On asymptotic distribution of prediction in functional linear regression

There has been substantial recent attention on problems involving a functional linear regression model with scalar response. Among them, there have been few works dealing with asymptotic distribution of prediction in functional linear regression models. In recent literature, the centeral limit theorem for prediction has been discussed, but the proof and conditions under which the random bias terms for a fixed predictor converge to zero have been ignored so that the impact of these terms on the convergence of the prediction has not been well understood. Clarifying the proof and conditions under which the bias terms converge to zero, we show that the asymptotic distribution of the prediction is normal. Furthermore, we have derived those results related to other terms that already obtained by others, under milder conditions. Finally, we conduct a simulation study to investigate performance of the asymptotic distribution under various parameter settings.     

Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses

Categorical longitudinal data are frequently applied in a variety of fields, and are commonly fitted by generalized linear mixed models (GLMMs) and generalized estimating equations models. The cumulative logit is one of the useful link functions to deal with the problem involving repeated ordinal responses. To check the adequacy of the GLMMs with cumulative logit link function, two goodness-of-fit tests constructed by the unweighted sum of squared model residuals using numerical integration and bootstrap resampling technique are proposed. The empirical type I error rates and powers of the proposed tests are examined by simulation studies. The ordinal longitudinal studies are utilized to illustrate the application of the two proposed tests.     

An F-type test for detecting departure from monotonicity in a functional linear model

When studying associations between a functional covariate and scalar response using a functional linear model (FLM), scientific knowledge may indicate possible monotonicity of the unknown parameter curve. In this context, we propose an F-type test of monotonicity, based on a full versus reduced nested model structure, where the reduced model with monotonically constrained parameter curve is nested within an unconstrained FLM. For estimation under the unconstrained FLM, we consider two approaches: penalised least-squares and linear mixed model effects estimation. We use a smooth then monotonise approach to estimate the reduced model, within the null space of monotone parameter curves. A bootstrap procedure is used to simulate the null distribution of the test statistic. We present a simulation study of the power of the proposed test, and illustrate the test using data from a head and neck cancer study.     

使用种次号加辅助区分号对“同类书”的集中方法

由于在文献分类编目工作中会遇到各种内容相同,而在装帧形式、版本形式等方面不同的“同类书”,而将这些“同类书”在目录组织进而在分类排架中组织在一起十分困难,为了方便读者对比和选择使用,阐述了采用种次号加辅助区分号将这些“同类书”集中的具体方法,结果表明,此种方法不仅目录组织清晰,还有助于读者对图书的检索和利用。     

State transition modeling of complex monitored health data

This article considers the analysis of complex monitored health data, where often one or several signals are reflecting the current health status that can be represented by a finite number of states, in addition to a set of covariates. In particular, we consider a novel application of a non-parametric state intensity regression method in order to study time-dependent effects of covariates on the state transition intensities. The method can handle baseline, time varying as well as dynamic covariates. Because of the non-parametric nature, the method can handle different data types and challenges under minimal assumptions. If the signal that is reflecting the current health status is of continuous nature, we propose the application of a weighted median and a hysteresis filter as data pre-processing steps in order to facilitate robust analysis. In intensity regression, covariates can be aggregated by a suitable functional form over a time history window. We propose to study the estimated cumulative regression parameters for different choices of the time history window in order to investigate short- and long-term effects of the given covariates. The proposed framework is discussed and applied to resuscitation data of newborns collected in Tanzania.     

Statistical inference based on generalized Lindley record values

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.     

数的定义:戴德金与弗雷格

本文主要考察戴德金和弗雷格对自然数概念所作的划时代的工作.借助这些工作,自然数概念由"直观上清晰明了的"转变为"逻辑上严格精密的".虽然他们以不同的方式给出了自然数的定义,但可以证明它们在数学上是等价的.在哲学上,两位思想家却存在着一些差别.虽然戴德金同意弗雷格将数看作客观独立的对象,但他拒绝将数还原为类或概念的外延的还原主义立场.戴德金反对将数还原为任何已知的对象,而视其为心灵创造的新事物,他同时坚持任何满足算术公理的事物都可看作数的代表.     

试论数字色彩应用

介绍色彩数字编程和色彩数字设计方法。将数字的可变性应用到色彩编程和色彩设计之中,以期对艺术设计中手工颜料调配、提高色彩的准确度及色彩的复制与研究提供参考。     

北流白话的介词及其用法

文章通过与现代汉语普通话介词的比较,确定了北流白话介词的数量和类型,并且比较全面地描写了北流白话的17个介词。