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微阵列实验的经验贝叶斯分析AI 解读

Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes. A simple nonparametric empirical Bayes model is…

利用 Gap 统计量估计数据集中的聚类数AI 解读

Summary We propose a method (the ‘gap statistic’) for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. K-means or hierarchical), comparing the change in within-cluster dispersion with that expected under an appropriate reference null distribution. Some theory is developed for the proposal and a simulation study shows that the gap statistic usually outperforms other methods that have been proposed in…

加性逻辑回归：提升法的统计视角（含讨论与作者回应）AI 解读

Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of…

自适应模型选择的协方差膨胀准则AI 解读

Summary We propose a new criterion for model selection in prediction problems. The covariance inflation criterion adjusts the training error by the average covariance of the predictions and responses, when the prediction rule is applied to permuted versions of the data set. This criterion can be applied to general prediction problems (e.g. regression or classification) and to general prediction rules (e.g. stepwise regression, tree-based models and neural nets). As a…

区域判定问题AI 解读

In the problem of regions, we wish to know which one of a discrete set of possibilities applies to a continuous parameter vector. This problem arises in the following way: we compute a descriptive statistic from a set of data, notice an interesting feature and wish to assign a confidence level to that feature. For example, we compute a density estimate and notice that the estimate is bimodal. What confidence can we assign to bimodality? A natural way to measure confidence is…

改进交叉验证：.632+ 自助法AI 解读

A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule? This is an important question both for comparing models and for assessing a final selected model. The traditional answer to this question is given by cross-validation. The cross-validation estimate of prediction error is nearly unbiased but can be highly variable. Here we discuss bootstrap estimates of prediction error, which can be thought of as…

摘要暂缺

利用专门构造的指数族进行密度估计AI 解读

We wish to estimate the probability density $g(y)$ that produced an observed random sample of vectors $y_1, y_2, \dots, y_n$. Estimates of $g(y)$ are traditionally constructed in two quite different ways: by maximum likelihood fitting within some parametric family such as the normal or by nonparametric methods such as kernel density estimation. These two methods can be combined by putting an exponential family "through" a kernel estimator. These are the specially designed…

回归与分类中的估计组合AI 解读

We consider the problem of how to combine a collection of general regression fit vectors to obtain a better predictive model. The individual fits may be from subset linear regression, ridge regression, or something more complex like a neural network. We develop a general framework for this problem and examine a cross-validation—based proposal called “model mix” or “stacking” in this context. We also derive combination methods based on the bootstrap and analytic methods and…

摘要暂缺

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…

SUMMARY We propose a simple adjustment for profile likelihoods. The aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods, such as bias, inconsistency and overoptimistic variance estimates. The adjustment is applied to the profile log-likelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function. For cases in which explicit…

线性平滑器与加性模型AI 解读

We study linear smoothers and their use in building nonparametric regression models. In the first part of this paper we examine certain aspects of linear smoothers for scatterplots; examples of these are the running-mean and running-line, kernel and cubic spline smoothers. The eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother, and several other topics such as the number of degrees of freedom of a…

方差稳定化与 BootstrapAI 解读

We investigate the use of a variance stabilizing transformation for the computation of a bootstrap t confidence interval. The transformation is estimated in an ‘automatic’ manner through an initial bootstrap step. A bootstrap t interval is then computed for the variance stabilized parameter and the interval is mapped back to the original scale. The resultant procedure is second-order correct in some settings, invariant and in a number of examples it performs better than the…

通过可加性与方差稳定化估计回归变换AI 解读

I propose a method for the nonparametric estimation of transformations for regression. It is much more flexible than the familiar Box-Cox procedure, allowing general smooth transformations of the variables, and is similar to the ACE (alternating conditional expectation) algorithm of Breiman and Friedman (1985). The ACE procedure uses scatterplot smoothers in an iterative fashion to find the maximally correlated transformations of the variables. Like ACE, my proposal can…

方差稳定化与自助法AI 解读

We investigate the use of a variance stabilizing transformation for the computation of a bootstrap t confidence interval. The transformation is estimated in an ‘automatic’ manner through an initial bootstrap step. A bootstrap t interval is then computed for the variance stabilized parameter and the interval is mapped back to the original scale. The resultant procedure is second-order correct in some settings, invariant and in a number of examples it performs better than the…

摘要暂缺

广义可加模型：若干应用AI 解读

Generalized additive models have the form η(x) = α + σ fj (x j ), where η might be the regression function in a multiple regression or the logistic transformation of the posterior probability Pr(y = 1 | x) in a logistic regression. In fact, these models generalize the whole family of generalized linear models η(x) = β′x, where η(x) = g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions fj (xj )…

Bootstrap 置信区间与 Bootstrap 近似AI 解读

The BCa bootstrap procedure (Efron 1987) for constructing parametric and nonparametric confidence intervals is considered. Like the bootstrap, this procedure can be applied to complicated problems in a wide range of situations. For models indexed by a scalar parameter θ with efficient estimator , the BCa procedure relies on the existence of a transformation g(·) such that () is approximately normally distributed with standard deviation 1 + ag(θ), although explicit knowledge…