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通过凸层级惩罚实现自适应截断的非参数回归AI 解读

SUMMARY We consider the problem of nonparametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when…

贝叶斯分数后验AI 解读

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback–Leibler (KL) neighborhood of the true parameter (or the KL divergence…

中等高维核机器中的特征剔除AI 解读

We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed…

We study the problem of nonparametric estimation under $\mathbb{L}_{p}$-loss, $p\in[1,\infty)$, in the framework of the convolution structure density model on $\mathbb{R}^{d}$. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. The original pointwise selection rule from a family of “kernel-type” estimators is proposed. For the selected estimator, we prove an $\mathbb{L}_{p}$-norm…

通过矩阵补全进行函数型数据分析AI 解读

Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony…

分段局部平稳误差下的自助辅助单位根检验AI 解读

In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to…

用于处理比较的倾向得分惩罚样条方法AI 解读

Valid causal inference from observational studies requires controlling for confounders. When time-dependent confounders are present that serve as mediators of treatment effects and affect future treatment assignment, standard regression methods for controlling for confounders fail. Similar issues also arise in trials with sequential randomization, when randomization at later time points is based on intermediate outcomes from earlier randomized assignments. We propose a…

多元时间序列的自适应贝叶斯时频分析AI 解读

This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to evolve differently over time. Local spectra within segments are fit through Whittle likelihood based penalized spline models of modified Cholesky components, which provide…

小角 X 射线散射实验中回转半径的最小均方误差估计AI 解读

Small-angle X-ray scattering (SAXS) is a technique that yields low-resolution structural information of biological macromolecules by exposing a large ensemble of molecules in solution to a powerful X-ray beam. The beam interacts with the molecules and the intensity of the scattered beam is recorded on a detector plate. The radius of gyration for a molecule, which is a measure of the spread of its mass, can be estimated from the lowest scattering angles of SAXS data. This…

基于最大似然的线性非高斯成分分析AI 解读

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis (PCA) is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a…

非参数时变系数模型中的贝叶斯带宽估计AI 解读

Bandwidth plays an important role in determining the performance of nonparametric estimators, such as the local constant estimator. In this article, we propose a Bayesian approach to bandwidth estimation for local constant estimators of time-varying coefficients in time series models. We establish a large sample theory for the proposed bandwidth estimator and Bayesian estimators of the unknown parameters involved in the error density. A Monte Carlo simulation study shows…

带状时空自回归模型AI 解读

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and…

函数型时间序列的筛自助法AI 解读

A bootstrap procedure for functional time series is proposed which exploits a general vector autoregressive representation of the time series of Fourier coefficients appearing in the Karhunen–Loève expansion of the functional process. A double sieve-type bootstrap method is developed, which avoids the estimation of process operators and generates functional pseudo-time series that appropriately mimics the dependence structure of the functional time series at hand. The method…

流形设定下的全局思考与局部拟合：局部线性嵌入的渐近分析AI 解读

Since its introduction in 2000, Locally Linear Embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of LLE under the manifold setup. We show that for a general manifold, asymptotically we may not obtain the Laplace–Beltrami operator, and the result may depend on nonuniform sampling unless a correct regularization is chosen. We also derive the corresponding kernel function, which indicates that LLE is not a Markov process. A comparison…

各向异性函数类上遍历扩散的不变密度自适应估计AI 解读

Consider some multivariate diffusion process $\mathbf{X}=(X_{t})_{t\geq0}$ with unique invariant probability measure and associated invariant density $\rho$, and assume that a continuous record of observations $X^{T}=(X_{t})_{0\leq t\leq T}$ of $\mathbf{X}$ is available. Recent results on functional inequalities for symmetric Markov semigroups are used in the statistical analysis of kernel estimators $\widehat{\rho}_{T}=\widehat{\rho}_{T}(X^{T})$ of $\rho$. For the basic…

变平面Cox模型AI 解读

We propose a projection pursuit technique in survival analysis for finding lower-dimensional projections that exhibit differentiated survival outcome. This idea is formally introduced as the change-plane Cox model, a non-regular Cox model with a change-plane in the covariate space dividing the population into two subgroups whose hazards are proportional. The proposed technique offers a potential framework for principled subgroup discovery. Estimation of the change-plane is…

非线性协整回归的模型检验AI 解读

Using the marked empirical processes, this paper develops a test of parametric specification in a nonlinear cointegrating regression model. Unlike the kernel-smoothed U-statistic considered in Gao et al. (2009) and Wang and Phillips (2012), our new test statistic avoids the use of bandwidth, which has some advantages for practitioners. Simulations and a real data example show that our new test has a good finite sample performance. Other contributions of this paper are to…

非参数两步筛 M 估计与推断AI 解读

This article studies two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root- n estimable. The asymptotic variance may…

利用加权经验过程检验非参数回归中的异方差AI 解读

Summary Heteroscedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroscedasticity for the non-parametric regression model with multiple covariates. It is based on a suitable residual-based empirical distribution function. The residuals are constructed by using local polynomial smoothing. Our test statistic involves a ‘detection function’ that can verify heteroscedasticity by exploiting just the…

高频股票价格变动的动态离散 Copula 模型AI 解读

Summary We develop a dynamic model for the intraday dependence between discrete stock price changes. The conditional copula mass function for the integer tick‐size price changes has time‐varying parameters that are driven by the score of the predictive likelihood function. The marginal distributions are Skellam and also have score‐driven time‐varying parameters. We show that the integration steps in the copula mass function for large dimensions can be accurately approximated…

函数数据的非参数图模型及其功能磁共振脑网络应用AI 解读

We introduce a nonparametric graphical model whose observations on vertices are functions. Many modern applications, such as electroencephalogram and functional magnetic resonance imaging (fMRI), produce data are of this type. The model is based on additive conditional independence (ACI), a statistical relation that captures the spirit of conditional independence without resorting to multi-dimensional kernels. The random functions are assumed to reside in a Hilbert space. No…

纵向与稀疏函数数据中非参数均值和协方差函数的有效估计AI 解读

We consider the estimation of mean and covariance functions for longitudinal and sparse functional data by using the full quasi-likelihood coupling a modification of the local kernel smoothing method. The proposed estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient in terms of their linear functionals. Their superiority to the competitors is further illustrated numerically through simulation studies. The method is applied to analyze…

带变量选择的贝叶斯近似核回归AI 解读

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coefficients. In this paper, we propose a novel framework that provides an effect size analog for each explanatory variable in Bayesian kernel regression models when…

再生核希尔伯特空间下的最优惩罚函数对函数回归AI 解读

Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these studies. Motivated from two real-life examples, we present in this paper a function-on-function regression model that can be used to analyze such kind of functional data. Our estimator of the 2D coefficient function is the optimizer of a form…