical regression problem without any constraints. For α∈(0,1) the…

高维模型中平滑泛函的估计：自助链与高斯近似AI 解读

Let X(n) be an observation sampled from a distribution Pθ(n) with an unknown parameter θ, θ being a vector in a Banach space E (most often, a high-dimensional space of dimension d). We study the problem of estimation of f(θ) for a functional f:E↦R of some smoothness s>0 based on an observation X(n)∼Pθ(n). Assuming that there exists an estimator θˆn=θˆn(X(n)) of parameter θ such that n(θˆ n−θ) is sufficiently close in distribution to a mean zero Gaussian random vector in E,…

最小范数插值估计与正则化经验风险最小化的稳健性AI 解读

This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on the errors are imposed. A quantitative bound for the prediction error is given, relating it to the Rademacher complexity of the covariates, the norm of the minimum norm interpolator of the errors and the size of the subdifferential around…

二元响应下高维个体化阈值的非正则与极小极大估计AI 解读

Given a large number of covariates Z, we consider the estimation of a high-dimensional parameter θ in an individualized linear threshold θTZ for a continuous variable X, which minimizes the disagreement between sign(X−θTZ) and a binary response Y. While the problem can be formulated into the M-estimation framework, minimizing the corresponding empirical risk function is computationally intractable due to discontinuity of the sign function. Moreover, estimating θ even in the…

广义韧性与稳健统计AI 解读

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be maliciously corrupted in many other ways, such as systematic measurement errors and missing covariates. We consider corruption in either TV or Wasserstein distance, and show that robust estimation is possible whenever the true population distribution satisfies a property called generalized resilience, which holds under moment or hypercontractive…

线性最小二乘的精确极小极大风险与样本协方差矩阵的下尾AI 解读

We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order d/n in dimension d with n samples. Here, we study the minimax expected excess risk over the full linear class, depending on the distribution of covariates. First, the least squares estimator is exactly minimax optimal in the well-specified case, for every distribution of covariates. We express…

大样本协方差矩阵尖峰特征值与线性谱统计量的渐近独立性AI 解读

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are proportional to each other. As a byproduct, we also establish the central limit theorem of the leading sample spiked eigenvalues by removing the block diagonal assumption on the population covariance matrix, which is commonly needed in the…

对抗训练分类准确率的精确统计分析AI 解读

Despite the wide empirical success of modern machine learning algorithms and models in a multitude of applications, they are known to be highly susceptible to seemingly small indiscernible perturbations to the input data known as adversarial attacks. A variety of recent adversarial training procedures have been proposed to remedy this issue. Despite the success of such procedures at increasing accuracy on adversarially perturbed inputs or robust accuracy, these techniques…

最大似然估计鞍点近似的渐近精度AI 解读

The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of n unobserved i.i.d. terms, the basic classical result is that the relative error in the density is of order 1/n. If instead the approximation is interpreted as a likelihood and maximised as a function of model parameters, the result is an approximation to the maximum likelihood estimate…

未知方差下的分布式自适应高斯均值估计：交互协议有助于适应AI 解读

Distributed estimation of a Gaussian mean with unknown variance under communication constraints is studied. Necessary and sufficient communication costs under different types of distributed protocols are derived for any estimator that is adaptively rate-optimal over a range of possible values for the variance. Communication-efficient and statistically optimal procedures are developed. The analysis reveals an interesting and important distinction among different types of…

惩罚回归学习动态治疗方案的泛化误差界AI 解读

A dynamic treatment regime (DTR) is a sequence of decision rules, one per stage of intervention, that maps up-to-date patient information to a recommended treatment. Discovering an appropriate DTR for a given disease is a challenging issue especially when a large set of prognostic variables are observed. To address this problem, we propose penalized regression-based learning methods with l1 penalty to estimate the optimal DTR that would maximize the expected outcome if…

网络干扰下处理效应估计的随机图渐近理论AI 解读

The network interference model for treatment effect estimation places experimental units at the vertices of an undirected exposure graph, such that treatment assigned to one unit may affect the outcome of another unit if and only if these two units are connected by an edge. This model has recently gained popularity as means of incorporating interference effects into the Neyman–Rubin potential outcomes framework; and several authors have considered estimation of various…

二阶差分估计量的中心极限定理及波动率与强度应用AI 解读

In this paper, we introduce a general method for estimating the quadratic covariation of one or more spot parameter processes associated with continuous time semimartingales, and present a central limit theorem that has this class of estimators as one of its applications. The class of estimators we introduce, that we call Two-Scales Quadratic Covariation (TSQC) estimators, is based on sums of increments of second differences of the observed processes, and the intervals over…

变换群不变分布的极限定理AI 解读

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory implies a law of large numbers for such invariant distributions: If the group satisfies suitable conditions, expectations can be estimated by averaging over subsets of transformations, and these estimators are strongly consistent. We show that, if a mixing condition holds, the averages also…

含噪声与跳跃高频数据下波动率的波动估计及检验AI 解读

We establish a feasible central limit theorem with convergence rate n1/8 for the estimation of the integrated volatility of volatility (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The central limit theorem is applied to provide interval estimates of the VoV and conduct hypothesis tests. Furthermore, when one is interested in the null hypothesis that the VoV is zero, we show…

伪函数系数回归及基于边际积分的稳健推断AI 解读

Functional-coefficient cointegrating models have become popular to model nonlinear nonstationarity in econometrics (Cai et al., 2009; Xiao, 2009). However, there is rare study on testing the existence of functional-coefficient cointegration. Consequently, functional-coefficient regressions involving nonstationary regressors may be spurious. This paper investigates the effect that spurious functional-coefficient regression has on the model diagnostics. We find that common…

瞬时与积分协方差特征值结构的检验AI 解读

For vector Itô semimartingale dynamics, we derive the asymptotic distributions of likelihood-ratio-type test statistics for the purpose of identifying the eigenvalue structure of both integrated and spot covariance matrices estimated using high-frequency data. Unlike the existing approaches where the cross-section dimension grows to infinity, our tests do not necessarily require large cross-section and thus allow for a wide range of applications. The tests, however, are…

动态固定效应 logit 模型的变换与矩条件AI 解读

This study proposes transformations for dynamic fixed effects logit models. First, these transformations construct valid moment conditions for the case with neither explanatory variables nor time dummies. Using valid moment conditions, we can obtain the first-order condition of the conditional maximum likelihood estimator proposed by Chamberlain (1985). Next, we derive valid moment conditions based on the transformations for the cases with strictly exogenous continuous…

预测回归中的 LASSO 方法AI 解读

Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities of the LASSO methods in this predictive regression framework. In the presence of stationary, local unit root, and cointegrated predictors, we show that the adaptive LASSO cannot asymptotically eliminate all cointegrating variables with…

随机系数模型的非参数估计：弹性网方法AI 解读

This paper investigates and extends the computationally attractive nonparametric random coefficients estimator of Fox et al. (2011). We show that their estimator is a special case of the nonnegative LASSO, explaining its sparse nature observed in many applications. Recognizing this link, we extend the estimator, transforming it into a special case of the nonnegative elastic net. The extension improves the estimator’s recovery of the true support and allows for more accurate…

线性 GMM 的双重修正稳健方差估计量AI 解读

We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula also corrects the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005), which corrects the bias from estimating the efficient weight matrix, so is doubly corrected. An important feature of the proposed double correction is that…

含非参数内生效应的横截面互动模型之筛工具变量估计AI 解读

In this study, we consider cross-sectional interaction models including spatial autoregressive models and peer effects models as special cases. Our model allows the endogenous effect – the effect of others’ outcomes on one’s own outcome – to be nonlinear and nonparametric. For the model estimation, we propose a sieve instrumental variable estimator and establish both its consistency and asymptotic normality. Furthermore, we propose a nonparametric specification test for the…