On smoothness of Tukey depth contours

The smoothness of Tukey depth contours is a regularity condition often encountered in asymptotic theory, among others. This condition ensures that the Tukey depth fully characterizes the underlying multivariate probability distribution. In this paper we demonstrate that this regularity condition is rarely satisfied. It is shown that even well-behaved probability distributions with symmetrical, smooth and (strictly) quasi-concave densities may have non-smooth Tukey depth contours, and that the smoothness behaviour of depth contours is fairly unpredictable.     

Investigating impacts of complex sampling on latent growth curve modelling

We investigate the impacts of complex sampling on point and standard error estimates in latent growth curve modelling of survey data. Methodological issues are illustrated with empirical evidence from the analysis of longitudinal data on life satisfaction trajectories using data from the British Household Panel Survey, a national representative survey in Great Britain. A multi-process second-order latent growth curve model with conditional linear growth is used to study variation in the two perceived life satisfaction latent factors considered. The benefits of accounting for the complex survey design are considered, including obtaining unbiased both point and standard error estimates, and therefore correctly specified confidence intervals and statistical tests. We conclude that, even for the rather elaborated longitudinal data models that were considered, estimation procedures are affected by variance-inflating impacts of complex sampling.     

Local influence diagnostics for incomplete overdispersed longitudinal counts

We develop local influence diagnostics to detect influential subjects when generalized linear mixed models are fitted to incomplete longitudinal overdispersed count data. The focus is on the influence stemming from the dropout model specification. In particular, the effect of small perturbations around an MAR specification are examined. The method is applied to data from a longitudinal clinical trial in epileptic patients. The effect on models allowing for overdispersion is contrasted with that on models that do not.     

A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates

We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER). Together, we call these conditions a ‘rejection principle for sequential tests’, which we then apply to some existing sequential multiple testing procedures to give simplified understanding of their FWER control. Next, the principle is applied to derive two new sequential multiple testing procedures with provable FWER control, one for testing hypotheses in order and another for closed testing. Examples of these new procedures are given by applying them to a chromosome aberration data set and finding the maximum safe dose of a treatment.     

Functional Partial Linear Single‐index Model

This paper deals with the problem of predicting the real‐valued response variable using explanatory variables containing both multivariate random variable and random curve. The proposed functional partial linear single‐index model treats the multivariate random variable as linear part and the random curve as functional single‐index part, respectively. To estimate the non‐parametric link function, the functional single‐index and the parameters in the linear part, a two‐stage estimation procedure is proposed. Compared with existing semi‐parametric methods, the proposed approach requires no initial estimation and iteration. Asymptotical properties are established for both the parameters in the linear part and the functional single‐index. The convergence rate for the non‐parametric link function is also given. In addition, asymptotical normality of the error variance is obtained that facilitates the construction of confidence region and hypothesis testing for the unknown parameter. Numerical experiments including simulation studies and a real‐data analysis are conducted to evaluate the empirical performance of the proposed method.     

煤炭大数据指数编制及经验模态分解模型研究

基于开放性数据源、连续观测昨多变量数据编制的大数据指数,与传统的统计调查指数存在的差异不仅在于数据本身的无限扩张,而且在于编制方法以及分解研究的规则、模型方面的差异。在大数据背景下,率先尝试性地提出大数据指数的定义和数据假设,将"互联网大数据指数"引入煤炭交易价格指数综合编制太原煤炭交易大数据指数,从而反映煤炭价格的变动趋势;导入经验模态分解模型,对所编制的煤炭大数据指数进行分解研究,尝试比较与传统的统计调查指数的差异。研究表明:新编制的煤炭价格大数据指数要比太原煤炭交易价格指数更为敏感和迅速,能更好地反映煤炭价格的变动趋势。随着"互联网+"和大数据战略的逐渐普及,基于互联网大数据编制的综合指数会影响到更多领域,将成为经济管理和社会发展各个领域的晴雨表和指示器;与传统统计调查指数逐步融合、互补或者升级,成为宏观经济大数据指数的重要组成部分。     

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.     

基于主成分logistic回归模型的餐饮商务信息意识研究

数据挖掘技术日趋成熟,广泛应用于金融、地产、投资、评估等各个领域。数据挖掘技术亦可应用于餐饮业,为其经营决策做出分析。其他领域的数据挖掘的成功案例也可以引用到餐饮行业中。本文对餐饮人士在餐饮商务中是否具备信息意识、对信息意识的重视程度进行调查,利用数据挖掘中主成分分析和 logistic 回归处理和分析收集来的数据,从而说明数据挖掘在餐饮业管理中的重要意义,反映餐饮人士信息意识状况。利用数据挖掘技术对餐饮商务资讯进行管理势必提高企业效率和盈利水平,促进餐饮业健康稳定的发展。