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排序集样本的刻画及其在分布函数估计中的应用AI 解读

Ranked-set sampling has been shown to provide improved estimators of the mean and variance when actual measurement of the observations is difficult but ranking of the elements in a sample is relatively easy. This result holds even if the ranking is imperfect. In this article, we provide a characterization of a ranked-set sample that makes the source of this additional information intuitively clear. It is applied to show that the empirical distribution function of a…

Steel 多处理对照多元符号检验的推广AI 解读

Steel (1959) introduced a nonparametric multivariate sign test to allow one to compare p ≥ 2 test treatments simultaneously with a control or standard treatment in a randomized-block setting. Steel proposed using blocks of size p + 1 composed of one observation from each treatment. Intuitively, it seems that the control should be observed more often that a test treatment, because the control is involved in all treatment-control comparisons and an individual test treatment is…

Simultaneous confidence regions and simultaneous prediction regions are considered using the expected coverage measure criterion of Naiman. Invariance methods are used to construct minimax procedures in multivariate linear models.

非参数回归中的自助法：局部自适应平滑与置信带AI 解读

The operation of the bootstrap in the context of nonparametric regression is considered. Bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator. The application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances. The technique of the bootstrap is to replace…

缩小线性回归置信带宽度的方法AI 解读

When constructing a confidence band in the linear regression model, there have been various efforts made to reduce the width of the band. One of them is to change the shape of a confidence band. Another effort is to restrict the region of the independent variables. This article proposes another possibility to narrow down the width of a band, which is to change the curvature of the band. Following that a theorem is given to combine these devices. Numerical comparisons are…

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一种更锐利的多重显著性检验 Bonferroni 程序AI 解读

A simple procedure for multiple tests of significance based on individual p-values is derived. This simple procedure is sharper than Holm's (1979) sequentially rejective procedure. Both procedures contrast the ordered p- values with the same set of critical values. Holm's procedure rejects an hypothesis only if its p-value and each of the smaller p-values are less than their corresponding critical-values. The new procedure rejects all hypotheses with smaller or equal…

有序备择下的非参数协方差分析AI 解读

SUMMARY The problem of comparing k populations with respect to a univariate response variable Y against an ordered alternative is considered when a covariate X is taken into account using the matched-observations method of Quade (1982). Two test statistics are considered: one is Quade's statistic generalized for arbitrary k and the second is the Terpstra-Jonckheere statistic generalized for grouped data. Some simulations are carried out to study their small sample…

自助乘积极限过程的收敛速率AI 解读

We establish rates for strong approximations of the bootstrapped product-limit process and the corresponding quantile process. These results are used to show weak convergence of bootstrapped total time on test and Lorenz curve processes to the same limiting Gaussian processes as for the unbootstrapped versions. We develop fully nonparametric confidence bands and tests for these curves and apply these results to prostate cancer. We also present almost sure results for the…

随机化估计与检验AI 解读

Stochastic procedures are randomized tests, estimates and confidence sets with two properties: (i) They are functions of an original sample and one or more artificially constructed auxiliary samples. (ii) They become nearly nonrandomized when the auxiliary samples increase in size. The stochastic procedures of this paper, which arise as approximations to numerically intractable procedures, involve iterated bootstrap techniques and random sampling schemes over abstract…

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同时置信带对模型误设的稳健性AI 解读

Confidence bands for the simple linear model are examined to assess their degrees of robustness to departures from the model. All calculations are made under an interval constraint on the range of interest for the predictor variable. The true model is taken to be a quadratic polynomial, and departure from the linear case is considered in terms of increasing magnitude of a curvature parameter. Proposed measures of robustness include the actual coverage probability under the…

多项比例的快速同时置信区间AI 解读

Opinion polls often give an indication of sampling error based on the standard conservative confidence intervals for a single binomial proportion. We give a lower bound for the simultaneous coverage probability when such intervals are applied to all of the proportions in a poll. This bound is equal to 1 – 2α. for small values of α. The same result is shown to apply to the standard confidence intervals for changes in proportions between surveys.

自助法与基于似然的置信域AI 解读

We describe a method for constructing likelihood-based confidence regions for a vector parameter, using the bootstrap and nonparametric density estimation. The technique is illustrated by application to a numerical example, and its theoretical properties are elucidated. It is argued that likelihood-based regions should not be approximated by ellipses, if we are to have any hope of capturing first-order departures from normality. Bootstrap algorithms for constructing…

扩展 Paulson 序贯选择方法AI 解读

Principles of multiple comparisons with the best treatment are used to construct a sequential procedure for selecting one of $k$ normal populations with equal, known variance. The procedure makes a stronger confidence than traditional Indifference Zone procedures, without (asymptotically) inflating sample sizes. It is shown to be substantially superior in asymptotic sample size behavior to existing procedures making the stronger statement.

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利用预测变量约束构造多元回归同时置信界AI 解读

This article presents a method for approximating the coverage probability of simultaneous confidence bounds for multiple regression functions when the vector of predictor variables is constrained to lie in a polyhedral convex set. The method is useful because it allows one to construct simultaneous confidence intervals with prescribed coverage probability for the regression function evaluated at various settings of the predictor variables, which are narrower than bounds…

大型模型族的快速模型选择程序AI 解读

An efficient procedure for model selection from large families of models is described. It is closely related to the all possible models approach but is considerably faster. It is based on two principles: first, if a model is accepted, then all models that include it are considered to be accepted; second, if a model is rejected, then all of its submodels are considered to be rejected. Application of the procedure to variable selection in multiple regression is illustrated.…

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Bootstrap 与基于似然的置信区域AI 解读

We describe a method for constructing likelihood-based confidence regions for a vector parameter, using the bootstrap and nonparametric density estimation. The technique is illustrated by application to a numerical example, and its theoretical properties are elucidated. It is argued that likelihood-based regions should not be approximated by ellipses, if we are to have any hope of capturing first-order departures from normality. Bootstrap algorithms for constructing…

随机删失下预期寿命估计量的一则注记AI 解读

Yang (1977) proposed an estimator of life expectancy based on the Kaplan—Meier estimator under a random censorship model. This note shows that this estimator, considered as a function of age, converges weakly to a Gaussian process on the whole line. A consistent estimator of the variance function of this limiting process is given and asymptotic confidence bands for the life expectancy are discussed.

有限总体抽样的贝叶斯统计推断AI 解读

Bayesian statistical inference for sampling a finite population is studied by using the Dirichlet-multinomial process as prior. It is shown that if the finite population variables have a Dirichlet-multinomial prior, then the posterior distribution of the inobserved variables given a sample is also Dirichlet-multinomial. If the population size tends to infinity (the sample size is fixed), sampling without replacement from a Dirichlet multinomial process is equivalent to the…

曲线回归的保守置信带AI 解读

This paper gives a method for constructing conservative Scheffe-type simultaneous confidence bands for curvilinear regression functions over finite intervals. The method is based on the use of a geometric inequality giving an upper bound for the uniform measure of the set of points within a given distance from y, an arbitrary piecewise differentiable path with finite length in $S^{k-1}$, the unit sphere in $R^k$. The upper bound is obtained by "straightening" the path so…

列联表的分组与关联：探索性典型相关方法AI 解读

The criteria of homogeneity and structure were proposed by Goodman (1981a) for determining whether certain rows or columns of a contingency table should be grouped. A data-based procedure (using the canonical form of bivariate distributions) is presented in this article to guide exploratory analysis to determine which rows or columns of a table may be grouped. This procedure facilitates the application of the homogeneity criterion. Relationships between the proposed method…