An exploratory data analysis in scale-space for interval-valued data

We propose an exploratory data analysis approach when data are observed as intervals in a nonparametric regression setting. The interval-valued data contain richer information than single-valued data in the sense that they provide both center and range information of the underlying structure. Conventionally, these two attributes have been studied separately as traditional tools can be readily used for single-valued data analysis. We propose a unified data analysis tool that attempts to capture the relationship between response and covariate by simultaneously accounting for variability present in the data. It utilizes a kernel smoothing approach, which is conducted in scale-space so that it considers a wide range of smoothing parameters rather than selecting an optimal value. It also visually summarizes the significance of trends in the data as a color map across multiple locations and scales. We demonstrate its effectiveness as an exploratory data analysis tool for interval-valued data using simulated and real examples.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

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.     

中国农村民间借贷市场融资约束环境下利率定价模型分析——以广东农村实地调查数据为例

通过对广东农户民间借贷行为实地调查的问卷进行数据分析,了解农村民间借贷中的资金供求关系,发现存在的融资约束问题,进而对融资约束环境下民间借贷资金利率定价过程进行实证分析;着重考察农村民间借贷利率受公共信息和私人信息影响的程度,从借款人和贷款人的角度分别建立定价模型进行经验分析。结果显示,定价模型在F检验1%水平上显著,其他模型具有R2的统计显著性;反映借款用途的变量在10%水平上显著,其他变量均在5%水平上显著。这说明该市场利率能够反映公共信息的影响,借款人和贷款人的利率定价也反映了各自私人信息中相关风险和财务能力因素的影响,得到的经验结论主要是:第一,农村民间借贷市场是自主交易的金融市场;第二,其利率定价过程基本市场化。     

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。     

中国宏观经济波动源的识别与原因分析

为了识别驱动中国宏观经济周期波动性的影响因素,依据中国经济的特殊性,基于1978-2014年42个宏观经济变量的样本数据集构建动态因子模型进行实证分析。研究发现,驱动中国宏观经济波动主要因素有5个潜在宏观因子,其中前四个主要因子分别揭示了驱动中国经济周期波动的主要波动源,它们分别为工业产出因子、外商直接投资(FDI)因子、设备利用率因子和全要素生产率因子。另外,讨论了熨平经济周期性波动的经济政策选择。     

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.     

Some maximum-indifference estimators for the slope of a univariate linear model

As known, the least-squares estimator of the slope of a univariate linear model sets to zero the covariance between the regression residuals and the values of the explanatory variable. To prevent the estimation process from being influenced by outliers, which can be theoretically modelled by a heavy-tailed distribution for the error term, one can substitute covariance with some robust measures of association, for example Kendall's tau in the popular Theil–Sen estimator. In a scarcely known Italian paper, Cifarelli [(1978), ‘La Stima del Coefficiente di Regressione Mediante l'Indice di Cograduazione di Gini’, Rivista di matematica per le scienze economiche e sociali, 1, 7–38. A translation into English is available at http://arxiv.org/abs/1411.4809 and will appear in Decisions in Economics and Finance] shows that a gain of efficiency can be obtained by using Gini's cograduation index instead of Kendall's tau. This paper introduces a new estimator, derived from another association measure recently proposed. Such a measure is strongly related to Gini's cograduation index, as they are both built to vanish in the general framework of indifference. The newly proposed estimator is shown to be unbiased and asymptotically normally distributed. Moreover, all considered estimators are compared via their asymptotic relative efficiency and a small simulation study. Finally, some indications about the performance of the considered estimators in the presence of contaminated normal data are provided.     

A nonparametric hypothesis test for heteroscedasticity

In this paper, a hypothesis test for heteroscedasticity is proposed in a nonparametric regression model. The test statistic, which uses the residuals from a nonparametric fit of the mean function, is based on an adaptation of the well-known Levene's test. Using the recent theory for analysis of variance when the number of factor levels goes to infinity, the asymptotic distribution of the test statistic is established under the null hypothesis of homocedasticity and under local alternatives. Simulations suggest that the proposed test performs well in several situations, especially when the variance is a nonlinear function of the predictor.     

Predictive Inference for Big,Spatial, Non‐Gaussian Data: MODIS Cloud Data and its Change‐of‐Support

Remote sensing of the earth with satellites yields datasets that can be massive in size, nonstationary in space, and non‐Gaussian in distribution. To overcome computational challenges, we use the reduced‐rank spatial random effects (SRE) model in a statistical analysis of cloud‐mask data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board NASA's Terra satellite. Parameterisations of cloud processes are the biggest source of uncertainty and sensitivity in different climate models’ future projections of Earth's climate. An accurate quantification of the spatial distribution of clouds, as well as a rigorously estimated pixel‐scale clear‐sky‐probability process, is needed to establish reliable estimates of cloud‐distributional changes and trends caused by climate change. Here we give a hierarchical spatial‐statistical modelling approach for a very large spatial dataset of 2.75 million pixels, corresponding to a granule of MODIS cloud‐mask data, and we use spatial change‐of‐Support relationships to estimate cloud fraction at coarser resolutions. Our model is non‐Gaussian; it postulates a hidden process for the clear‐sky probability that makes use of the SRE model, EM‐estimation, and optimal (empirical Bayes) spatial prediction of the clear‐sky‐probability process. Measures of prediction uncertainty are also given.