论文检索

多元判别分析与最大惩罚似然密度估计AI 解读

SUMMARY A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f̂ = Bπ of the true density f, where B is a stochastic operator and π is the raw histogram. Then, we investigate the…

变量选择的影响：贝叶斯诊断视角AI 解读

Variable selection is ubiquitous in statistical practice. Forward selection, backwards elimination, or a combination thereof are among the most popular techniques. Statistical texts teach direct interpretation of coefficients after variable selection. For scientific purposes, the desired interpretation is unconditional on the variable selection. In this article an influence analysis of variable selection is performed from a Bayesian viewpoint. Variable selection is shown to…

单一离散分量广义线性混合模型的偏差校正AI 解读

General expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component, in generalised linear mixed models with canonical link function and a single source of extraneous variation. The estimators involve first and second order Laplace expansions of the integrated likelihood and a related procedure known as penalised quasi-likelihood. Numerical studies of a series…

线性模型中的一致变量选择AI 解读

A method of estimating linear model dimension and variable selection is proposed. This new criterion, which generalizes the Cp criterion, the Akaike information criterion (AIC), the Bayes information criterion, and the phiv criterion and is consistent under certain conditions, is based on a new class of penalty functions and a procedure of sorting covariates based on t-statistics. In the course of introducing this method, we discuss the important role of the penalty function…

单一离散度分量广义线性混合模型的偏差校正AI 解读

General expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component, in generalised linear mixed models with canonical link function and a single source of extraneous variation. The estimators involve first and second order Laplace expansions of the integrated likelihood and a related procedure known as penalised quasi-likelihood. Numerical studies of a series…

逆问题中的最大平滑似然密度估计AI 解读

We consider the problem of estimating a pdf $f$ from samples $X_1, X_2, \ldots, X_n$ of a random variable with pdf $\mathscr{K}f$, where $\mathscr{K}$ is a compact integral operator. We employ a maximum smoothed likelihood formalism inspired by a nonlinearly smoothed version of the EMS algorithm of Silverman, Jones, Wilson and Nychka. We show that this nonlinearly smoothed algorithm is itself an EM algorithm, which helps explain the strong convergence properties of the…

二元核回归的带宽选择器AI 解读

SUMMARY For two and higher dimensional kernel regression, currently available bandwidth selection procedures are based on cross-validation or related penalizing ideas. However, these techniques have been shown to suffer from high sample variability and, in addition, can sometimes be difficult to implement when a vector of bandwidths needs to be selected. In this paper we propose a selector based on an iterative plug-in approach for bivariate kernel regression. It is shown to…

多元回归的风险膨胀准则AI 解读

A new criterion is proposed for the evaluation of variable selection procedures in multiple regression. This criterion, which we call the risk inflation, is based on an adjustment to the risk. Essentially, the risk inflation is the maximum increase in risk due to selecting rather than knowing the "correct" predictors. A new variable selection procedure is obtained which, in the case of orthogonal predictors, substantially improves on AIC, $C_p$ and BIC and is close to…

通过 EM 算法获得的最大惩罚似然估计的方差AI 解读

SUMMARY We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The solution proposed represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed by Meng and Rubin that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping…

基于惩罚 Whittle 似然的非参数谱密度估计AI 解读

The penalized likelihood approach is not well developed in time series analysis, even though it has been applied successfully in a number of nonparametric function estimation problems. Chow and Grenander proposed a penalized likelihood-type approach to the nonparametric estimation of the spectral density of Gaussian processes. In this article this estimator is extended to more general stationary processes, its practical implementation is developed in some detail, and some…

This paper describes a dynamic or state-space approach for analyzing discrete time or grouped survival data. Simultaneous estimation of baseline hazard functions and of time-varying covariate effects is based on maximization of posterior densities or, equivalently, a penalized likelihood, leading to Kalman-type smoothing algorithms. Data-driven choice of unknown smoothing parameters is possible via an EM-type procedure. The methods are illustrated by applications to real…

像素平均后错位图像的位移估计AI 解读

In problems where the recorded signal comprises two or more bands (i.e., wavelengths), it is often the case that the bands are not perfectly aligned in the focal plane. Such misregistration may be caused by atmospheric or oceanographic effects, which refract different bands to differing degrees, or it may result from features of the design of the recording equipment. This article develops two methods for estimating the lag, or the amount by which the bands are out of…

偏最小二乘法的一种解释AI 解读

Univariate partial least squares (PLS) is a method of modeling relationships between a Y variable and other explanatory variables. It may be used with any number of explanatory variables, even far more than the number of observations. A simple interpretation is given that shows the method to be a straightforward and reasonable way of forming prediction equations. Its relationship to multivariate PLS, in which there are two or more Y variables, is examined, and an example is…

存在不可忽略无回答的分类数据模型AI 解读

When categorical outcomes are subject to nonignorable nonresponse, log-linear models may be used to adjust for the nonresponse. The models are fitted to the data in an augmented frequency table in which one index corresponds to whether or not the subject is a respondent. The likelihood function is maximized over pseudo-observed cell frequencies with respect to this log-linear model using an EM algorithm. Each E step of the EM algorithm determines the pseudo-observed cell…

错位且经像素平均的图像中的位移估计AI 解读

In problems where the recorded signal comprises two or more bands (i.e., wavelengths), it is often the case that the bands are not perfectly aligned in the focal plane. Such misregistration may be caused by atmospheric or oceanographic effects, which refract different bands to differing degrees, or it may result from features of the design of the recording equipment. This article develops two methods for estimating the lag, or the amount by which the bands are out of…

离散时间生存数据的动态建模与惩罚似然估计AI 解读

This paper describes a dynamic or state-space approach for analyzing discrete time or grouped survival data. Simultaneous estimation of baseline hazard functions and of time-varying covariate effects is based on maximization of posterior densities or, equivalently, a penalized likelihood, leading to Kalman-type smoothing algorithms. Data-driven choice of unknown smoothing parameters is possible via an EM-type procedure. The methods are illustrated by applications to real…

非线性加性 ARX 模型AI 解读

We consider in this article a class of nonlinear additive autoregressive models with exogenous variables for nonlinear time series analysis and propose two modeling procedures for building such models. The procedures proposed use two backfitting techniques (the ACE and BRUTO algorithms) to identify the nonlinear functions involved and use the methods of best subset regression and variable selection in regression analysis to determine the final model. Simulated and real…

通过Gibbs采样进行变量选择AI 解读

A crucial problem in building a multiple regression model is the selection of predictors to include. The main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices. In this framework the promising subsets of predictors can be identified as those…

大麻非刑事化对医院急诊涉药事件的影响：1975—1978年AI 解读

Between 1973 and 1978, 12 states with collectively over one-third of the total U.S. population enacted laws that decriminalized the possession of marijuana. This article uses standard metropolitan statistical area (SMSA) level data on hospital emergency room drug episodes collected by the Drug Abuse Warning Network to measure the effect of changes in drug penalties on substance abuse crises. The regression models demonstrate that marijuana decriminalization was accompanied…

连续体回归与岭回归AI 解读

SUMMARY We demonstrate the close relationship between first-factor continuum regression and standard ridge regression. The difference is that continuum regression inserts a scalar compensation factor for that part of the shrinkage in ridge regression that has no connection with tendencies towards collinearity. We interpret this to mean that first-factor continuum regression is preferable in principle to ridge regression if we want protection against near collinearity but do…

变量选择问题中的观测影响评估AI 解读

Variable selection techniques are often used in combination with multiple linear regression to produce a parsimonious model that fits the data well. It is clearly undesirable for the final model to depend strongly on the inclusion of a few influential cases in the data set. This article discusses a measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression. When variables are selected objectively, deletion of…

平滑样条密度估计：无量纲自动算法AI 解读

As a sequel to an earlier article by Gu and Qiu, this article describes and illustrates a dimensionless automatic algorithm for nonparametric probability density estimation using smoothing splines. The algorithm is designed to calculate an adaptive finite dimensional solution to the penalized likelihood problem, which was shown by Gu and Qiu to share the same asymptotic convergence rates as the nonadaptive infinite dimensional solution. The smoothing parameter is updated…

变量选择问题中的观测影响评估AI 解读

Variable selection techniques are often used in combination with multiple linear regression to produce a parsimonious model that fits the data well.It is clearly undesirable for the final model to depend strongly on the inclusion of a few influential cases (data points) in the data set.This article discusses a measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression.When variables are selected objectively using…

Cox 模型中的非参数估计AI 解读

Nonparametric estimation of the relative risk in a generalized Cox model with multivariate time dependent covariates is considered. Estimation is based on a penalized partial likelihood. Using techniques from Andersen and Gill, and Cox and O'Sullivan, upper bounds on rate of convergence in a variety of norms are obtained. These upper bounds match the optimal rates available for linear nonparametric regression and density estimation. The results are uniform in the smoothing…