论文检索

高维影响度量AI 解读

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the…

稀疏高斯图模型中的最优分类AI 解读

Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix $\Sigma$, where the precision matrix $\Omega=\Sigma^{-1}$ is unknown but is presumably sparse. The useful features, also unknown, are sparse and each contributes weakly (i.e., rare and weak) to the classification decision. By obtaining a reasonably good estimate of $\Omega$, we formulate…

平滑样条模型中的局部与全局渐近推断AI 解读

This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577–580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii)…

高维样本协方差矩阵特征向量经验谱分布的收敛速率AI 解读

The eigenvector Empirical Spectral Distribution (VESD) is adopted to investigate the limiting behavior of eigenvectors and eigenvalues of covariance matrices. In this paper, we shall show that the Kolmogorov distance between the expected VESD of sample covariance matrix and the Marčenko–Pastur distribution function is of order $O(N^{-1/2})$. Given that data dimension $n$ to sample size $N$ ratio is bounded between 0 and 1, this convergence rate is established under finite…

超高维非凸惩罚回归的校准AI 解读

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is…

量子态层析与含噪矩阵补全的渐近等价性AI 解读

Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for…

波动率过程秩的检验：随机扰动方法AI 解读

In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Itô semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Itô semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank…

非参数工具变量模型的准贝叶斯分析AI 解读

This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional assumption on the data generating process, we consider a quasi-likelihood induced from the conditional moment restriction, and put priors on the function-valued parameter. We call the resulting posterior quasi-posterior, which corresponds to…

排序算法的渐近理论AI 解读

We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which is rarely feasible in practice. Instead, individuals routinely provide partial preference information, such as pairwise comparisons of items, and…

假设检验中距离统计量与 RKHS 统计量的等价性AI 解读

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a…

高维度对有限样本的影响AI 解读

High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one. With the probabilistic view, we establish the concentration property and robust spark bound for large random design matrix generated from elliptical distributions, with the former related to the sure screening property and the latter…

完整参数空间上的经验似然AI 解读

We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90–120] by partitioning its domain into the collection of its contours and mapping the contours through a continuous sequence of similarity transformations onto the full parameter space. The resulting extended empirical likelihood is a natural generalization of the original empirical likelihood to the full parameter space; it has the same asymptotic properties and identically shaped contours as the original…

高维稀疏线性回归的近乎最优极小极大估计量AI 解读

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0

固定或增长维度下的协方差矩阵检验AI 解读

Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given…

高维正态分布经典似然比检验的中心极限定理AI 解读

For random samples of size $n$ obtained from $p$-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis, and their limiting distributions under the null hypothesis were proved to be chi-square distributions as $n$ goes to infinity and $p$ remains fixed. In this paper, we consider the…

高斯白噪声模型中的非参数 Bernstein–von Mises 定理AI 解读

Bernstein–von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact $1-\alpha$ frequentist coverage level and whose $L^{2}$-diameter shrinks at the minimax rate of convergence (within logarithmic factors)…

非平稳非对称 GARCH 模型的统计推断AI 解读

This paper considers the statistical inference of the class of asymmetric power-transformed $\operatorname{GARCH}(1,1)$ models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two…

随机分块模型最大似然估计及其变分近似的渐近正态性AI 解读

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the…

基于新量子似然比的量子局部渐近正态性AI 解读

We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.

边际经验似然与确定独立特征筛选AI 解读

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified…

大型稀疏网络社区检测的伪似然方法AI 解读

Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and…

波动率占用时间AI 解读

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a…

含测量误差的高维 Itô 过程稀疏波动率矩阵最优估计AI 解读

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Itô process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a…

高维稀疏主成分的最优检测AI 解读

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on…