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摘要暂缺

缺失数据、插补与自助法AI 解读

Missing data refers to a class of problems made difficult by the absence of some portions of a familiar data structure. For example, a regression problem might have some missing values in the predictor vectors. This article concerns nonparametric approaches to assessing the accuracy of an estimator in a missing data situation. Three main topics are discussed: bootstrap methods for missing data, these methods' relationship to the theory of multiple imputation, and…

伽马射线暴数据的生存分析AI 解读

Gamma-ray bursts are short but powerful pulses of electromagnetic radiation coming from space. Specially equipped satellites have observed the arrival of several hundred bursts during the past two decades. The origin of these bursts, whether from near the earth, across the galaxy, or out of the deep cosmos, has become a major question for astronomers. At the heart of this question lies a statistical puzzle relating to familiar issues in survival analysis: Kaplan-Meier-type…

从置信区间进行贝叶斯与似然计算AI 解读

Recently there has been considerable progress on setting good approximate confidence intervals for a single parameter θ in a multi-parameter family. Here we use these frequentist results as a convenient device for making Bayes, empirical Bayes and likelihood inferences about θ. A simple formula is given that produces an approximate likelihood function Lx†(θ) for θ, with all nuisance parameters eliminated, based on any system of approximate confidence intervals. The…

由置信区间进行贝叶斯与似然计算AI 解读

Recently there has been considerable progress on setting good approximate confidence intervals for a single parameter θ in a multi-parameter family. Here we use these frequentist results as a convenient device for making Bayes, empirical Bayes and likelihood inferences about θ. A simple formula is given that produces an approximate likelihood function Lx†(θ) for θ, with all nuisance parameters eliminated, based on any system of approximate confidence intervals. The…

Bootstrap 后的 Jackknife：标准误与影响函数AI 解读

SUMMARY This paper shows how to derive more information from a bootstrap analysis, information about the accuracy of the usual bootstrap estimates. Suppose that we observe data x = (x 1 x 2, . . ., xn), compute a statistic of interest s(x) and further compute B bootstrap replications of s, say s(x*1) s(x*2), . . ., s(x*B), where B is some large number like 1000. Various accuracy measures for s(x) can be obtained from the bootstrap values, e.g. the bootstrap estimates of…

基于非对称极大似然的泊松过度离散估计AI 解读

A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…

基于非对称最大似然的 Poisson 过度离散估计AI 解读

A common difficulty in regression problems with Poisson (or binomial or other exponential family) response variables is over-dispersion: the scatter around the fitted regression is too large by the standards of Poisson variability. This article concerns the description, estimation, and testing of various patterns of overdispersion, with particular emphasis on the Poisson case. Asymmetric maximum likelihood (AML) is a method of fitting regressions for the conditional…

指数族中更准确的置信区间AI 解读

Fisher's theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest θ, the standard intervals θ ^ ± zασ ^ where θ ^ is the maximum likelihood estimator, ô is an estimate of standard error based on differentiation of the log likelihood function, and zα is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals…

以危险率表示Fisher信息AI 解读

If $\{g_\theta(t)\}$ is a regular family of probability densities on the real line, with corresponding hazard rates $\{h_\theta(t)\}$, then the Fisher information for $\theta$ can be expressed in terms of the hazard rate as follows: $\mathscr{I}_\theta \equiv \int \big(\frac{\dot{g}_\theta}{g_\theta}\big)^2 g_\theta = \int \big(\frac{\dot{h}_\theta}{h_\theta}\big)^2 g_\theta, \theta \in \mathbb{R},$ where the dot denotes $\partial/\partial\theta$. This identity shows that…

更高效的Bootstrap计算AI 解读

This article concerns computational methods for the bootstrap that are more efficient than the straightforward Monte Carlo methods usually used. The bootstrap is considered in its simplest form: in a one-sample nonparametric problem, where the goal is to estimate the bias or variance of some statistic by bootstrap sampling, or to set approximate confidence intervals for a parameter of interest in terms of various percentiles of the bootstrap distribution. The methods of this…

Logistic 回归、生存分析与 Kaplan–Meier 曲线AI 解读

We discuss the use of standard logistic regression techniques to estimate hazard rates and survival curves from censored data. These techniques allow the statistician to use parametric regression modeling on censored data in a flexible way that provides both estimates and standard errors. An example is given that demonstrates the increased structure that can be seen in a parametric analysis, as compared with the nonparametric Kaplan-Meier survival curves. In fact, the…

改进的 Bootstrap 置信区间AI 解读

We consider the problem of setting approximate confidence intervals for a single parameter θ in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, , can be quite misleading. In practice, tricks based on transformations, bias corrections, and so forth, are often used to improve their accuracy. The bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to…

双指数族及其在广义线性回归中的应用AI 解读

In one-parameter exponential families such as the binomial and Poisson, the variance is a function of the mean. Double exponential families allow the introduction of a second parameter that controls variance independently of the mean. Double families are used as constituent distributions in generalized linear regressions, in which both means and variances are allowed to depend on observed covariates. The theory is applied to two examples—a logistic regression and a large…

预测规则的表观错误率有多大偏差？AI 解读

A regression model is fitted to an observed set of data. How accurate is the model for predicting future observations? The apparent error rate tends to underestimate the true error rate because the data have been used twice, both to fit the model and to check its accuracy. We provide simple estimates for the downward bias of the apparent error rate. The theory applies to general exponential family linear models and general measures of prediction error. Special attention is…

二维列联表的独立性检验：卡方统计量的新解释AI 解读

The classical chi-square test for independence in a two-way contingency table often rejects the independence hypothesis at an extremely small significance level, particularly when the sample size is large. This paper proposes some alternative distributions to independence, to help interpret the $\chi^2$ statistic in such situations. The uniform alternative, in which every possible contingency table of the given dimension and sample size receives equal probability, leads to…

一类参数问题的 Bootstrap 置信区间AI 解读

We consider the following class of problems: having observed a multivariate normal data vector y with unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in…

We consider the following class of problems: having observed a multivariate normal data vector y with unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in…

非嵌套线性模型的比较AI 解读

I consider the usual linear-model situation, except that there are two possible linear subspaces that may contain the true mean vector, and neither of the two subspaces is nested within the other. Approximate confidence intervals are developed for the difference in mean squared error (MSE) of prediction using the two models, not assuming that either model is necessarily correct. The confidence intervals are based on parametric bootstrap methods, applied to Mallows's Cp…

非嵌套线性模型的比较AI 解读

I consider the usual linear-model situation, except that there are two possible linear subspaces that may contain the true mean vector, and neither of the two subspaces is nested within the other. Approximate confidence intervals are developed for the difference in mean squared error (MSE) of prediction using the two models, not assuming that either model is necessarily correct. The confidence intervals are based on parametric bootstrap methods, applied to Mallows's Cp…

摘要暂缺

预测规则错误率的估计：对交叉验证的改进AI 解读

We construct a prediction rule on the basis of some data, and then wish to estimate the error rate of this rule in classifying future observations. Cross-validation provides a nearly unbiased estimate, using only the original data. Cross-validation turns out to be related closely to the bootstrap estimate of the error rate. This article has two purposes: to understand better the theoretical basis of the prediction problem, and to investigate some related estimators, which…

极大似然与决策理论AI 解读

This paper discusses five questions concerning maximum likelihood estimation: What kind of theory is maximum likelihood? How is maximum likelihood used in practice? To what extent can this theory and practice be justified from a decision-theoretic viewpoint? What are maximum likelihood's principal virtues and defects? What improvements have been suggested by decision theory?

删失数据与 BootstrapAI 解读

This article concerns setting standard errors and confidence intervals for the parameters of an unknown distribution when the data is subject to right censoring. The bootstrap, which is an elaboration of the jackknife, provides a general method for answering such questions. The validity of bootstrap methods is investigated using real data, computer simulations, and, in the final section, brief theoretical considerations.