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密度估计的平滑惩罚反卷积方法AI 解读

This article addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the contaminated observations and minimizes a reconstruction error penalized by an integrated squared mth derivative. Theory for deconvolution has mainly focused on kernel- or wavelet-based techniques, but other methods including…

基于分位数的众数回归自助法推断AI 解读

In this article, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian…

动态收缩过程AI 解读

Summary We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such…

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…

稀疏采样数据的函数自回归AI 解读

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with nonnegligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation…

贝叶斯多变量函数型动态线性模型AI 解读

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data—functional, time dependent, and multivariate components—we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the…

允许多领域归属的多结果贝叶斯模型：塞舌尔儿童发展研究AI 解读

The Seychelles Child Development Study (SCDS) examines the effects of prenatal exposure to methylmercury on the functioning of the central nervous system. The SCDS data include 20 outcomes measured on 9-year old children that can be classified broadly in four outcome classes or "domains": cognition, memory, motor, and social behavior. Previous analyses and scientific theory suggest that these outcomes may belong to more than one of these domains, rather than only a single…

快速二维 P 样条：三明治平滑器AI 解读

Summary We propose a fast penalized spline method for bivariate smoothing. Univariate P-spline smoothers are applied simultaneously along both co-ordinates. The new smoother has a sandwich form which suggested the name ‘sandwich smoother’ to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the…

异方差测量误差下的密度估计AI 解读

We consider density estimation when the variable of interest is subject to heteroscedastic measurement error. The density is assumed to have a smooth but unknown functional form that we model with a penalized mixture of B-splines. We treat the situation in which multiple mismeasured observations of each variable of interest are observed for at least some of the subjects, and the measurement error is assumed to be additive and normal. The measurement error variance function…

关于条件生长曲线方法的讨论AI 解读

Overview.Wei and He are to be congratulated on an innovative and important article.The conditional approach to growth charts described in their article is important in a practical sense, and the use of quantile regression is both natural and well motivated.We look forward to further application of their idea to actual practice, because the concept of "falling behind" in one's growth cycle has two meanings: the usual standard growth chart, and the conditional growth chart…

惩罚样条的精确似然比检验AI 解读

Penalised-spline-based additive models allow a simple mixed model representation where the variance components control departures from linear models. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose exactlikelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines.…

We consider regression when the predictor is measured with error and an instrumental variable (IV) is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identifiability. In addition, we exploit a characterization of the IV estimator as a…

摘要暂缺

用半参数惩罚样条估计公司债利率期限结构AI 解读

This article provides a new methodology for estimating the term structure of corporate debt using a semiparametric penalized spline model. The method is applied to a case study of AT&T bonds. Typically, very few data are available on individual corporate bond prices, too little to find a nonparametric estimate of term structure from these bonds alone. This problem is solved by “borrowing strength” from Treasury bond data. More specifically, we combine a nonparametric model…

局部多项式回归与模拟外推AI 解读

Summary The paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski's simulation–extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses SIMEX's particular estimation method and considers higher…

单一方差分量线性混合模型中的似然比检验AI 解读

Summary We consider the problem of testing null hypotheses that include restrictions on the variance component in a linear mixed model with one variance component and we derive the finite sample and asymptotic distribution of the likelihood ratio test and the restricted likelihood ratio test. The spectral representations of the likelihood ratio test and the restricted likelihood ratio test statistics are used as the basis of efficient simulation algorithms of their null…

部分线性单指标模型的惩罚样条估计AI 解读

Single-index models are potentially important tools for multivariate nonparametric regression. They generalize linear regression by replacing the linear combination α0Tx with a nonparametric component, η0(α0Tx), where η0(·) is an unknown univariate link function. By reducing the dimensionality from that of a general covariate vector x to a univariate index α0Tx, single-index models avoid the so-called “curse of dimensionality.” We propose penalized spline (P-spline)…

测量误差问题中的贝叶斯平滑样条与回归样条AI 解读

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and…

摘要暂缺

加性模型拟合的全自动带宽选择方法AI 解读

This article describes a fully automated bandwidth selection method for additive models that is applicable to the widely used backfitting algorithm of Buja, Hastie, and Tibshirani. The proposed plug-in estimator is an extension of the univariate local linear regression estimator of Ruppert, Sheather, and Wand and is shown to achieve the same Op (n –2/7) relative convergence rate for bivariate additive models. If more than two covariates are present, theoretical justification…

局部估计方程AI 解读

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric estimators of a “parameter” depending on a predictor. The nonparametric component is estimated via local polynomials with loess or kernel weighting; asymptotic theory is derived for the…

局部多项式回归与密度估计的经验偏差带宽AI 解读

A data-based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials. The estimator, called the empirical-bias bandwidth selector (EBBS), is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function. EBBS minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term. The variance term used is exact, not asymptotic, though it…

利用局部多项式回归拟合二元加性模型AI 解读

While the additive model is a popular nonparametric regression method, many of its theoretical properties are not well understood, especially when the backfitting algorithm is used for computation of the estimators. This article explores those properties when the additive model is fitted by local polynomial regression. Sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given. Asymptotic approximations to the…

回归模型两侧的非参数变换AI 解读

SUMMARY One way to model heteroscedasticity and skewness of the error distribution in regression is to transform both sides of the regression equation. If it is possible to transform the regression equation to result in normally distributed errors, then we can obtain more efficient parameter estimates and valid prediction intervals. One problem with this approach is that the choice of transformation is usually restricted to the power or shifted power family. Often there is…