Nonparametric Density Estimation: The L 1 View.
非参数密度估计:L1 视角AI 解读 ↓
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非参数密度估计:L1 视角AI 解读 ↓
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Differentiation of Integrals Consistency Lower Bounds for Rates of Convergence Rates of Convergence in L1 The Automatic Kernel Estimate: L1 and Pointwise Convergence Estimates Related to the Kernel Estimate and the Histogram Estimate Simulation, Inequalities, and Random Variate Generation The Transformed Kernel Estimate Applications in Discrimination Operations on Density Estimates Estimators Based on Orthogonal Series Index.
当处理发生溢出:时空因果效应估计的神经网络框架
Real-world public health policies are often enacted by local jurisdictions, but their effects can ripple through connected populations. For causal evaluation, this creates a difficult spatiotemporal problem: intermittent policy updates create path-level treatments, and because spillover depends on neighboring treatment paths along with the focal-unit's own history, controlling time-varying confounding requires high-dimensional, multimodal information from both sources. To…
ARMA 过程谱密度函数的分解
Quasi-periodic oscillations are characterized by fitting Lorentzian functions to a nonparametric estimate of the power spectral density, a two-step procedure that separates estimation from modeling and does not accommodate measurement error. We develop a parametric alternative based on autoregressive moving-average (ARMA) processes observed with measurement error. We derive an exact decomposition of the ARMA spectral density into real-valued components, one for each class of…
异质性高维分位数回归的全局推断
Quantile regression has received considerable attention in high dimensional methodology due to its robustness and ability to accommodate heteroskedasticity. Despite this attention, current inferential methods for high dimensional quantile regression have significant limitations---only testing significance, testing at a single quantile at a time, or assuming homoskedasticity. To generalize the inferences that can be drawn in high dimensional quantile regression, we introduce…
Uniform confidence bands are widely used in empirical analysis for uncertainty qualification of nonparametric inference of unknown functions. A variety of simple implementation methods, including multiplier bootstrap, have been proposed and theoretically justified. However, an implementation over a literally continuous index set is generally computationally infeasible, and practitioners therefore compute the critical value by evaluating the statistic on a finite evaluation…
RBF 核高斯过程最大似然估计的精确渐近理论
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…
半监督核岭 Fréchet 回归
Fréchet regression provides a framework for predicting random object-valued responses by minimizing the conditional expected squared distances. We propose semi-supervised kernel ridge Fréchet regression (SS-KRFR) to exploit unlabeled covariates when labeled samples are scarce. The method learns kernel spectral features from both labeled and unlabeled covariates, then utilizes labeled responses to estimate the conditional Fréchet function by kernel ridge regression. We derive…