论文检索

非参数众数回归AI 解读

Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of $Y$ and $X$. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and…

贝叶斯流形回归AI 解读

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a $d$-dimensional subspace with $d\ll D$. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally…

可能非唯一最优治疗策略下平均结局的统计推断AI 解读

We consider challenges that arise in the estimation of the mean outcome under an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular and asymptotically linear (RAL) estimator of the…

批量多臂老虎机问题AI 解读

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.

稀疏精度矩阵估计：最优收敛率与自适应估计AI 解读

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained $\ell_{1}$ minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces. The…

单指标与部分线性单指标积分模型的估计AI 解读

Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially…

通过低秩近似优化网络社区检测AI 解读

Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to find communities, which is computationally infeasible. Some fast spectral algorithms have been proposed for specific methods or models, but only on a case-by-case basis. Here, we propose a general approach for maximizing a function of a…

随机区块模型的拟合优度检验AI 解读

The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by subtracting the estimated block mean effect from the adjacency matrix. Asymptotic null distribution is obtained using recent advances in random matrix theory. The test is proved to have full power against alternative models…

超高维部分线性可加分位数回归AI 解读

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates…

因子模型中的投影主成分分析AI 解读

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor…

不同模型误设程度下变点模型的渐近理论AI 解读

Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate ($n$) and are asymptotically described by minimizers of a jump process. Under complete mis-specification by a smooth curve, that is, when a change-point model is…

相关误差回归中的最优设计AI 解读

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that…

含噪度数的推断：差分隐私 β 模型与合成图AI 解读

The $\beta$-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the $\beta$-model, and show that the MLE never exists for the degree partition $\beta$-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the…

半鞅跳跃活跃度的近最优估计AI 解读

In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimate of the jump activity, together with corresponding confidence intervals. Our estimate improves upon previous work, achieving near-optimal rates of…

双度序列维度增长的有向指数随机图模型渐近理论AI 解读

Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and…

具有影响点的函数型线性回归AI 解读

The paper considers functional linear regression, where scalar responses $Y_{1},\ldots,Y_{n}$ are modeled in dependence of i.i.d. random functions $X_{1},\ldots,X_{n}$. We study a generalization of the classical functional linear regression model. It is assumed that there exists an unknown number of “points of impact,” that is, discrete observation times where the corresponding functional values possess significant influences on the response variable. In addition to…

低密度区域的自适应估计及其支撑恢复应用AI 解读

A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a Hölder continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Some new type of risk bound with respect to a density-dependent standardized loss of this…

通过 Hilbert 空间变换开展密度函数的函数型数据分析AI 解读

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and, therefore, commonly used Hilbert space based methods of functional data analysis are not applicable. To address this problem, we introduce a transformation approach, mapping probability densities to a Hilbert space of functions through a…

利用高阶二次变差从不规则间距数据估计高斯随机场光滑度AI 解读

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field…

Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical…

稀疏协方差矩阵泛函的估计AI 解读

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other $\ell_{r}$ norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of…

超高维广义半变系数模型的模型选择与结构识别AI 解读

In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO…

模型误设下的自助法置信集AI 解读

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension $p$: the bootstrap approximation works if $p^{3}/n$ is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is…

高维 Spearman 秩相关矩阵的谱统计及其应用AI 解读

Let $\mathbf{Q}=(Q_{1},\ldots,Q_{n})$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let $\mathbf{Z}=(Z_{1},\ldots,Z_{n})$, where $Z_{j}$ is the mean zero variance one random variable obtained by centralizing and normalizing $Q_{j}$, $j=1,\ldots,n$. Assume that $\mathbf{X}_{i},i=1,\ldots,p$ are i.i.d. copies of $\frac{1}{\sqrt{p}}\mathbf{Z}$ and $X=X_{p,n}$ is the $p\times n$ random matrix with $\mathbf{X}_{i}$…