An empirical likelihood goodness-of-fit test for time series

Summary. Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α -mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model. The technique is based on a comparison with kernel smoothing estimators. The empirical likelihood formulation of the test has two attractive features. One is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood's ability to Studentize internally. The other is that the asymptotic distribution of the test statistic is free of unknown parameters, avoiding plug-in estimation. We apply the test to a discretized diffusion model which has recently been considered in financial market analysis.     

Pseudo–Modelling of Outliers for Estimation of Regression And Time Series Models

This paper documents situations where the variance inflation model for outliers has undesirable properties. The model is commonly used to accommodate outliers in a Bayesian analysis of regression and time series models. The alternative approach provided here does not suffer from these undesirable properties but gives inferences similar to those of the variance inflation model when this is appropriate. It can be used with regression, time series, and regression with correlated errors in a unified way, and adheres to the scientific principle that inference should be based on the data after obvious outliers have been discarded. Only one parameter is required for outliers; it is interpretable as the a priori willingness to remove observations from the analysis.     

Exposure Reconstruction for the TCDD-Exposed NIOSH Cohort Using a Concentration- and Age-Dependent Model of Elimination

Recent studies demonstrating a concentration dependence of elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) suggest that previous estimates of exposure for occupationally exposed cohorts may have underestimated actual exposure, resulting in a potential overestimate of the carcinogenic potency of TCDD in humans based on the mortality data for these cohorts. Using a database on U.S. chemical manufacturing workers potentially exposed to TCDD compiled by the National Institute for Occupational Safety and Health (NIOSH), we evaluated the impact of using a concentration- and age-dependent elimination model (CADM) (Aylward et al., 2005) on estimates of serum lipid area under the curve (AUC) for the NIOSH cohort. These data were used previously by Steenland et al. (2001) in combination with a first-order elimination model with an 8.7-year half-life to estimate cumulative serum lipid concentration (equivalent to AUC) for these workers for use in cancer dose-response assessment. Serum lipid TCDD measurements taken in 1988 for a subset of the cohort were combined with the NIOSH job exposure matrix and work histories to estimate dose rates per unit of exposure score. We evaluated the effect of choices in regression model (regression on untransformed vs. ln-transformed data and inclusion of a nonzero regression intercept) as well as the impact of choices of elimination models and parameters on estimated AUCs for the cohort. Central estimates for dose rate parameters derived from the serum-sampled subcohort were applied with the elimination models to time-specific exposure scores for the entire cohort to generate AUC estimates for all cohort members. Use of the CADM resulted in improved model fits to the serum sampling data compared to the first-order models. Dose rates varied by a factor of 50 among different combinations of elimination model, parameter sets, and regression models. Use of a CADM results in increases of up to five-fold in AUC estimates for the more highly exposed members of the cohort compared to estimates obtained using the first-order model with 8.7-year half-life. This degree of variation in the AUC estimates for this cohort would affect substantially the cancer potency estimates derived from the mortality data from this cohort. Such variability and uncertainty in the reconstructed serum lipid AUC estimates for this cohort, depending on elimination model, parameter set, and regression model, have not been described previously and are critical components in evaluating the dose-response data from the occupationally exposed populations.     

Semiparametric linear transformation models for current status data

Current status data arise when the death of every subject in a study cannot be determined precisely, but is known only to have occurred before or after a random monitoring time. The authors discuss the analysis of such data under semiparametric linear transformation models for which they propose a general inference procedure based on estimating functions. They determine the properties of the estimates they propose for the regression parameters of the model and illustrate their technique using tumorigenicity data.     

基于Simpson公式改进的FAGM(1,1)模型及其应用研究

本文分析了传统FAGM（1,1）模型建模过程中存在的误差,提出了一种基于Simpson公式改进的FAGM（1,1）模型。首先,基于分数阶累加生成算子和分数阶累减生成算子建立分数阶FAGM（1,1）模型。其次,利用Simpson积分公式对FAGM（1,1）模型的背景值进行改进,建立SFAGM（1,1）模型。进一步,应用遗传算法确定SFAGM（1,1）模型的最优阶数以提高模型的预测精度。最后,以中国人均GDP为例,对比分析GM（1,1）模型、Simpson改进的GM（1,1）模型（SGM（1,1））、FAGM（1,1）模型、SFAGM（1,1）模型的模拟结果,并对"十三五"时期的人均GDP进行预测,其结果表明SFAGM（1,1）模型比GM（1,1）、SGM（1,1）、FAGM（1,1）在人均GDP的预测方面有更高的精度,"十三五"期间人均GDP年平均增长率为10.64%,到2020年达到83146.97元,是2010年人均GDP的2.69倍,以2010年的人均GDP为基准,到2020年将能够实现翻一番的目标。     

低碳视角下农业集约化、绿色化与资源再生化 的实现机制研究

在实现"碳达峰碳中和"目标的重要历史机遇期,推动实现农业集约化、绿色化和资源再生化,构建资源节约型、绿色低碳型、生态循环型的农业发展模式,对于农业可持续发展具有重要意义。以2000-2018年我国31个省份为研究对象,通过面板向量自回归模型(PVAR),刻画资源消耗、农业产出、农业碳排放之间的动态传导机制。结果表明:(1)东部农业"碳达峰"节点出现较早,东北、西部相对较晚;2018年农业碳排放居前三的省份为湖南、黑龙江、河南,居后三的为北京、天津、上海;(2)资源消耗和农业产出之间呈现"低投入高产出"的农业集约化生产模式,但影响力微弱;农业产出和农业碳排放之间"高产出高排放"的情形长期面临农业绿色化的严峻考验;农业碳排放与资源消耗之间呈现"低排放低投入"的资源再生化现象,影响力短期微弱长期较强;(3)推动实现农业集约化、绿色化、资源再生化的关键在于探索降低农业碳排放的多重路径。因此,应强化农业集约化生产,充分发展资源再生化模式,探索形成农业绿色化格局新路径,以此来加快实现碳减排目标,推动农业可持续发展。     

多元正态分布广义方差区间估计的改进

讨论了多元正态分布广义方差的区间估计问题,给出了在覆盖率及长度上均优于最优仿射同变区间估计的改进估计．     

A Population Approach to Analysis of Variance Models

Several authors have contributed to what can now be considered a rather complete theory for analysis of variance in cases with orthogonal factors. By using this theory on an assumed basic reference population, the orthogonality concept gives a natural definition of independence between factors in the population. By looking upon the treated units in designed experiments as a formal sample from a future population about which we want to make inference, a natural parametrization of expectations and variances connected to such experiments arises. This approach seems to throw light upon several controversial questions in the theory of mixed models. Also, it gives a framework for discussing the choice of conditioning in models     

Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M -estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non-linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results