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1851—1985年北半球爆炸性火山活动的探索性分析AI 解读

Studies of regional climate following volcanic eruptions suggest that explosive volcanism exerts a short-term cooling effect. To understand the effects of explosive volcanism on historic temperatures, it is necessary to identify changes through time in the frequency of explosive eruptions. This article presents an exploratory analysis of a record of explosive eruptions in the Northern Hemisphere over the period 1851–1985. This record is modeled as a nonstationary Poisson…

核密度估计的自助法带宽选择AI 解读

A bootstrap-based choice of bandwidth for kernel density estimation is introduced. The method works by estimating the integrated mean squared error (IMSE) for any given bandwidth and then minimizing over all bandwidths. A straightforward application of the bootstrap method to estimate the IMSE fails because it does not capture the bias component. A smoothed bootstrap method based on an initial density estimate is described that solves this problem. It is possible to…

检验简单有序备择的单侧学生化极差检验AI 解读

Consider the usual balanced one-way fixed effects analysis of variance (ANOVA) model X ij = μ i + ε ij (1 ≤ j ≤ n; 1 ≤ i ≤ k), where the ε ij are independent N(0, [sgrave]2) random variables and μ i is the mean of the ith treatment (1 ≤ i ≤ k). The μ i and [sgrave] 2 are unknown parameters. Let X i be the sample mean of the ith treatment based on n observations (1 ≤ i ≤ k), and let S 2 be an unbiased estimate of [sgrave]2, which is distributed independently of the X i as a…

摘要暂缺

球面多面体管状邻域的体积与统计推断AI 解读

For statistical procedures including Scheffe-type simultaneous confidence bounds for response surfaces and likelihood ratio tests for an additional regressor with unspecified parameters in a regression model, the confidence level or size can be expressed in terms of probabilities of the form $P\lbrack U \in D(\Gamma, \theta)\rbrack$, where $\Gamma$ is a subset of $S^m$ (the unit sphere in $R^{m + 1}), U$ is uniformly distributed in $S^m$ and $D(\Gamma, \theta)$ denotes the…

Hotelling 管体积定理：同时推断与数据分析中的应用AI 解读

We illustrate with contemporary examples Hotelling's geometric approach to simultaneous probability calculations. Hotelling reduces the evaluation of certain normal theory significance probabilities to finding the volume of a tube about a curve in a hypersphere, and shows that this volume is often exactly given by length times cross-sectional area. We review Hotelling's result together with some recent complements, and then use the approach to set simultaneous prediction…

重复测量设计中区组间秩统计量的效率AI 解读

For factorial designs, tests that rely on the method of n rankings, for example, the Friedman test, suffer a potential loss of power since they depend only on within-block ranks. This deficiency is overcome by ranking across blocks as is done in the aligned rank tests and the rank transform procedures. This article examines a broad class of powerful interblock rank statistics for testing for both treatment effects and ordered alternatives and for performing multiple…

Bootstrap 同时置信集的改进AI 解读

Simultaneous confidence sets for a collection of parametric functions may be constructed in several different ways. These ways include: (a) the exact pivotal method that underlies Tukey's (1953) and Scheffé's (1953) simultaneous confidence intervals for linear parametric functions in the normal linear model; (b) the method of asymptotic pivots, which is an approximate extension of the pivotal method; (c) the method of bootstrapped roots developed in Beran (1988). These three…

与对照组比较实验中同时推断的样本量分配AI 解读

A common experiment is to compare p ≥ 2 test treatments with a control in a one-way layout. The object of the experiment can be to establish which test treatments are statistically significantly different from or better than the control or to give simultaneous confidence bounds on the amount of improvement that each of the test treatments offers over the control. Frequently, further experimentation is done with the promising treatments. We consider the problem of optimal…

误差自相关线性回归中的精确检验与置信集AI 解读

This article proposes a general method to build exact tests and confidence sets in linear regressions with first-order autoregressive Gaussian disturbances. Because of a nuisance parameter problem, we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context. Given an exact confidence set for the autocorrelation coefficient, we describe how to obtain a similar simultaneous confidence set for the…

经验函数的自助法AI 解读

We develop the complete bootstrapped parallel to the asymptotic theory of weighted empirical and quantile processes. Utilizing this parallel theory, we present a general body of techniques to establish the asymptotic validity of the bootstrap method of constructing confidence bands for statistical functions. These techniques are demonstrated to be applicable to the construction of asymptotic bootstrap confidence bands for a variety of concrete functions.

生命科学统计学AI 解读

1. Introduction. Statistics and the Life Sciences. Examples and Overview. 2. Description of Populations and Samples. Introduction. Frequency Distributions: Techniques for Data. Frequency Distributions: Shapes and Examples. Descriptive Statistics: Measures of Center. Boxplots. Measures of Dispersion. Effect of Transformation of Variables (Optional). Samples and Populations: Statistical Inference. Perspective. 3. Random Sampling, Probability, and the Binomial Distribution.…

两个总体累积风险的图形比较AI 解读

We consider graphs, confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group. In particular, we consider the relative change Δ(t) in a cumulative rate function which is used to define a generalized proportional hazard model. This model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model. We introduce an…

摘要暂缺

临床剂量探索研究中的多重检验程序AI 解读

Test procedures in clinical dose finding studies are considered when it can be assumed that increasing dose levels lead to a larger or at least equal efficacy. If one is interested in various comparisons within the set of dose levels, one arrives at a problem of multiple testing against ordered alternatives. Some multiple test procedures controlling the multiple level of significance are compared in a simulation study. It follows that a simple procedure that only uses…

使用 Bootstrap 构造分布函数置信带AI 解读

We first discuss the construction of bootstrap confidence bands for the distribution function F of a population for simple random sampling but do not assume that F is continuous. The known alternative approach is to use the quantiles from the tabled Kolmogorov distribution. This approach is known to be conservative. It has already been shown in Bickel and Freedman (1981) that the bootstrap confidence band has the correct coverage probability asymptotically. We show by…

一般相关均值下的成对比较AI 解读

A commonly occurring statistical inference problem in practice is that of making simultaneous comparisons among three or more treatment means μi (1 ≤ i ≤ k) for certain experimental designs. One way to do this, the T method proposed by Tukey (1953), constructs simultaneous confidence intervals for all pairwise differences of the treatment means μi – μj (1 ≤ i, j ≤ k, i ≈ j). The joint confidence level of these confidence intervals, however, depends in a very complicated…

线性回归中非线性假设、不等式约束与非嵌套假设的精确同时检验AI 解读

In the classical linear model, comparison of two arbitrary hypotheses on the regression coefficients is considered. Problems involving nonlinear hypotheses, inequality restrictions, or non-nested hypotheses are included. Exact bounds on the null distribution of likelihood ratio statistics are derived (based on the central Fisher distribution). As a special case, a bounds test similar to the Durbin-Watson test is proposed. Multiple testing problems are studied: the bounds…

两个总体累积风险的图形比较AI 解读

We consider graphs, confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group. In particular, we consider the relative change Δ(t) in a cumulative rate function which is used to define a generalized proportional hazard model. This model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model. We introduce an…

含缺失数据的不平衡设计中的 Friedman 型统计量与一致多重比较AI 解读

A generalization of the Friedman test using the marginal likelihood principle (Kalbfleisch and Prentice 1973) is presented and its asymptotic power given. It allows use of a variety of score functions and handles ties and unbalanced designs. Some well-known statistics [including the tests of Kruskal and Wallis (1952), Prentice (1979), and Rinaman (1983)] are proven to be special cases, whereas others (e.g., Klotz 1980; Groggel and Skillings 1986; Rai 1987; Skillings and Mack…

含缺失数据的不平衡设计中的Friedman型统计量与一致多重比较AI 解读

A generalization of the Friedman test using the marginal likelihood principle (Kalbfleisch and Prentice 1973) is presented and its asymptotic power given. It allows use of a variety of score functions and handles ties and unbalanced designs. Some well-known statistics [including the tests of Kruskal and Wallis (1952), Prentice (1979), and Rinaman (1983)] are proven to be special cases, whereas others (e.g., Klotz 1980; Groggel and Skillings 1986; Rai 1987; Skillings and Mack…

Kolmogorov–Smirnov损失下分布函数的最优不变估计AI 解读

Given a random sample of size $n$ from an unknown continuous distribution function $F$, we consider the problem of estimating $F$ nonparametrically from a decision theoretic approach. In our treatment, we assume the Kolmogorov-Smirnov loss function and the group of all one-to-one monotone transformations of real numbers onto themselves which leave the sample values invariant. Under this setup, we obtain a best invariant estimator of $F$ which is shown to be unique. This…

平衡的同时置信集AI 解读

Suppose that T(θ) = {Tu (θ)} is a family of parametric functions indexed by the variable u. For each u, an approximate confidence set Cn,u for Tu (θ) may be obtained by referring a function of Tu (θ) and the sample to an estimated quantile dn,u of that function's sampling distribution. This approach is sometimes called the pivotal method for constructing a confidence set, even when it is not based on a true pivot. A simultaneous confidence set Cn for T(θ) is then obtained by…

允许缺失观测与时变协变量的重复有序分类结果分析AI 解读

This article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome. The method, which allows both time-dependent covariates and missing observations, consists of two analytic steps. In the first step, the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by McCullagh (1980).…