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.     

Bias-corrected confidence bands in nonparametric regression

Bias-corrected confidence bands for general nonparametric regression models are considered. We use local polynomial fitting to construct the confidence bands and combine the cross-validation method and the plug-in method to select the bandwidths. Related asymptotic results are obtained. Our simulations show that confidence bands constructed by local polynomial fitting have much better coverage than those constructed by using the Nadaraya–Watson estimator. The results are also applicable to nonparametric autoregressive time series models.     

论牟宗三先生评王畿

牟宗三先生对王畿哲学体系有细腻的分疏,重点剖析了他的“四无”说、先天正心之学和后天诚意之学,极有价值。本文对其中几处提出了一些不同看法。至于对王畿在王学分化中定位的评述,牟氏纠正了黄宗羲有关判断的失误。     

高校教育精准扶贫模式探究——以华中农业大学精准扶贫建始县为例

教育扶贫是高校精准扶贫地方的主要路径。基于华中农业大学在建始县精准扶贫的实践所取得的成效及遇到的问题,通过对三螺旋理论进行了深化与拓展,构建了以产业为纽带,农户、企业、高校、政府四主体相互作用的四螺旋模型,探索各主体充分发挥优势,协同创新的作用机理,提出基于四螺旋模型的高校精准扶贫地方的新路径,即：找准农户致贫或返贫的原因;高校与政府联动,做好扶贫规划;高校与企业联动,抓好产业建设;加强高校、企业与地方政府联动,攻克难点问题;四主体联动,强化过程管理。     

安徽省朱子学术研讨会观点综述

介绍安徽朱子研究会2004年学术年会众多专家学者关于朱熹“存天理,灭人欲”思想和“为民”思想、朱熹道德伦理学说的构建、朱熹哲学的世界意义、《四书章句集注》、朱熹研究的方法论等方面的有关观点。     

南京历史文化特征及其现代意义

中华文明体系主要由四大文化板块构成,其中长江文化板块是支撑南京成为中华古都的重要条件.南京具有雄视长江、领袖东南、近海控淮的地缘优势,这决定了她担负着在中国大格局中必然崛起的历史使命.除汉、唐之间作为"六朝都城"之外,从元末以后到1949年的581年时间内,南京与北京这两个古都的互动主导着整个中国的政治格局和民族命运,充分体现了南京城市的独特地位和非凡的区位优势,也是南京对中国历史所做出的重大贡献.为此,通览整个中国的文明历程,公元211年以后南京的崛起,应列为我国历史上的重大事件,即南京的崛起开辟了长江文化板块乃至中国发展的新格局和新时代.     

Multiparous women's confidence to have a publicly-funded homebirth: a qualitative study

Background

Hospital birth is commonly thought to be a safer option than homebirth, despite many studies showing similar rates of safety for low risk mothers and babies when cared for by qualified midwives with systems of back-up in place. Recently in Australia, demand has led to the introduction of a small number of publicly-funded homebirth programs. Women's confidence in having a homebirth through a publicly-funded homebirth program in Australia has not yet been explored.

Aim

The aim of the study was to explore the reasons why multiparous women feel confident to have a homebirth within a publicly-funded model of care in Australia.

Methods

Ten multiparous English-speaking women who chose to have a homebirth with the St George Hospital Homebirth Program were interviewed in the postnatal period using semi-structured, open-ended questions. Interviews were transcribed, then a thematic analysis was undertaken.

Results

Women, having already experienced a normal birth, demonstrated a strong confidence in their ability to give birth at home and described a confidence in their bodies, their midwives, and the health system. Women weighed up the risks of homebirth through information they gathered and integration with their previous experience of birth, their family support and self-confidence.

Discussion

Women choosing publicly-funded homebirth display strong confidence in both themselves to give birth at home, and their belief in the health system's ability to cope with any complications that may arise.

Implications for practice

Many women may benefit from access to publicly-funded homebirth models of care. This should be further investigated.     

Sample Splitting and Threshold Estimation

Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously‐distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are super‐consistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either cross‐section or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates (the threshold and the regression slopes) is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of Durlauf and Johnson (1995).     

统计四大工程建设的法制保障研究

 推进基本单位名录库、企业一套表制度、数据采集处理软件系统和联网直报系统四大工程建设,这是当前我国统计工作的核心任务。然而,目前的法律制度还存在诸多缺陷和空白。因此,应当修订或出台相关规定,为统计四大工程建设提供坚实的法制保障。     

金融要素扭曲与企业创新活动

本文利用世界银行的企业调查数据并将四大国有商业银行的市场份额作为金融要素市场化的代理指标,分析了金融要素扭曲对企业创新活动的影响。实证研究发现：金融要素扭曲对企业的研发投入和创新成果都具有抑制作用,这种抑制作用在不同所有制企业间具有异质性,相比国有企业,私营企业的创新活动受金融要素扭曲的抑制作用更大。中小企业的研发投入对金融要素的扭曲的敏感性要高于大型企业,在过程创新中,金融要素扭曲对中小型企业的影响更大,但在产品创新过程中,金融要素的扭曲的对大型企业的影响则更强。本文的研究提供了金融要素扭曲对经济增长有负面的影响的来自企业创新的微观证据。因此,全面推进的金融要素市场化改革有助于企业的创新活动,从而为国家经济转型提供持续创新与发展的动力。