Inference of the derivative of nonparametric curve based on confidence distribution

Abstract

This paper focuses on inference based on the confidence distributions of the nonparametric regression function and its derivatives, in which dependent inferences are combined by obtaining information about their dependency structure. We first give a motivating example in production operation system to illustrate the necessity of the problems studied in this paper in practical applications. A goodness-of-fit test for polynomial regression model is proposed on the basis of the idea of combined confidence distribution inference, which is the Fisher’s combination statistic in some cases. On the basis of this testing results, a combined estimator for the p-order derivative of nonparametric regression function is provided as well as its large sample size properties. Consequently, the performances of the proposed test and estimation method are illustrated by three specific examples. Finally, the motivating example is analyzed in detail. The simulated and real data examples illustrate the good performance and practicability of the proposed methods based on confidence distribution.     

清代广西三界庙地理分布与三界神信仰探析

三界庙在清代广西各府中都有分布,主要集中分布在南宁、浔州、郁林、平乐、梧州等五府(州),呈现出一种沿着西江流域自东向西递减的分布规律,在郁江两岸分布最为密集。清代广西已经初步形成了三界神祭祀圈,而这种祭祀圈的出现与三界神的现实功利色彩有着密不可分的关系。     

浅析中国土族人口分布格局及其社会发展

人口分布格局,既是人在空间分布上呈现出来的地理状态,又是许多附着于分布环境上的社会人文变量的外在表现,因此对其进行研究具有探索自然和认识社会的双重意义。本文就中国土族人口的分布格局进行探讨,从历史和现实两方面分析了形成这种分布的原因,并在此基础上探讨了与人口分布格局密切相关的人口城市化、人口流动、人口素质提高、区域经济发展等社会热点问题,以期为政府政策的制定提供可靠的依据。     

The modified slash Lindley–Weibull distribution with applications to nutrition data

This work presents an extension of the slash Lindley–Weibull distribution, of which it can be considered a modification. The new family is obtained by using the quotient of two independent random variables: a two-parameter Lindley–Weibull distribution divided by a power of the exponential distribution with parameter equal to 2. We present the pdf and cdf of the new distribution, analyzing their risk functions. Some statistical properties are studied and the moments and coefficients of asymmetry and kurtosis are shown. The parameter estimation problem is carried out by the maximum likelihood method. The method is assessed by a Monte Carlo simulation study. We use nutrition data, which are characterized by high kurtosis, to illustrate the usefulness of the proposed model.     

代际研究中终生收入估算偏差问题探讨

在我国代际收入流动性问题研究中,微观数据分析常用父代40岁左右的单年收入替代其终生收入,由此导致代际收入弹性估计偏大问题。文章假定微观个体观测值服从对数正态分布并进行建模,对个体终生收入做出统计预测。模拟得到学历为硕士人群的工资年增长率是本科人群的1.06倍,收入达到峰值的时间则晚了约8年,对全部人群父代的终生收入用其40岁左右收入逼近的思路可依据父代教育水平进行再次细分。     

中国人口之分布: 附统计表与密度图

以最新、最权威的第六次人口普查数据及相关统计年鉴数据为基础,运用人口结构指数和相关统计分析方法,从空间属性和社会属性两个层面对成都市人口空间分布特征进行分析。研究表明：（1）从空间属性层面分析,成都市人口总量分布不均衡,空间分布悬殊较大,以五个主城区为中心,呈同心圆状向郊区急剧降低态势。同时,人口集中性及不均衡性较强,并呈现上升趋势;（2）从社会属性层面分析,少数民族人口主要分布在城市的西部与西北部;流动人口分布在中心城区和工业区;高学历人口集中在高等院校和科研院所的所在地;一二三产业人口呈同心圆由城市中心向外逐层分布趋势。     

On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

Bayesian nonparametric modelling of the link function in the single-index model using a Bernstein–Dirichlet process prior

This paper proposes the use of the Bernstein–Dirichlet process prior for a new nonparametric approach to estimating the link function in the single-index model (SIM). The Bernstein–Dirichlet process prior has so far mainly been used for nonparametric density estimation. Here we modify this approach to allow for an approximation of the unknown link function. Instead of the usual Gaussian distribution, the error term is assumed to be asymmetric Laplace distributed which increases the flexibility and robustness of the SIM. To automatically identify truly active predictors, spike-and-slab priors are used for Bayesian variable selection. Posterior computations are performed via a Metropolis-Hastings-within-Gibbs sampler using a truncation-based algorithm for stick-breaking priors. We compare the efficiency of the proposed approach with well-established techniques in an extensive simulation study and illustrate its practical performance by an application to nonparametric modelling of the power consumption in a sewage treatment plant.     

Robust inference for estimating equations with nonignorably missing data based on SIR algorithm

Nonresponse is a very common phenomenon in survey sampling. Nonignorable nonresponse – that is, a response mechanism that depends on the values of the variable having nonresponse – is the most difficult type of nonresponse to handle. This article develops a robust estimation approach to estimating equations (EEs) by incorporating the modelling of nonignorably missing data, the generalized method of moments (GMM) method and the imputation of EEs via the observed data rather than the imputed missing values when some responses are subject to nonignorably missingness. Based on a particular semiparametric logistic model for nonignorable missing response, this paper proposes the modified EEs to calculate the conditional expectation under nonignorably missing data. We can apply the GMM to infer the parameters. The advantage of our method is that it replaces the non-parametric kernel-smoothing with a parametric sampling importance resampling (SIR) procedure to avoid nonparametric kernel-smoothing problems with high dimensional covariates. The proposed method is shown to be more robust than some current approaches by the simulations.