A simple,automatic and adaptive bivariate density estimator based on conditional densities

The standard approach to non-parametric bivariate density estimation is to use a kernel density estimator. Practical performance of this estimator is hindered by the fact that the estimator is not adaptive (in the sense that the level of smoothing is not sensitive to local properties of the density). In this paper a simple, automatic and adaptive bivariate density estimator is proposed based on the estimation of marginal and conditional densities. Asymptotic properties of the estimator are examined, and guidance to practical application of the method is given. Application to two examples illustrates the usefulness of the estimator as an exploratory tool, particularly in situations where the local behaviour of the density varies widely. The proposed estimator is also appropriate for use as a pilot estimate for an adaptive kernel estimate, since it is relatively inexpensive to calculate.     

A Unified Approach to the Approximation of Multivariate Densities

Approximation of a density by another density is considered in the case of different dimensionalities of the distributions. The results have been derived by inverting expansions of characteristic functions with the help of matrix techniques. The approximations obtained are all functions of cumulant differences and derivatives of the approximating density. The multivariate Edgeworth expansion follows from the results as a special case. Furthermore, the density functions of the trace and eigenvalues of the sample covariance matrix are approximated by the multivariate normal density and a numerical example is given     

基于iCARE理论的《大学英语》课程定位研究与教改实践

《大学英语》是高校一门重要的公共基础课,厘清课程性质是推进教学改革的基础。在梳理不同时期《大学英语》教学大纲有关规定,借鉴国外高校现代语言课程定位基础上,提出《大学英语》课程定位是EGP,提高"交互密度"是保证学习效率和效果的关键。河北科技大学在多年教改实践基础上,创建了iCARE教学理论,并从六个方面推进《大学英语》课程改革,形成具有校本特色的《大学英语》教学模式,取得良好教改成效。     

具有不同偏好网络结构的群体评价信息集结方法

以评价者为节点,评价者之间偏好相似性测度为连接的网络为群体偏好网络,讨论了评价群体在偏好网络均衡状态时3种不同网络结构(星形网络、闭链结构和完整网络)的群体评价信息集结方法,将具有网络结构信息的节点数据转化为平面数据,提出了平面密度加权平均算子和平面密度加权几何平均中间算子。给出了平面数据的划分方法及平面密度算子的趋同性测度,并将算子应用于各网络结构的评价群体评价问题。     

基于条件概率积分变换的多元Copula函数选择

本文构建了基于条件概率积分变换的Copula函数选择方法,通过对条件概率积分变换下Anderson-Darling(AD)、Kolmogorov-Smirnov(KS)、Cramér-von Mises(CM)这三种统计量的比较,讨论在不同样本容量和变量维数下其对多种Copula函数的拟合效果。利用GSPTSE、INMEX.MX和NDX三大股指样本,将基于条件概率积分变换的Copula函数选择方法与核密度估计和极大似然估计选择法的效果进行系统比较。结果表明,基于条件概率积分变换的检验法可以有效解决多元Copula函数的选择问题,其拟合优度检验更精确、更稳定;核密度估计检验在大样本下比较稳定,而小样本下稳定性较差;相比之下,极大似然值检验法则不稳定。     

甜菜施肥和种植密度综合效应初探

应用多元二次肥料效应数学模型,根据种肥、追肥、密度和甜菜产量结果,得出粉沙壤土肥料密度综合效应方程y＝1954．524＋10．334x1＋31．890x2＋130．027x3＋68．925x1x2＋7．775x1x3＋26．700x2x3＋124．435＋41．082－124．811。用此方程估测甜菜产量和实际产量极为接近。     

Moment‐Independent Sensitivity Analysis Using Copula

In risk assessment, the moment‐independent sensitivity analysis (SA) technique for reducing the model uncertainty has attracted a great deal of attention from analysts and practitioners. It aims at measuring the relative importance of an individual input, or a set of inputs, in determining the uncertainty of model output by looking at the entire distribution range of model output. In this article, along the lines of Plischke et al., we point out that the original moment‐independent SA index (also called delta index) can also be interpreted as the dependence measure between model output and input variables, and introduce another moment‐independent SA index (called extended delta index) based on copula. Then, nonparametric methods for estimating the delta and extended delta indices are proposed. Both methods need only a set of samples to compute all the indices; thus, they conquer the problem of the “curse of dimensionality.” At last, an analytical test example, a risk assessment model, and the levelE model are employed for comparing the delta and the extended delta indices and testing the two calculation methods. Results show that the delta and the extended delta indices produce the same importance ranking in these three test examples. It is also shown that these two proposed calculation methods dramatically reduce the computational burden.     

城市人口密度、国内市场规模与就业增长

我国经济“高增长、低就业”现象的原因在于我国贸易成本过高，国内市场规模较少。解决我国就业问题的关键在于减少行政干预，顺应市场要求，促进人口在空间上的适度集中，提高人口密度，提高消费效率，扩大市场规模。应进一步完善城乡一体的户籍制度，完善整合城乡劳动力市场，提高要素流动能力等。     

A New Quantile Function with Applications to Reliability Analysis

In this article, we propose a new class of distributions defined by a quantile function, which nests several distributions as its members. The quantile function proposed here is the sum of the quantile functions of the generalized Pareto and Weibull distributions. Various distributional properties and reliability characteristics of the class are discussed. The estimation of the parameters of the model using L-moments is studied. Finally, we apply the model to a real life dataset.     

Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.