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通过得分贡献符号翻转实现广义线性模型的稳健检验AI 解读

Summary Generalized linear models are often misspecified because of overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type I error rate control. We provide a novel semiparametric test, based on sign flipping individual score contributions. The parameter tested is allowed to be multi-dimensional and even high dimensional. Our test is often robust against the…

利用耦合构造无偏马尔可夫链蒙特卡洛方法AI 解读

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel. We discuss practical couplings for popular MCMC algorithms. We…

高维工具变量回归的统计推断AI 解读

This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear model for the dependent variable, we develop a novel adaptation of the parametric one-step update to a generic second-stage estimator. We provide conditions under which the scaled update is asymptotically normal. We then introduce a…

特征值的 Lasso 收缩AI 解读

Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

高维双重函数型图模型AI 解读

Summary We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a…

利用 K 近邻融合套索的自适应非参数回归AI 解读

Summary The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the $K$-nearest-neighbours fused lasso, involves computing the $K$-nearest-neighbours graph of the design points and then performing the fused lasso…

高维 Hotelling T² 检验的自适应推广AI 解读

We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling’s $T^{2}$. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the…

稀疏矩阵检测的统计与计算极限AI 解读

This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and columns are individually $k$-sparse. We provide a tight characterization of the statistical and computational limits for sparse matrix detection, which precisely describe when achieving optimal detection is easy, hard or impossible,…

条件独立性检验的困难与广义协方差度量AI 解读

It is a common saying that testing for conditional independence, that is, testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Valid statistical tests are required to have a size that is smaller than a pre-defined significance level, and different tests…

期望低秩随机矩阵的特征向量逐元素分析AI 解读

Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of bounds are available for average errors between empirical and population statistics of eigenvectors, few results are tight for entrywise analyses, which are critical for a number of problems such as community detection. This paper…

不依赖特定分布与相关结构的高维均值双样本检验AI 解读

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This two-sample test based on a nontrivial extension of the one-sample central limit theorem (Ann. Probab. 45 (2017) 2309–2352) provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment. In…

GRID：高维非参数回归的变量选择与结构发现方法AI 解读

We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical…

高维尖峰模型中的假设检验AI 解读

We consider the five classes of multivariate statistical problems identified by James (Ann. Math. Stat. 35 (1964) 475–501), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James’ problems involves the eigenvalues of $E^{-1}H$ where $H$ and $E$ are proportional to high-dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the…

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…

温度化后验及其变分近似的集中性AI 解读

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive data sets is often challenging, when possible at all. The classical MCMC algorithms are prohibitively slow when both the model dimension and the sample size are large. Variational Bayesian methods aim at approximating the posterior by a distribution in a tractable family $\mathcal{F}$. Thus, MCMC are replaced by an optimization algorithm which is orders of magnitude…

Knockoff 方法的稳健推断AI 解读

We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_{1},\ldots ,X_{p}$. We wish to do so while offering finite-sample guarantees about the fraction of false positives—selected variables $X_{j}$ that in fact have no effect on $Y$ after the other features are known. When the number of features $p$ is large (perhaps even larger than the sample size $n$), and we have no prior…

多维扩散过程漂移向量场的非参数统计推断AI 解读

The problem of determining a periodic Lipschitz vector field $b=(b_{1},\ldots ,b_{d})$ from an observed trajectory of the solution $(X_{t}:0\le t\le T)$ of the multi-dimensional stochastic differential equation \begin{equation*}dX_{t}=b(X_{t})\,dt+dW_{t},\quad t\geq 0,\end{equation*} where $W_{t}$ is a standard $d$-dimensional Brownian motion, is considered. Convergence rates of a penalised least squares estimator, which equals the maximum a posteriori (MAP) estimate…

直接插值：无岭惩罚核回归也能泛化AI 解读

In the absence of explicit regularization, Kernel “Ridgeless” Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable…

动态因子网络模型及其国际贸易应用AI 解读

We introduce a dynamic network model with probabilistic link functions that depend on stochastically time-varying parameters. We adopt a blockmodel framework and allow the high-dimensional vector of link probabilities to be a function of a low-dimensional set of dynamic factors. The resulting dynamic factor network model has a basic and transparent structure. However, parameter estimation, signal extraction of stochastic loadings and dynamic factors, and the econometric…

识别协整面板中的潜在分组模式AI 解读

We consider a panel cointegration model with latent group structures that allows for heterogeneous long-run relationships across groups. We extend Su, Shi, and Phillips (2016, Econometrica 84(6), 2215–2264) classifier-Lasso (C-Lasso) method to the nonstationary panels and allow for the presence of endogeneity in both the stationary and nonstationary regressors in the model. In addition, we allow the dimension of the stationary regressors to diverge with the sample size. We…

大型似不相关回归系统：惩罚准极大似然估计AI 解读

In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate…

存在出口时的企业生产率估计：中国制造业证据AI 解读

Summary Motivated by the long‐standing interest of economists in understanding the nexus between firm productivity and export behavior, this paper develops a novel structural framework for control‐function‐based nonparametric identification of the gross production function and latent firm productivity in the presence of endogenous export opportunities that is robust to recent unidentification critiques of proxy estimators. We provide a workable identification strategy,…

双重差分模型中的双重／去偏机器学习AI 解读

Summary This paper provides an orthogonal extension of the semiparametric difference-in-differences estimator proposed in earlier literature. The proposed estimator enjoys the so-called Neyman orthogonality (Chernozhukov et al., 2018), and thus it allows researchers to flexibly use a rich set of machine learning methods in the first-step estimation. It is particularly useful when researchers confront a high-dimensional data set in which the number of potential control…

高维时间序列的门限因子模型AI 解读

We consider a threshold factor model for high-dimensional time series in which the dynamics of the time series is assumed to switch between different regimes according to the value of a threshold variable. This is an extension of threshold modeling to a high-dimensional time series setting under a factor structure. Specifically, within each threshold regime, the time series is assumed to follow a factor model. The regime switching mechanism creates structural changes in the…