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匹配型平均处理效应估计量的高斯与自助法近似AI 解读

We establish Gaussian approximation bounds for covariate and rank-matching-based Average Treatment Effect (ATE) estimators. By analyzing these estimators through the lens of stabilization theory, we employ the Malliavin–Stein method to derive our results. Our bounds precisely quantify the impact of key problem parameters, including the number of matches and treatment balance, on the accuracy of the Gaussian approximation. Additionally, we develop multiplier bootstrap…

动态交互事件网络中的全局协变量效应检验AI 解读

In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the observation horizon. In addition, covariates are observed and the goal is to model the impact of the covariates on the interactions. We distinguish two types of covariates: global, system-wide covariates (i.e., covariates taking the same…

持久贝蒂数及其他稳定化统计量的自助法AI 解读

We investigate multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. The work relates to other general results in the area of stabilizing statistics, including central limit theorems for geometric and topological functionals of Poisson and binomial processes in the critical regime, where limit theorems prove difficult to use in practice, motivating the use of a bootstrap approach. A smoothed bootstrap…

高维与非欧几里得数据的多尺度几何特征提取及应用AI 解读

A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. Based on geometric considerations, we map each pair of data points into a real-valued feature function defined on the unit interval. Further statistical analysis is then based on the collection of feature functions. The potential of the method is illustrated by different applications, including classification and anomaly detection. Connections to other concepts, such as random…

非参数密度丝状结构估计的理论分析AI 解读

This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density $f$. Points on the filament are considered as local extrema of the density when traversing the support of $f$ along the integral curve driven by the vector field of second eigenvectors of the Hessian of $f$. We “parametrize” points on the filaments by such integral curves, and thus both the estimation of integral curves and of filaments will be considered…

时变自回归模型中波动方差函数的峰数识别AI 解读

In many applications, time series exhibit nonstationary behavior that might reasonably be modeled as a time-varying autoregressive (AR) process. In the context of such a model, we discuss the problem of testing for modality of the variance function. We propose a test of modality that is local and, when used iteratively, can be used to identify the total number of modes in a given series. This problem is closely related to peak detection and identification, which has…

基于最小体积集合与逆回归的多变量波动函数检验AI 解读

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii)Â of a bathtub shape, and (iii) in a given parametric form. The…

高斯局部平稳过程的非参数准最大似然估计AI 解读

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. Our results apply, in particular, to estimation under shape constraints. As…

基于超额质量泛函的局部平稳时间序列判别AI 解读

Discrimination of time series is an important practical problem with applications in various scientific fields. We propose and study a novel approach to this problem. Our approach is applicable to cases where time series in different categories have a different “shape.” Although based on the idea of feature extraction, our method is not distance-based, and as such does not require aligning the time series. Instead, features are measured for each time series, and…

随机过程的条件最小体积预测区域AI 解读

Motivated by interval/region prediction in nonlinear time series, we propose a minimum volume (MV) predictor for a strictly stationary process. The MV predictor varies with respect to the current position in the State space and has the minimum Lebesgue measure among all regions with the nominal coverage probability. We have established consistency, convergence rates, and asymptotic normality for both coverage probability and Lebesgue measure of the estimated MV predictor…

高维中的集中性与拟合优度：渐近分布无关方法AI 解读

A novel approach for constructing goodness-of-fit techniques in arbitrary finite dimensions is presented. Testing problems are considered as well as the construction of diagnostic plots. The approach is based on some new notions of mass concentration, and in fact, our basic testing problems are formulated as problems of ‘‘goodness-of-concentration.’’ It is this connection to concentration of measure that makes the approach conceptually simple. The presented test statistics…

轮廓估计、集中函数与序约束下的最大似然密度估计AI 解读

Based on empirical Lévy-type concentration functions, a new graphical representation of the ML-density estimator under order restrictions is given. This representation generalizes the well-known representation of the Grenander estimator of a monotone density as the slope of the least concave majorant of the empirical distribution function to higher dimensions and arbitrary order restrictions. From the given representation it follows that a density estimator called…

衡量概率质量集中与估计密度轮廓簇：超额质量方法AI 解读

By using empirical process theory, the so-called excess mass approach is studied. It can be applied to various statistical problems, especially in higher dimensions, such as testing for multimodality, estimating density contour clusters, estimating nonlinear functionals of a density, density estimation, regression problems and spectral analysis. We mainly consider the problems of testing for multimodality and estimating density contour clusters, but the other problems also…