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多自变量单调函数的可行非参数估计AI 解读

This article presents a two-stage estimation procedure that uses an ad hoc but very easily implemented isotonization of a kernel estimator. This procedure yields an isotonic estimator with the convergence properties of the kernel estimator. Although the isotonization in the second stage does not satisfy the least squares condition, this hybrid estimator may be considered to be a multidimensional generalization of similar procedures for the one-dimensional case suggested by…

随机排序变概率系统抽样中Horvitz–Thompson估计量的方差估计比较AI 解读

The National Stream Survey (NSS) and Environmental Monitoring and Assessment Program (EMAP) use variable probability, systematic sampling, and the Horvitz-Thompson estimator to estimate population parameters of ecological interest. A common strategy of variance estimation for systematic sampling is to assume that the population order had been randomized prior to sampling and to estimate variance under this randomized population model. The Yates-Grundy variance estimator is…

二项分布试验次数N估计量的不稳定行为AI 解读

The problem of estimating the number of trials in a Binomial distribution is known to be particularly difficult in certain circumstances. Both the maximum likelihood and method-of-moments estimators can produce very erratic results, being extremely sensitive to minor fluctuations in the data. But existing asymptotic theory for these estimators does not provide any insight into this peculiar behavior, as the theory typically produces asymptotic Normal distributions with…

析因设计的完全非参数假设（一）：多元重复测量设计AI 解读

We introduce nonparametric versions for many of the hypotheses tested in analysis of variance and repeated measures models, such as the hypotheses of no main effects, no interaction effects, and no factor effects. These natural extensions of the nonparametric hypothesis of equality of the k distributions in the k sample problem have appealing practical interpretations. We concentrate on multivariate repeated measures designs and obtain simple rank statistics for testing…

二元数据方差分量的极大似然估计AI 解读

We consider a class of probit-normal models for binary data and describe ML and REML estimation of variance components for that class as well as best prediction for the realized values of the random effects. ML estimates are calculated using an EM algorithm; for complicated models EM includes a Gibbs step. The computations are illustrated through two examples.

不完全修复模型中最小修复假设的检验AI 解读

Models assuming minimal repair specify that on repair, a failed system is returned to the working state, while the effective age of the system is held constant; that is, the distribution of the time until the next failure of the repaired system is the same as for a system of the same age that has not yet failed. These models are common in the literature of operations research and reliability, and many probabilistic results as well as inferential procedures depend on the…

序贯插补与贝叶斯缺失数据问题AI 解读

For missing data problems, Tanner and Wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors. Their method of constructing the complete data sets is closely related to the Gibbs sampler. Both required iterations, and, similar to the EM algorithm, convergence can be slow. We introduce in this article an alternative procedure that involves imputing the missing data…

Laplace 方法在有限混合分布中的应用AI 解读

An exact Bayesian analysis of finite mixture distributions is often computationally infeasible, because the number of terms in the posterior density grows exponentially with the sample size. A modification of the Laplace method is presented and applied to estimation of posterior functions in a Bayesian analysis of finite mixture distributions. The procedure, which involves computations similar to those required in maximum likelihood estimation, is shown to have high…

参数空间边界众数情形下后验期望的Laplace近似AI 解读

This article gives asymptotic expansions for posterior expectations when the mode is on the boundary of the parameter space. The idea, based on the divergence theorem, is to reduce the high-dimensional integrals over the parameters space to surface integrals over the boundary of the parameter space and then apply the usual interior-mode Laplace method to the latter integrals. It is shown that these approximations have second-order accuracy. The method is illustrated with…

含噪图像的分割与分析模型AI 解读

This article proposes a statistical model for image generation that provides automatic segmentation of images into intensity-differentiated regions and facilitates the quantitative assessment of uncertainty associated with identified image features. The model is specified hierarchically within the Bayesian paradigm. At the lowest level in the hierarchy, a Gibbs distribution is used to specify a probability distribution on the space of all possible partitions of the…

像素平均后错位图像的位移估计AI 解读

In problems where the recorded signal comprises two or more bands (i.e., wavelengths), it is often the case that the bands are not perfectly aligned in the focal plane. Such misregistration may be caused by atmospheric or oceanographic effects, which refract different bands to differing degrees, or it may result from features of the design of the recording equipment. This article develops two methods for estimating the lag, or the amount by which the bands are out of…

判断排序不完美对秩集样本 Mann–Whitney–Wilcoxon 检验性质的影响AI 解读

In this article we address the issue of imperfect judgment rankings in ranked-set sampling and, in particular, their effect on the properties of test procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistic, U rss. We consider the impact of these imperfect rankings on the null distribution of the statistic and the resulting effect on the nominal level of associated hypothesis tests. We propose a model for the probabilities of imperfect…

基于秩间距的分布无关两样本检验AI 解读

For the two-sample problem, rank spacings of one sample are the positive integer distances between combined-sample ordered ranks from that sample. Elementary mathematical development yields distribution-free orthogonal components analogous to L statistics used by Kaigh for assessing one-sample uniformity. Rank spacings components are linear combinations of ordered ranks with Hahn polynomial vector weight functions. The first four rank spacings components provide…

逐步决策程序与置信集的关系AI 解读

This article considers the relationship between two standard methods of inference on a set of A: unknown parameters, namely stepwise decision procedures and the construction of simultaneous confidence intervals. Illustrative examples with k = 2 are discussed for one-sided step-down and step-up decision procedures and for a two-sided step-down decision procedure. For these examples with normal distributional assumptions, a set of confidence intervals associated with the…

偏最小二乘法的一种解释AI 解读

Univariate partial least squares (PLS) is a method of modeling relationships between a Y variable and other explanatory variables. It may be used with any number of explanatory variables, even far more than the number of observations. A simple interpretation is given that shows the method to be a straightforward and reasonable way of forming prediction equations. Its relationship to multivariate PLS, in which there are two or more Y variables, is examined, and an example is…

用于预测的神经网络模型AI 解读

In this article we introduce a neural net designed for nonlinear statistical prediction. The net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions. A Bayesian inferential procedure for this model, based on the Kalman filter, is derived. The resulting learning algorithm generalizes the so-called onedimensional Newton method, an updating algorithm currently popular in the neural net…

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

随机缺失数据下均值泛函的非参数估计AI 解读

This article considers a distribution-free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology. Without parametric modeling of the missing mechanism or the joint distribution, kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern. A generalization of the method of Cheng and Wei is verified under the assumption of missing at random.…

稳健非参数回归的 L1 方法AI 解读

Consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy-tailed error distribution. The two standard approaches to such a problem are each flawed. Robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form, whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods, which are not resistant…

存在不可忽略无回答的分类数据模型AI 解读

When categorical outcomes are subject to nonignorable nonresponse, log-linear models may be used to adjust for the nonresponse. The models are fitted to the data in an augmented frequency table in which one index corresponds to whether or not the subject is a respondent. The likelihood function is maximized over pseudo-observed cell frequencies with respect to this log-linear model using an EM algorithm. Each E step of the EM algorithm determines the pseudo-observed cell…

一种双重删失数据的非参数估计及其在艾滋病研究中的应用AI 解读

In many epidemiologic studies of human immunodeficiency virus (HIV) disease, interest focuses on the distribution of the length of the interval of time between two events. Two such problems are considered here, estimation of the distribution of time or number of sexual contacts between infection of an individual (an index case) and transmission of HIV to their sexual partner, and estimation of the distribution of time between infectiousness as a blood donor and the…

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