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线性混合模型预测量的边际与条件多重推断AI 解读

In spite of its high practical relevance, cluster specific multiple inference for linear mixed model predictors has hardly been addressed so far. While marginal inference for population parameters is well understood, conditional inference for the cluster specific predictors is more intricate. This work introduces a general framework for multiple inference in linear mixed models for cluster specific predictors. Consistent confidence sets for multiple inference are constructed…

相依数据的偏最小二乘法AI 解读

We consider the partial least squares algorithm for dependent data and study the consequences of ignoring the dependence both theoretically and numerically. Ignoring nonstationary dependence structures can lead to inconsistent estimation, but a simple modification yields consistent estimation. A protein dynamics example illustrates the superior predictive power of the proposed method.

样条估计量的统一框架AI 解读

This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler–Reinsch basis in terms of exponential splines allows the derivation of an expression for the asymptotic equivalent kernel on the real line for all spline estimators simultaneously. The corresponding bandwidth, which drives the asymptotic behaviour of spline…

惩罚样条两种框架下的平滑参数选择AI 解读

Summary There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated by minimizing criteria that approximate the average mean-squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. The asymptotic properties of both smoothing parameter estimators for penalized…

可加模型的直接同时推断及营养不足建模应用AI 解读

This article proposes a simple and fast approach to build simultaneous confidence bands and perform specification tests for smooth curves in additive models. The method allows for handling of spatially heterogeneous functions and its derivatives as well as heteroscedasticity in the data. It is applied to study the determinants of chronic undernutrition of Kenyan children, with a particular focus on the highly nonlinear age pattern in undernutrition. Model estimation using…

惩罚样条估计的同时置信带AI 解读

In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist…

广义惩罚样条平滑的若干渐近结果AI 解读

Summary The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for non-normal responses. The results are extended in two ways. First, assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models. We consider the asymptotic rates such that the Laplace approximation is…

相关误差下惩罚样条平滑的一则说明AI 解读

We investigate the behavior of data-driven smoothing parameters for penalized spline regression in the presence of correlated data. It has been shown for other smoothing methods that mean squared error minimizers, such as (generalized) cross-validation or the Akaike information criterion, are extremely sensitive to misspecifications of the correlation structure resulting in over- or (under-)fitting the data. In contrast to this, we show that a maximum likelihood–based choice…