每日简报

通过 Lasso 实现回归收缩与变量选择AI 解读

SUMMARY We propose a new method for estimation in linear models. The ‘lasso’ minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It…

通过 EM 算法对不完整数据进行最大似然估计AI 解读

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least…

模型维度的估计AI 解读

The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

回归模型与生命表AI 解读

Summary The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations…

摘要暂缺

倾向得分在观察性因果效应研究中的核心作用AI 解读

The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates. Applications include: (i) matched sampling on the univariate propensity score, which is a generalization of discriminant matching, (ii) multivariate adjustment by subclassification on the propensity…

贪婪函数逼近：梯度提升机AI 解读

Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent “boosting” paradigm is developed for additive expansions based on any fitting criterion.Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and…

History Conceptual Foundations Uses and Kinds of Inference The Logic of Content Analysis Designs Unitizing Sampling Recording Data Languages Constructs for Inference Analytical Techniques The Use of Computers Reliability Validity A Practical Guide

具有单位根的自回归时间序列估计量分布AI 解读

Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of…

通过弹性网进行正则化与变量选择AI 解读

Summary We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together. The elastic net is particularly useful when the number of predictors (p) is much bigger than the number…

摘要暂缺

使用广义线性模型分析纵向数据AI 解读

This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory…

时间序列回归中的单位根检验AI 解读

This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The…

自助法：重新审视刀切法AI 解读

We discuss the following problem: given a random sample $\mathbf{X} = (X_1, X_2, \cdots, X_n)$ from an unknown probability distribution $F$, estimate the sampling distribution of some prespecified random variable $R(\mathbf{X}, F)$, on the basis of the observed data $\mathbf{x}$. (Standard jackknife theory gives an approximate mean and variance in the case $R(\mathbf{X}, F) = \theta(\hat{F}) - \theta(F), \theta$ some parameter of interest.) A general method, called the…

缺失数据的统计分析AI 解读

Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data:…

概率、随机变量与随机过程AI 解读

Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing…

基于马尔可夫链的蒙特卡洛抽样方法及其应用AI 解读

A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.

竞争风险子分布的比例风险模型AI 解读

With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is…

基于 Kendall 秩相关系数的回归系数估计AI 解读

The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence…

贝叶斯因子AI 解读

In a 1935 paper and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P-values, less attention has been given to the Bayes factor as a…

稳健局部加权回归与散点图平滑AI 解读

The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that…

推断与缺失数据AI 解读

When making sampling distribution inferences about the parameter of the data, θ, it is appropriate to ignore the process that causes missing data if the missing data are ‘missing at random’ and the observed data are ‘observed at random’, but these inferences are generally conditional on the observed pattern of missing data. When making direct-likelihood or Bayesian inferences about θ, it is appropriate to ignore the process that causes missing data if the missing data are…

最小角回归AI 解读

The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version…

非凹惩罚似然变量选择及其 Oracle 性质AI 解读

Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized likelihood approaches are proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously. Hence they enable us to…