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通过信号压缩进行函数对函数线性回归AI 解读

We consider functional linear regression models with a functional response and multiple functional predictors, with the goal of finding the best finite-dimensional approximation to the signal part of the response function. Defining the integrated squared correlation coefficient between a random variable and a random function, we propose to solve a penalized generalized functional eigenvalue problem, whose solutions satisfy that projections on the original predictors generate…

基于分位数偏相关的变量筛选AI 解读

In quantile linear regression with ultra-high dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables…

基于分组正交贪婪算法的阈值估计AI 解读

A threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude-dependent frequencies. Statistical inference for the TAR model encounters a major difficulty in the estimation of thresholds, however. This article develops an efficient procedure to estimate the thresholds. The procedure first transforms multiple-threshold detection to a regression variable selection…

基于上确界范数误差率的高维模型精细阈值检测AI 解读

We propose a new estimator, the thresholded scaled Lasso, in high-dimensional threshold regressions. First, we establish an upper bound on the ℓ∞ estimation error of the scaled Lasso estimator of Lee, Seo, and Shin. This is a nontrivial task as the literature on high-dimensional models has focused almost exclusively on ℓ1 and ℓ2 estimation errors. We show that this sup-norm bound can be used to distinguish between zero and nonzero coefficients at a much finer scale than…

基于距离相关的高维多响应回归交互项筛选AI 解读

Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identification method, called the interaction pursuit via distance correlation (IPDC), in the setting of high-dimensional multi-response interaction models that…

基于均值、空间符号与空间秩的高维数据检验AI 解读

Tests based on mean vectors and spatial signs and ranks for a zero mean in one-sample problems and for the equality of means in two-sample problems have been studied in the recent literature for high-dimensional data with the dimension larger than the sample size. For the above testing problems, we show that under suitable sequences of alternatives, the powers of the mean-based tests and the tests based on spatial signs and ranks tend to be same as the data dimension tends…

部分混合过程与动力系统的Bernstein型不等式及其学习应用AI 解读

We establish a Bernstein-type inequality for a class of stochastic processes that includes the classical geometrically $\phi$-mixing processes, Rio’s generalization of these processes and many time-discrete dynamical systems. Modulo a logarithmic factor and some constants, our Bernstein-type inequality coincides with the classical Bernstein inequality for i.i.d. data. We further use this new Bernstein-type inequality to derive an oracle inequality for generic regularized…

稀疏高维环境下从观测数据估计联合干预效应AI 解读

We consider the estimation of joint causal effects from observational data. In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown linear structural equation model with independent errors. We derive asymptotic variances of our estimators when the underlying causal structure is partly known, as well as high-dimensional consistency…

高维线性回归置信区间的极小极大速率与自适应性AI 解读

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high-dimensional linear regression with random design. We first establish the convergence rates of the minimax expected length for confidence intervals in the oracle setting where the sparsity parameter is given. The focus is then on the problem of adaptation to sparsity for the construction of confidence intervals. Ideally, an adaptive confidence interval…

依赖条件下恢复高维均值稀疏差异的速率最优方法AI 解读

The paper considers the problem of recovering the sparse different components between two high-dimensional means of column-wise dependent random vectors. We show that dependence can be utilized to lower the identification boundary for signal recovery. Moreover, an optimal convergence rate for the marginal false nondiscovery rate (mFNR) is established under dependence. The convergence rate is faster than the optimal rate without dependence. To recover the sparse signal…

高维稳健 M 估计量的一致性与渐近正态性AI 解读

We study theoretical properties of regularized robust $M$-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates. We first establish a form of local statistical consistency for the penalized regression estimators under fairly mild conditions on the error distribution: When the derivative of the loss function is bounded and satisfies a local…

Hilbert 空间中几何中位数的在线估计：非渐近置信球AI 解读

Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with very large samples of high dimensional data. The collected data may be contaminated by noise so that robust location indicators, such as the geometric median, may be preferred to the mean. In this context, an estimator of the geometric median based on a fast and efficient averaged nonlinear stochastic gradient algorithm has been developed by…

利用特征函数的有效估计AI 解读

The method of moments procedure proposed by Carrasco and Florens (2000) permits full exploitation of the information contained in the characteristic function and yields an estimator which is asymptotically as efficient as the maximum likelihood estimator. However, this estimation procedure depends on a regularization or tuning parameter α that needs to be selected. The aim of the present paper is to provide a way to optimally choose α by minimizing the approximate mean…

城市犯罪时空面板计数模型的似然推断与预测AI 解读

Summary We develop a panel count model with a latent spatio‐temporal heterogeneous state process for monthly severe crimes at the census‐tract level in Pittsburgh, Pennsylvania. Our dataset combines Uniform Crime Reporting data with socio‐economic data. The likelihood is estimated by efficient importance sampling techniques for high‐dimensional spatial models. Estimation results confirm the broken‐windows hypothesis whereby less severe crimes are leading indicators for…

经验贝叶斯棒球再论：纵向数据的经验贝叶斯方法AI 解读

Summary Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A recent convex optimization reformulation of the nonparametric maximum likelihood estimator of Kiefer and Wolfowitz ( Annals of Mathematical Statistics 1956; 27 : 887–906) is employed to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with an application to predict baseball batting averages, and the age…

利用随机变分不等式技术构造 Lasso 置信区间与置信区域AI 解读

Summary Sparse regression techniques have been popular in recent years because of their ability in handling high dimensional data with built-in variable selection. The lasso is perhaps one of the most well-known examples. Despite intensive work in this direction, how to provide valid inference for sparse regularized methods remains a challenging statistical problem. We take a unique point of view of this problem and propose to make use of stochastic variational inequality…

利用形状约束估计思想检验线性回归模型AI 解读

Summary A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non-parametric double-cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of…

混合数据的高维半参数潜在图模型AI 解读

Summary We propose a semiparametric latent Gaussian copula model for modelling mixed multivariate data, which contain a combination of both continuous and binary variables. The model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the Gaussian copula distribution. The goal is to infer the conditional independence relationship between the latent random variables, based on the observed mixed data. Our work has two main…

高维门限因子模型的最小二乘估计AI 解读

This paper studies large dimensional factor models with threshold-type regime shifts in the loadings. We estimate the threshold by concentrated least squares, and factors and loadings by principal components. The estimator for the threshold is superconsistent, with convergence rate that depends on the time and cross-sectional dimensions of the panel, and it does not affect the estimator for factors and loadings: this has the same convergence rate as in linear factor models.…

面板数据平均处理效应估计：渐近理论与实施AI 解读

Hsiao, Ching and Wan (2012) propose a novel method to estimate the average treatment effect using panel data. In this paper, we accomplish the following: (i) We relax some of the distributional assumptions made in HCW and show that the HCW method works for a much wider range of data generating processes; (ii) We derive the asymptotic distribution of HCW’s average treatment effect estimator which facilitates inference; (iii) When there exists a large number of control units,…

结构不稳定高维因子模型的识别与估计AI 解读

This paper tackles the identification and estimation of a high dimensional factor model with unknown number of latent factors and a single break in the number of factors and/or factor loadings occurring at unknown common date. First, we propose a least squares estimator of the change point based on the second moments of estimated pseudo factors and show that the estimation error of the proposed estimator is Op(1). We also show that the proposed estimator has some degree of…

利用最大交叉相关检验高维白噪声AI 解读

SUMMARY We propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series. Based on an approximation by the $L_\infty$-norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing departure from white noise that is not…

具有半参数相关效应的惩罚分位数回归：异质性偏好应用AI 解读

Summary This paper proposes new ℓ 1 ‐penalized quantile regression estimators for panel data, which explicitly allows for individual heterogeneity associated with covariates. Existing fixed‐effects estimators can potentially suffer from three limitations which are overcome by the proposed approach: (i) incidental parameters bias in nonlinear models with large N and small T ; (ii) lack of efficiency; and (iii) inability to estimate the effects of time‐invariant regressors. We…

高维尖峰 Fisher 矩阵的极端特征值及其应用AI 解读

Consider two $p$-variate populations, not necessarily Gaussian, with covariance matrices $\Sigma_{1}$ and $\Sigma_{2}$, respectively. Let $S_{1}$ and $S_{2}$ be the corresponding sample covariance matrices with degrees of freedom $m$ and $n$. When the difference $\Delta$ between $\Sigma_{1}$ and $\Sigma_{2}$ is of small rank compared to $p,m$ and $n$, the Fisher matrix $S:=S_{2}^{-1}S_{1}$ is called a spiked Fisher matrix. When $p,m$ and $n$ grow to infinity proportionally,…