Semiparametric multiple kernel estimators and model diagnostics for count regression functions

Abstract

This study concerns semiparametric approaches to estimate discrete multivariate count regression functions. The semiparametric approaches investigated consist of combining discrete multivariate nonparametric kernel and parametric estimations such that (i) a prior knowledge of the conditional distribution of model response may be incorporated and (ii) the bias of the traditional nonparametric kernel regression estimator of Nadaraya-Watson may be reduced. We are precisely interested in combination of the two estimations approaches with some asymptotic properties of the resulting estimators. Asymptotic normality results were showed for nonparametric correction terms of parametric start function of the estimators. The performance of discrete semiparametric multivariate kernel estimators studied is illustrated using simulations and real count data. In addition, diagnostic checks are performed to test the adequacy of the parametric start model to the true discrete regression model. Finally, using discrete semiparametric multivariate kernel estimators provides a bias reduction when the parametric multivariate regression model used as start regression function belongs to a neighborhood of the true regression model.     

一种改进型专家模糊核聚类赋权方法研究

针对传统基于判断矩阵的专家模糊核聚类赋权方法，由于归一化条件的制约，导致离群点对聚类结果产生不良影响的问题，提出一种改进型模糊核聚类算法。该方法在聚类过程中，通过放宽归一化约束条件，削弱离群点对聚类结果的影响；并且针对传统基于信息熵与一致性系数线性耦合的聚类标准的局限性，提出一种基于偏差熵的赋权方法，依据专家对自身类别的聚类贡献度，确定专家权重，克服了传统方法的不足。算例表明，该方法可行、有效。     

Nonparametric beta kernel estimator for long and short memory time series

In this article we introduce a nonparametric estimator of the spectral density by smoothing the periodogram using beta kernel density. The estimator is proved to be bounded for short memory data and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations show that the proposed estimator automatically adapts to the long- and the short-range dependency of the process. A cross-validation procedure is studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the performance of the beta kernel estimator. The Canadian Journal of Statistics 48: 582–595; 2020 © 2020 Statistical Society of Canada     

Convergence de I estimateur a noyau de derivees de Radon-Nikodym generales dans le cas melangeant

In many situations, nonparametric inference in point-process theory consists in estimating a Radon-Nikodym derivative of a nonnegative measure p with respect to another nonnegative measure v, where p and v are intensities of point processes. We consider the case of a mixing andstrictly stationary sequence of point processes and establish convergence results for the kernel estimator.     

中国出口附加值率的产业特征及其演进路径分析——基于核密度函数分解技术

基于中国投入产出表,应用核密度估计及其分解技术,本文分析了中国加入WTO之后,各产业出口附加值率的分布及其动态变化.结果表明:中国各产业出口附加值率经历了先快速下降、再适度反弹,而后趋于平稳的演进路径;但三大产业的出口附加值率在演进方向、力度、强度和时间分布上呈现出不同的特征.进一步分析发现:三大产业出口附加值率动态演进的首要原因在于均值效应,其次为残差效应,效果最小的是方差效应.因而,促进出口附加值率增加既要推进各产业的整体发展,又要兼顾不同产业的个体特征.     

郑州商城文化内涵解读

郑州商城物质遗存具有丰富的文化内涵,这一早商物质文明所蕴育的价值取向、思维方式和审美情趣反射出商民族的精神内核,为我们认识其制度层面的构建以及行为模式的发展提供了重要依据。     

Inductive Inference: An Axiomatic Approach

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality–case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality–case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality. Special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems. Interpreting the same result for rankings of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with rankings by the likelihood functions.     

On the probability distribution of economic growth

Three important and significantly heteroscedastic gross domestic product series are studied. Omnipresent heteroscedasticity is removed and the distributions of the series are then compared to normal, normal mixture and normal–asymmetric Laplace (NAL) distributions. NAL represents a skewed and leptokurtic distribution, which is in line with the Aghion and Howitt [1 Aghion, P. and Howitt, P. 1992. A model of growth through creative destruction. Econometrica, 60: 323–351. [Crossref], [Web of Science ®] [Google Scholar]] model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL fits the data better than the alternatives.