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含变点的线性变量误差模型推断AI 解读

A new linear structural errors-in-variables regression with changepoint model is considered. In this model we consider the likelihood ratio test based on the maximum Hotelling T 2 for the test of no change against the alternative of exactly one change. If there is a change, either known a priori or by testing, then we estimate the unknown changepoint parameter and some other related parameters by maximum likelihood. The limiting distribution of the changepoint estimator is…

多分类回归AI 解读

An automatic procedure that uses linear splines and their tensor products is proposed for fitting a regression model to data involving a polychotomous response variable and one or more predictors. The fitted model can be used for multiple classification. The automatic fitting procedure involves maximum likelihood estimation, stepwise addition, stepwise deletion, and model selection by the Akaike information criterion, cross-validation, or an independent test set. A modified…

基于含噪支持函数数据的凸集估计AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

大西洋鳕鱼种群年龄构成的序约束贝叶斯估计AI 解读

The management of a commercial fishery often requires estimates of the age composition. These estimates are typically based on age and length data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey. We use data from annual research cruises of Georges Bank conducted by the Canadian Department of Fisheries and Oceans to show how inferences for Atlantic cod (Gadus morhua) can be improved. Traditionally, two-phase…

空间疾病发生率的回归方法：估计函数途径AI 解读

Epidemiologists commonly study the geographical variation of disease rates to generate and refine testable hypotheses regarding etiology. Poisson regression is often used to estimate the parameters that characterize the effects of risk factors on disease. Hierarchical models have been proposed to utilize spatial locations and neighbors as surrogates for unknown or unmeasured risk factors in the analysis of disease rates. Although hierarchical models are useful in modeling…

利用多个二元结局研究致畸作用的潜变量模型AI 解读

Multiple outcomes are commonly measured in the study of birth defects. The reason is that most teratogens do not cause a single, uniquely defined defect, but rather result in a range of effects, including major malformations, minor anomalies, and deficiencies in birth weight, length and head circumference. The spectrum of effects associated with a particular teratogen is sometimes described as a “syndrome.” In this article we develop a latent variable model to characterize…

协调两个或多个抽样调查中共同变量的估计AI 解读

In practice, for many sample surveys the estimates of several population totals are based on one set of weights, which reproduces the known population totals of auxiliary variables. Such a set can always be obtained by using the general regression estimator. If some variables, not necessarily with known population totals, are jointly collected in two sample surveys, then it may be desirable that the weights of both surveys produce the same estimates for the unknown…

基于因果式残差正交化的向量自回归脉冲响应函数AI 解读

A data-determined method for testing structural models of the errors in vector autoregressions is discussed. The method can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification. In one dimension, it turns out that standard t statistics can be used to test the various overidentifying restrictions that are implied by a model. In another dimension, the method…

含协整与标量分量的向量自回归模型推断AI 解读

For the partially nonstationary vector autoregressive model of Ann and Reinsel, I further assume that the first differenced series has scalar components of lower order and study estimation of these models along with asymptotic properties of the estimators. It is shown that Gaussian reduced rank estimation can be easily carried out by simple modification of the Ahn and Reinsel's method. The asymptotic distribution for the estimator of the nonstationary parameter is a locally…

蝾螈交配数据的再分析：修正 Laplace 近似方法AI 解读

The salamander mating dataset of McCullagh and Nelder has drawn the attention of statisticians because of its challenging structure: the design is crossed rather than nested. The standard Laplace approximation used to evaluate marginal likelihood functions fails in this case because the dimension of the integral is the square root of the sample size. A modification has been proposed by Shun and McCullagh. This article reanalyzes the salamander data using this modified…

多元二元响应重复测量的模型AI 解读

This article presents a logit model for a vector of binary variables observed for each subject under multiple conditions. The model contains a vector of random effects to account for correlations among the repeated measurements. A nonparametric treatment of the random effects implies a multivariate log-linear model having quasi-symmetric structure for the cross-classification of responses at the various conditions. The fit yields estimates of within-subject effects comparing…

免疫测定中经自助法调整的校准置信区间AI 解读

In immunoassay, a nonlinear heteroscedastic regression model is used to characterize assay concentration-response, and the model fitted to data from standard samples is used to calibrate unknown test samples. Usual large-sample methods to construct individual confidence intervals for calibrated concentrations have been observed in empirical studies to be seriously inaccurate in terms of achieving the nominal level of coverage. We show theoretically that this inaccuracy is…

不平衡析因设计的非参数假设与秩统计量AI 解读

Factorial designs are studied with independent observations, fixed number of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics are derived for testing the nonparametric hypotheses of no main effects, no interaction, and no factor effects in unbalanced crossed classifications. The formulation of all results includes tied…

基于似然比的生存函数置信带AI 解读

Thomas and Grunkemeier introduced a nonparametric likelihood ratio approach to confidence interval estimation of survival probabilities based on right-censored data. We construct simultaneous confidence bands using this approach. The boundaries of the bands are contained within [0, 1]. A procedure essentially equivalent to a bias correction is developed. The resulting increase in coverage accuracy is illustrated by an example and a simulation study. We look at various…

贝叶斯线性模型中删例重要性抽样权重的变异性AI 解读

I consider a standard specification of the Bayesian linear model and derive necessary and sufficient conditions for the variance of the case-deletion importance sampling weights to be finite. The conditions have an intuitive interpretation in terms of familiar frequentist measures of leverage and influence and are easy to verify. I present two real data examples in which the necessary conditions fail to hold for some observations and the corresponding importance sampling…

正态均值的乘积分割模型AI 解读

I consider probability models for the estimation of normal means that allow for some of the means to be equal. These probability models, called product partition models, specify prior probabilities for a random partition. The posterior probability of the partition given the observations has the same form. The resulting estimate of the means—the product estimate—is obtained by conditioning on the partition and summing over all possible partitions. The large number of…

线性回归模型的贝叶斯模型平均AI 解读

We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of interest. This approach is often not practical. In this…

广义线性混合模型的最大似然算法AI 解读

Maximum likelihood algorithms are described for generalized linear mixed models. I show how to construct a Monte Carlo version of the EM algorithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate and improve the use of importance sampling ideas. Calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorithm as a framework to compare maximum likelihood to the…

混合线性模型中的有界影响估计AI 解读

Bounded influence estimation (also known as generalized M or GM estimation) in the regression model is reviewed. The definitions of bounded influence estimation proposed by Mallows and Schweppe are then extended to the mixed linear model. This is achieved by applying appropriate weight functions to maximum likelihood and restricted maximum likelihood estimating equations. The asymptotic properties of the new estimators are obtained, and the estimators are applied to an…

简化单调回归方法AI 解读

Medical researchers often desire to categorize patients into monotonic response groups based on the relationship between continuous variables. Isotonic regression fits consist of level sets of increasing value, for which the estimated response is constant. However, the number of level sets obtained is often large, preventing simple description. This article introduces two new nonparametric methods called reduced isotonic regression and reduced monotonic regression, the…

混合自适应样条AI 解读

An adaptive spline method for smoothing is proposed that combines features from both regression spline and smoothing spline approaches. One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous “curvature” of true functions at different locations. This method can be applied to many multivariate function estimation problems, which is illustrated by an application to smoothing temperature data on the globe. The method's performance…

响应曲线的时间加速模型AI 解读

We propose a nonparametric method of data analysis for situations where the data consist of a sample of curves and a covariate is present. We assume the observed curves to be time-accelerated versions of a basic underlying stochastic process and assume the time acceleration factor for each observed process, determining the “eigenzeit,” to be a smooth function of the covariate. We discuss an iterative procedure to estimate the components of the model nonparametrically, using…

地理聚合数据的空间平滑及发病率地图构建AI 解读

We address the commonly encountered situation in spatial statistics where data such as counts of incidences of a certain disease are available only in geographically aggregated form. We develop fairly general models and propose a modified version of the locally weighted least squares method to recover the unknown smooth spatial function that is assumed to generate the observations. In the special case of count data, the target function is the intensity function, conditional…

判定历史天文表之间的依赖关系AI 解读

The authorship of portions of some ancient and medieval astronomical manuscripts is a current historical issue. This article develops a statistical method for determining whether or not a link exists between a pair of mathematically defined historical astronomical tables. The existence or nonexistence of such links aids the analysis of the origins of these documents. Nonparametric methods are used to determine whether traces of the errors in one table may be found in the…