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一类局部与全局稳健的回归估计量AI 解读

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We…

Logistic 回归模型的先验 elicitation、变量选择与贝叶斯计算AI 解读

Summary Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived…

有限非平稳时间序列滤波的三种等价方法AI 解读

To estimate the components in an unobserved autoregressive integrated moving average components model, three different approaches can be used--Kalman filtering plus smoothing, Wiener-Kolmogorov filtering, and penalized least squares smoothing. It is shown, in the article, that the three approaches are equivalent. As an application, it is shown that any of the three approaches can be used to filter a series with the Hodrick-Prescott filter but that Wiener-Kolmogorov filtering…

事件历史分析的非参数乘法风险率模型AI 解读

A major issue in exploring and analyzing life history data with multiple states and events is the development and availability of flexible methods that allow simultaneous incorporation and estimation of baseline hazards, detection and modelling of nonlinear functional forms of covariates and time-varying effects, and the possibility to include time-dependent covariates. In this paper we consider a nonparametric multiplicative hazard model that takes into account these…

二元分位数平滑样条AI 解读

Summary It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as nonparametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used…

多元贝叶斯变量选择与预测AI 解读

Summary The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high…

混合采样方法综述AI 解读

A composite is formed by collecting multiple sample units and combining them in their entirety or in part, to form a new sample. The sample units that make up the composite may retain their integrity or be homogenized through physical processes such as ball milling, sieving, shaking, or centrifuging. One or more subsequent measurements are taken on the composite and the information on the sample units is lost. This counterintuitive loss of information has fueled opposition…

嵌套与交叉曲线样本分析的平滑样条模型AI 解读

We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized…

混合采样方法综述AI 解读

A composite is formed by collecting multiple sample units and combining them in their entirety or in part, to form a new sample. The sample units that make up the composite may retain their integrity or be homogenized through physical processes such as ball milling, sieving, shaking, or centrifuging. One or more subsequent measurements are taken on the composite and the information on the sample units is lost. This counterintuitive loss of information has fueled opposition…

变量选择后回归中的有效置信区间AI 解读

We consider a linear regression model with regression parameters (θ 1 ,...,θ p ) and error variance parameter σ 2 . Our aim is to find a confidence interval with minimum coverage probability 1 − α for a parameter of interest θ 1 in the presence of nuisance parameters (θ 2 ,...,θ p ,σ 2 ). We consider two confidence intervals, the first of which is the standard confidence interval for θ 1 with coverage probability 1 − α. The second confidence interval for θ 1 is obtained…

纵向数据的半参数随机混合模型AI 解读

We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting…

识别多元时间序列模型的统一方法AI 解读

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

现代回归方法AI 解读

This new edition of Regression Methods has been updated and enhanced to include all-new information on the latest advances and research in the evolving field of regression analysis. It provides a unique treatment of fundamental regression methods, such as diagnostics, transformations, robust regression, and ridge regression. Unifying key concepts and procedures, this new edition emphasizes applications to provide a more hands-on and comprehensive understanding of regression…

多元时间序列模型识别的统一方法AI 解读

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

局部平稳过程的自适应协方差估计AI 解读

It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a "best" local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal…

混合效应平滑样条方差分析AI 解读

Summary We propose a general family of nonparametric mixed effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a…

二阶导数函数型回归及其近红外光谱应用AI 解读

Summary A linear regression method to predict a scalar from a discretized smooth function is presented. The method takes into account the functional nature of the predictors and the importance of the second derivative in spectroscopic applications. This motivates a functional inner product that can be used as a roughness penalty. Using this inner product, we derive a linear prediction method that is similar to ridge regression but with different shrinkage characteristics. We…

专利数据分析：混合泊松回归模型方法AI 解读

Count-data models are used to analyze the relationship between patents and research and development spending at the firm level, accounting for overdispersion using a finite mixed Poisson regression model with covariates in both Poisson rates and mixing probabilities. Maximum likelihood estimation using the EM and quasi-Newton algorithms is discussed. Monte Carlo studies suggest that (a) penalized likelihood criteria are a reliable basis for model selection and can be used to…

专利数据分析：混合泊松回归模型方法AI 解读

Count-data models are used to analyze the relationship between patents and research and development spending at the firm level, accounting for overdispersion using a finite mixed Poisson regression model with covariates in both Poisson rates and mixing probabilities. Maximum likelihood estimation using the EM and quasi-Newton algorithms is discussed. Monte Carlo studies suggest that (1) penalized likelihood criteria are a reliable basis for model selection and can be used to…

论筛法与惩罚法AI 解读

We develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates (MLE's) in parametric, semiparametric and nonparametric models. We find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices: the degree of smoothness of the functional and the local size of the underlying parameter space. We show that when the local size of…

核不完全已知的反卷积及其在 FDG PET 血液曲线建模中的应用AI 解读

Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the…

卷积核未完全确定时的反卷积及其在 FDG PET 血液曲线建模中的应用AI 解读

Camouflaged deconvolution arises when the kernel in a simple convolution model is not completely specified. We consider a situation in which the same fixed signal is repeatedly measured by separate convolutions with imprecisely known kernels. We develop a regularization methodology for application to these problems. The method involves simultaneous estimation of the target signal and the unknown parameters of the convolution kernels. Cross-validation is used to determine the…

CART 与最佳正交基：一种联系AI 解读

We study what we call "dyadic CART" --a method of nonparametric regression which constructs a recursive partition by optimizing a complexity penalized sum of squares, where the optimization is over all recursive partitions arising from midpoint splits. We show that the method is adaptive to unknown degrees of anisotropic smoothness. Specifically, consider the anisotropic smoothness classes of Nikoľskii, consisting of bivariate functions $f(x_1, x_2)$ whose finite difference…

广义半线性模型的有效估计AI 解读

The generalized semilinear model (GSLIM) extends the generalized linear model by allowing the addition of an unknown smooth function to the predictor parameter, producing a semiparametric model. Some previously proposed score-based estimators for the parametric component in this model are not √n consistent. We propose efficient estimators for both the parametric and nonparametric components of the GSLIM. The estimator for the parametric component is the solution to an…