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多元失效时间数据的变量选择AI 解读

In this paper, we proposed a penalised pseudo-partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients. Under certain regularity conditions, we show the consistency and asymptotic normality of the penalised likelihood estimators. We further demonstrate that, for certain penalty functions with proper choices of regularisation parameters, the resulting estimator can correctly identify the true model,…

离散观测马尔可夫跳跃过程的统计推断AI 解读

Summary Likelihood inference for discretely observed Markov jump processes with finite state space is investigated. The existence and uniqueness of the maximum likelihood estimator of the intensity matrix are investigated. This topic is closely related to the imbedding problem for Markov chains. It is demonstrated that the maximum likelihood estimator can be found either by the EM algorithm or by a Markov chain Monte Carlo procedure. When the maximum likelihood estimator…

非参数混合效应模型中的最优平滑AI 解读

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with parametric random effects and flexible fixed effects, and employ the penalized least squares method to estimate the models. The issue to be addressed is the selection of smoothing parameters through the generalized cross-validation method,…

惩罚偏离可加性的非参数回归AI 解读

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions imposed can lead to serious bias. Here, a new estimator is proposed which allows penalizing the nonadditive part of a regression function. This offers a smooth choice between the full and the additive model. As a byproduct, this penalty…

加性模型平滑回拟合的带宽选择AI 解读

The smooth backfitting introduced by Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443–1490] is a promising technique to fit additive regression models and is known to achieve the oracle efficiency bound. In this paper, we propose and discuss three fully automated bandwidth selection methods for smooth backfitting in additive models. The first one is a penalized least squares approach which is based on higher-order stochastic expansions for the residual sums of…

平方根惩罚：分类与边界估计中的间隔自适应AI 解读

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the excess risk, that is, rates that can be faster than n−1/2, where n is the sample size. We show that our method also gives adaptive estimators for the problem of edge estimation.

多元非平稳时间序列的 SLEX 分析AI 解读

We develop a procedure for analyzing multivariate nonstationary time series using the SLEX library (smooth localized complex exponentials), which is a collection of bases, each basis consisting of waveforms that are orthogonal and time-localized versions of the Fourier complex exponentials. Under the SLEX framework, we build a family of multivariate models that can explicitly characterize the time-varying spectral and coherence properties. Every model has a spectral…

概率分布引出的统计方法AI 解读

Elicitation is a key task for subjectivist Bayesians. Although skeptics hold that elicitation cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subject-matter expert colleagues. This article reviews the state of the art, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively and how they respond to questions…

高维数据聚类中的贝叶斯变量选择AI 解读

Over the last decade, technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates (p ≫ n). A common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables. In this article we propose a methodology for addressing these problems simultaneously. Given a set of variables, we formulate the clustering problem in terms of a…

摘要暂缺

不依赖模型形式的变量选择AI 解读

Summary The importance of variable selection in regression has grown in recent years as computing power has encouraged the modelling of data sets of ever-increasing size. Data mining applications in finance, marketing and bioinformatics are obvious examples. A limitation of nearly all existing variable selection methods is the need to specify the correct model before selection. When the number of predictors is large, model formulation and validation can be difficult or even…

基于上升性质的蒙特卡洛 EM 算法AI 解读

Summary The expectation–maximization (EM) algorithm is a popular tool for maximizing likelihood functions in the presence of missing data. Unfortunately, EM often requires the evaluation of analytically intractable and high dimensional integrals. The Monte Carlo EM (MCEM) algorithm is the natural extension of EM that employs Monte Carlo methods to estimate the relevant integrals. Typically, a very large Monte Carlo sample size is required to estimate these integrals within…

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…

相依删失下边际比例风险回归的似然方法AI 解读

In many public health problems, an important goal is to identify the effect of some treatment/intervention on the risk of failure for the whole population. A marginal proportional hazards regression model is often used to analyze such an effect. When dependent censoring is explained by many auxiliary covariates, we utilize two working models to condense high-dimensional covariates to achieve dimension reduction. Then the estimator of the treatment effect is obtained by…

基于尖峰—平板先验的变量选择：频率学派与贝叶斯策略AI 解读

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the…

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.…

惩罚样条回归的理论AI 解读

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to…

收缩切片逆回归札记AI 解读

We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the…

用于非参数函数估计的多尺度广义线性模型AI 解读

We present a method for extracting information about both the scale and trend of local components of an inhomogeneous function in a nonparametric generalised linear model. Our multiscale framework combines recursive partitions, which allow for the incorporation of scale in a natural manner, with systems of piecewise polynomials supported on the partition intervals, which serve to summarise the smooth trend within each interval. Our estimators are formulated as solutions of…

用于纳入先验信息的约束逆回归AI 解读

Inverse regression methods facilitate dimension-reduction analyses of high-dimensional data by extracting a small number of factors that are linear combinations of the original predictor variables. But the estimated factors may not lend themselves readily to interpretation consistent with prior information. Our approach to solving this problem is to first incorporate prior information via theory- or data-driven constraints on model parameters, and then apply the proposed…

平滑回拟合的实践应用AI 解读

Summary Compared with the classical backfitting of Buja, Hastie and Tibshirani, the smooth backfitting estimator (SBE) of Mammen, Linton and Nielsen not only provides complete asymptotic theory under weaker conditions but is also more efficient, robust and easier to calculate. However, the original paper describing the SBE method is complex and the practical as well as the theoretical advantages of the method have still neither been recognized nor accepted by the statistical…

高维协变量下非参数回归的差分型方差估计AI 解读

Summary We consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates t ∈ ℝd, d=1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an estimator, difference schemes which minimize the asymptotic mean-squared error can be computed for d=1 and d=2. However, from numerical studies it is known that for finite sample sizes the performance of these…

通过融合 Lasso 实现稀疏性与平滑性AI 解读

Summary The lasso penalizes a least squares regression by the sum of the absolute values (L1-norm) of the coefficients. The form of this penalty encourages sparse solutions (with many coefficients equal to 0). We propose the ‘fused lasso’, a generalization that is designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes the L1-norm of both the coefficients and their successive differences. Thus it encourages sparsity of the…

非规则问题中的模型选择：数量性状基因座定位应用AI 解读

Two methods of model selection are discussed for changepoint-like problems, especially those arising in genetic linkage analysis. The first is a method that selects the model with the smallest p-value, while the second is a modification of the Bayes information criterion. The methods are compared theoretically and on examples from the literature. For these examples, they are roughly comparable although the p-value-based method is somewhat more liberal in selecting a…