任意秩多元线性模型中的最优预测

本文研究了任意秩多元线性模型中可预测变量的最优预测,特别地,我们考虑了一类特殊的预测函数,Φ－线性预测函数,给出了Φ－可预测变量和最优Φ线性一无偏预测的定义,得到了Φ－可预测变量的最优Φ－线性无偏预测,并证明了它在几乎处处意主意义下的唯一性。     

关于Reissner-Mindlin板问题的线性格式

本文给出Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｌｉｎ板问题的线性格式[1]中的汽泡函数的最优选取。     

线性等式约束下有限总体中的最优预测

本研究了带线性等式的约束条件的有限总体中的最优预测问题,给出了条件可预测变量和条件最优线性无偏测的定义,得到了条件可预测变量的所有条件最优线性无偏预测,并证明了它在几乎处处意义下的唯一性。     

多元线性模型中两类预测的最优性判别

在一般多元线性模型中就基于岭估计的预测量与最优线性无偏预测量的最优性判别问题进行了讨论,得到了基于岭估计的预测量在矩阵迹意义下优于最优线性无偏预测量的充要条件.     

任意秩有限总体中无偏预测和估计的构造关系

研究了有限总体均值向量的无偏估计和线性可预测变量的无偏预测之间的关系,利用分块矩阵广义逆直接对加权风险函数进行分解,提出了一种由均值向量的无偏估计来构造无偏预测的新方法,并找到了它们之间的构造关系.特别地,线性可预测变量的最优线性无偏预测(BLUP)可由均值向量的最佳线性无偏估计(BLUE)惟一地表示(有关惟一性在几乎处处意义下理解).     

增长曲线模型中两个最优线性预测

对一般增长曲线模型中一类线性可预测变量KY0L和φ-可预测变量的最优预测进行了研究，在一定条件下分别得到了最优线性无偏预测和最优φ-线性无偏预测，并证明了它们在几乎处处意义下的唯一性．     

一般生长曲线模型中最优预测的稳健性

研究了一般生长曲线模型中最优线性无偏预测的稳健性,得到了线性可预测变量的这种预测关于协方差阵具有稳健性的充要条件.     

两个线性模型间最优线性无偏预测的等价性

设M1和M2是两个带有预测量的线性模型,通过使用矩阵秩方法,本文给出了模型M1下预测量的最优线性无偏预测同时也是模型M2下的最优线性无偏预测的充分必要条件.作为这个结果的应用,我们给出了两个线性混合模型间最优线性无偏预测等价性的充分必要条件.     

基于压缩主成分估计的预测优良性的一个充要条件

本文在均方误差矩阵判别准则和风险函数的差别准则下,对广义线性模型的最优预测与经典预测的优良性进行比较分析,获得了比较基于压缩主成分估计的两类预测优良性的充要条件,并运用统计模拟对该充要条件进行了实证分析.     

多元线性模型中条件最优预测的稳健性

研究了多元线性模型中条件最优线性无偏预测的稳健性问题,得到了条件线性可预测变量的这种预测关于协方差矩阵具有稳健性的充要条件.     

Bayesian point estimation and prediction

In the Bayesian viewpoint, point estimation and prediction are treated from a decision-making standpoint. If a loss function can be determined which associates a loss with every possible error of estimation or prediction, then the optimal estimator or predictor is that value which minimizes expected loss. In most applications, the loss function is assumed to be linear or quadratic in the error of estimation or prediction, although there are many practical situations in which these simple functions are quite inappropriate. In this paper, we investigate the properties of Bayesian point estimates under other loss functions; both the general case and two special cases (power and exponential loss functions) are considered. For the special cases, we also investigate the sensitivity of Bayesian point estimation and prediction to misspecification in the loss function and discuss the practical implications of the results.     

Prediction and calibration in generalized linear models

This paper concerns prediction and calibration in generalized linear models. A new predictive procedure, giving improved prediction intervals, is briefly reviewed and further theoretical results, useful for calculations, are presented. Indeed, the calibration problem is faced within the classical approach and a suitable solution is obtained by inverting the associated improved prediction procedure. This calibration technique gives accurate confidence regions and it constitutes a substantial improvement over both the estimative solution and the naive solution, which involves, even for non-linear and non-normal models, the results available for the linear Gaussian case. Finally, some useful explicit formulae for the construction of prediction and calibration intervals are presented, with regard to generalized linear models with alternative error terms and link functions. This research was partially supported by a grant from Ministero dell’Instruzione, dell’Università e della Ricerca, Italy.     

二次损失下任意秩有限总体中的线性Minimax预测

本文对通常的二次损失作了适当的修改,在此基础上研究了一个预测在齐次线性预测函数类中的极大极小性。得到了任意秩有限总体中线性可预测变量的唯一线性Minimax预测(有关唯一性在几乎处处意义下理解)。     

Design of hybrid genetic- SVD ANFIS networks for fatigue life modelling of GRP composites

Genetic algorithm (GA) and singular value decomposition (SVD) are deployed for the optimal design of both Gaussian membership functions of antecedents and the vector of linear coefficients of consequents, respectively, of adaptive neurofuzzy inference systems (ANFIS) networks that are used for fatigue life modelling and prediction of unidirectional GRP Composites. The aim of such modelling is to show how the fatigue life varies with the variation of important parameters namely, maximum stress, stress ratio, fiber angle. It is demonstrated that SVD can be effectively used to optimally find the vector of linear coefficients of conclusion parts in ANFIS models and their Gaussian membership functions in premise parts are determined by GA.     

Prediction with a Generalized Cost of Error Function

Classical prediction theory limits itself to quadratic cost functions, and hence least-square predictors. However, the cost functions that arise in practice in economics and management situations are not likely to be quadratic in form, and frequently will be non-symmetric. It is the object of this paper to throw light on prediction in such situations and to suggest some practical implications. It is suggested that a useful, although sub-optimal, manner of taking into account generalized cost functions is to add a constant bias term to the predictor. Two theorems are proved showing that under fairly general conditions the bias term can be taken to be zero when one uses a symmetric cost function. If the cost function is a non-symmetric linear function, an expression for the bias can be simply obtained.     

Real estate price prediction under asymmetric loss

This paper deals with the problem of how to adjust a predictive mean in a practical situation of prediction where there is asymmetry in the loss function. A standard linear model is considered for predicting the price of real estate using a normal-gamma conjugate prior for the parameters. The prior of a subject real estate agent is elicited but, for comparison, a diffuse prior is also considered. Three loss functions are used: asymmetric linear, asymmetric quadratic and LINEX, and the parameters under each of these postulated forms are elicited. Theoretical developments for prediction under each loss function in the presence of normal errors are presented and useful tables of adjustment factor values given. Predictions of the dependent price variable for two properties with differing characteristics are made under each loss function and the results compared.     

Functional data analysis for cash flow and transactions intensity continuous-time prediction using Hilbert-valued autoregressive processes

In this paper we use a functional autoregressive model as a robust predictor of the cash flow and intensity of transactions in a credit card payment systems. Intraday economic time series are treated as random continuous functions projected onto low dimensional subspace. Wavelet bases are considered for data smoothing. We compare two linear wavelet methods for the prediction problem of a continuous-time stochastic process on an entire time interval. Ex poste prediction is used to check the models.     

Interaction Model and Model Selection for Function-on-Function Regression

Regression models with interaction effects have been widely used in multivariate analysis to improve model flexibility and prediction accuracy. In functional data analysis, however, due to the challenges of estimating three-dimensional coefficient functions, interaction effects have not been considered for function-on-function linear regression. In this article, we propose function-on-function regression models with interaction and quadratic effects. For a model with specified main and interaction effects, we propose an efficient estimation method that enjoys a minimum prediction error property and has good predictive performance in practice. Moreover, converting the estimation of three-dimensional coefficient functions of the interaction effects to the estimation of two- and one-dimensional functions separately, our method is computationally efficient. We also propose adaptive penalties to account for varying magnitudes and roughness levels of coefficient functions. In practice, the forms of the models are usually unspecified. We propose a stepwise procedure for model selection based on a predictive criterion. This method is implemented in our R package FRegSigComp. Supplemental materials are available online.     

Some results on Tchebycheffian spline functions

This report derives explicit solutions to problems involving Tchebycheffian spline functions. We use a reproducing kernel Hilbert space which depends on the smoothness criterion, but not on the form of the data, to solve explicitly Hermite-Birkhoff interpolation and smoothing problems. Sard's best approximation to linear functionals and smoothing with respect to linear inequality constraints are also discussed. Some of the results are used to show that spline interpolation and smoothing is equivalent to prediction and filtering on realizations of certain stochastic processes.     

矩阵损失下有限总体中的局部线性Minimax预测

该文在矩阵损失下研究线性预测函数的局部极大极小性．在适当的假设下,得到了任意秩有限总体中的可预测变量的唯一的局部线性Ｍｉｎｉｍａｘ预测．（有关唯一性在几乎处处意义下理解）．