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空间回归的加性模型构建AI 解读

Summary Spatial regression is an important predictive tool in many scientific applications and an additive model provides a flexible regression relationship between predictors and a response variable. We develop a regularized variable selection technique for building a spatial additive model. We find that the methods developed for independent data do not work well for spatially dependent data. This motivates us to propose a spatially weighted l2-error norm with a group lasso…

两层混合模型中非参数推断的反卷积方法AI 解读

Summary We develop a general non-parametric approach to the analysis of clustered data via random effects. Assuming only that the link function is known, the regression functions and the distributions of both cluster means and observation errors are treated non-parametrically. Our argument proceeds by viewing the observation error at the cluster mean level as though it were a measurement error in an errors-in-variables problem, and using a deconvolution argument to access…

仅有汇总信息时聚类二元与计数数据的非参数推断AI 解读

Summary Data in the form of pairs (X,Y), where the response Y is a count, arise in many applications, including problems involving stratified or two-stage sampling. Such data are often analysed by using random-effects models, where the distribution of Y, conditional on X and on an unobserved random parameter Θ, is taken to be either binomial or Poisson, and the distribution of Θ is connected through a link function to a random effect. The latter is sometimes supposed to be…

存在依赖性终止时复发事件数据的现有分析方法AI 解读

There has been a recent surge of interest in modeling and methods for analyzing recurrent events data with risk of termination dependent on the history of the recurrent events. To aid the future users in understanding the implications of modeling assumptions and modeling properties, we review the state of the art statistical methods and present novel theoretical properties, identifiability results and practical consequences of key modeling assumptions of several fully…

嵌套误差回归模型中均方预测误差的非参数估计AI 解读

Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and mean-squared prediction error is the main way in which prediction performance is measured. In this paper we suggest a new approach to estimating mean-squared prediction error. We introduce a matched-moment, double-bootstrap algorithm, enabling…

变换后 Fay–Herriot 模型中的均方误差估计AI 解读

Summary The problem of accurately estimating the mean-squared error of small area estimators within a Fay–Herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable. For bias-corrected empirical best linear unbiased predictor small area point estimators, mean-squared error formulae and estimators are provided, with biases of smaller order than the reciprocal of the number of small…

小区域预测的参数自助法AI 解读

Summary The particularly wide range of applications of small area prediction, e.g. in policy making decisions, has meant that this topic has received substantial attention in recent years. The problems of estimating mean-squared predictive error, of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers, although existing methodology is still restricted to a narrow range of models. To overcome this difficulty we…