Smooth estimation of a monotone hazard and a monotone density under random censoring

We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n^2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).     

Do High‐Frequency Data Improve High‐Dimensional Portfolio Allocations?

This paper addresses the debate about the usefulness of high‐frequency (HF) data in large‐scale portfolio allocation. We construct global minimum variance portfolios based on the constituents of the S&P 500. HF‐based covariance matrix predictions are obtained by applying a blocked realized kernel estimator, different smoothing windows, various regularization methods and two forecasting models. We show that HF‐based predictions yield a significantly lower portfolio volatility than methods employing daily returns. Particularly during the 2008 financial crisis, these performance gains hold over longer horizons than previous studies have shown, translating into substantial utility gains for an investor with pronounced risk aversion. Copyright © 2013 John Wiley & Sons, Ltd.     

高速公路交通事故概率预测方法研究

准确的高速公路交通事故概率预测可提高高速公路行车安全。通过分析高速公路交通事故的影响因素,建立高速公路交通事故影响因素体系,构造贝叶斯网络,提出基于贝叶斯网络的高速公路交通事故概率预测方法。此方法利用数据库先验概率信息及贝叶斯预测模型,得出高速公路交通事故概率值,以此判断事故危险等级。     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.     

Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric Regression, and Density Estimation

The past forty years have seen a great deal of research into the construction and properties of nonparametric estimates of smooth functions. This research has focused primarily on two sides of the smoothing problem: nonparametric regression and density estimation. Theoretical results for these two situations are similar, and multivariate density estimation was an early justification for the Nadaraya-Watson kernel regression estimator.
A third, less well-explored, strand of applications of smoothing is to the estimation of probabilities in categorical data. In this paper the position of categorical data smoothing as a bridge between nonparametric regression and density estimation is explored. Nonparametric regression provides a paradigm for the construction of effective categorical smoothing estimates, and use of an appropriate likelihood function yields cell probability estimates with many desirable properties. Such estimates can be used to construct regression estimates when one or more of the categorical variables are viewed as response variables. They also lead naturally to the construction of well-behaved density estimates using local or penalized likelihood estimation, which can then be used in a regression context. Several real data sets are used to illustrate these points.     

Estimation of dynamic models with nonparametric simulated maximum likelihood

We propose an easy-to-implement simulated maximum likelihood estimator for dynamic models where no closed-form representation of the likelihood function is available. Our method can handle any simulable model without latent dynamics. Using simulated observations, we nonparametrically estimate the unknown density by kernel methods, and then construct a likelihood function that can be maximized. We prove that this nonparametric simulated maximum likelihood (NPSML) estimator is consistent and asymptotically efficient. The higher-order impact of simulations and kernel smoothing on the resulting estimator is also analyzed; in particular, it is shown that the NPSML does not suffer from the usual curse of dimensionality associated with kernel estimators. A simulation study shows good performance of the method when employed in the estimation of jump-diffusion models.     

Functional coefficient regression models with time trend

We consider the problem of estimating a varying coefficient regression model when regressors include a time trend. We show that the commonly used local constant kernel estimation method leads to an inconsistent estimation result, while a local polynomial estimator yields a consistent estimation result. We establish the asymptotic normality result for the proposed estimator. We also provide asymptotic analysis of the data-driven (least squares cross validation) method of selecting the smoothing parameters. In addition, we consider a partially linear time trend model and establish the asymptotic distribution of our proposed estimator. Two test statistics are proposed to test the null hypotheses of a linear and of a partially linear time trend models. Simulations are reported to examine the finite sample performances of the proposed estimators and the test statistics.     

山区公路的路侧事故与改善措施分析

路侧安全设计与改善已成为提高道路安全性能的一项重要手段,是公路设计与维护的重要组成部分。山区公路线形复杂,地形、环境等自然条件较为险峻的区域,很多路段难于提供必要的净空区,安全隐患复杂,容易导致翻车、坠车等严重路侧事故,造成大量的人员伤亡和财产损失。道路交通事故约三分之一的致命事故发生在路侧。本文通过对数例路侧事故的深度研究,分析了云南山区严重路侧事故不断发生的主要原因,包括超速行驶、路面湿滑、防护设施缺乏等驾驶员、车辆,道路以及环境等方面的原因,提出了相应的改善对策和措施,对改善山区道路的几何设计、路面管理与维护、路侧风险识别与控制和安全防护设施的合理设置,减少车辆冲入路外引起的路侧事故及危险性具有重要意义。     

金融资产厚尾分布及常用的风险度量

本文首先运用正态分布、带有位置-尺度参数的t分布、logistic分布、极值分布、-stable分布和核密度估计对上证综指收益率分布进行拟合,结果表明核密度估计优于其他分布。其次,在进行尾部风险拟合和度量风险方面,通过设定相关指标,在显著性水平为1%时,-stable分布更适合衡量风险程度,在此基础上提出了调和-stable分布,并得到一个同构表示解。最后,本文给出了蒙特卡洛-stable分布模拟和经验值下的MDD、DaR和CDaR,并得到了模型值和经验值之间的乘离率。     

An evaluation of financial institutions: Impact on consumption and investment using panel data and the theory of risk-bearing

The theory of the optimal allocation of risk and the Townsend Thai panel data on financial transactions are used to assess the impact of the major formal and informal financial institutions of an emerging market economy. We link financial institution assessment to the actual impact on clients, rather than ratios and non-performing loans. We derive both consumption and investment equations from a common core theory with both risk and productive activities. The empirical specification follows closely from this theory and allows both OLS and IV estimation. We thus quantify the consumption and investment smoothing impact of financial institutions on households including those running farms and small businesses. A government development bank (BAAC) is shown to be particularly helpful in smoothing consumption and investment, in no small part through credit, consistent with its own operating system, which embeds an implicit insurance operation. Commercial banks are smoothing investment, largely through formal savings accounts. Other institutions seem ineffective by these metrics.     

Local minimax pointwise estimation of a multivariate density

We consider the problem of the nonparametric minimax estimation of a multivariate density at a given point. A concept of smoothness classes in nonparametric minimax estimation problems is proposed. The smoothness of a function is characterized by the approximability of the function at a point by an integral of the product of this function with an approximate identity. We propose a singular integral estimator, an integral of this approximate identity with respect to the empirical distribution function. Under some assumptions on the approximate identity, the bias of the estimator is shown to be of smaller order asymptotically than the variance, and the estimator itself is shown to be asymptotically locally minimax with respect to the quadratic risk in a proper topology.     

EWMA-GARCH模型与GARCH模型在估计收益率波动上的差异的实证及理论分析

VaR作为衡量风险的指标,其核心则在于对波动,亦即方差的估计。基于时间序列,关于条件方差的经典模型是GARCH模型,尽管后来又衍生出了EGARCH,PARCH等复杂模型,但在实务中GARCH模型仍占有重要的地位。文章分析了一种比较新的结合了EWMA模型的GARCH模型(以下称为EWMA-GARCH模型)计算VaR的参数估计方法,以检验其在估计波动上的实用性,并对实证检验结果做了理论分析。分析结果表明,尽管该结合模型缺乏完整的理论支持,但是其计算效果仍比较良好,当然这样良好的结果是建立在因缺乏理论依据而导致的对模型的其他要求之上的.至于是采用受理论支持的模型还是并不输实践价值的模型,文章也给出了一定的建议。     

Estimating the error variance in regression after a preliminary test of restrictions on the coefficients

Maximum-likelihood estimation of the variance of the disturbances in a linear regression is considered in the context of exact linear restrictions on the coefficient vector. The exact risk function for the associated preliminary-test estimator of this variance is derived and evaluated numerically on the basis of relative quadratic loss. Our results indicate that in practical situations the risk of the pre-test estimator differs only slightly from that of the naive estimator which ignores the restrictions without testing. Applying the coefficient restrictions without testing their validity is not recommended.     

Studying the association between air pollution and lung cancer incidence in a large metropolitan area using a kernel density function

In the absence of patient-specific data, composite level data are often used in epidemiological studies. However, since individual exposure levels cannot accurately be inferred from aggregate data, such an approach may lead to erroneous estimates of health effects of potential environmental risk factors. In the present study, we attempt to address this information-loss problem by using the “kernel density function”, which estimates the intensity of events across a surface, by calculating the overall number of cases situated within a given search radius from a target point. The present paper illustrates the use of this analytical technique for a study of association between the geographical distributions of lung cancer cases and SO₂ air pollution estimates in the Greater Haifa Metropolitan Area (GHMA). In the analysis, the results obtained by kernel smoothing are contrasted with those obtained by areal aggregation techniques more commonly used in empirical studies.     

基于Echo State Neural Networks的短期交通流预测算法

在城市交通环境,交通流的正确预测是比较困难,因为多个十字路口,这使得预置的交通控制模型之间的相互作用和intertwinement不能保持始终高性能在所有的交通情况。     

Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters

We consider nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. Most of the existing works on asymptotic distributions of a nonparametric/semiparametric estimator or a test statistic are based on some deterministic smoothing parameters, while in practice it is important to use data-driven methods to select the smoothing parameters. In this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters. We also allow for general weakly dependent data.     

Quadratic hedging schemes for non-Gaussian GARCH models

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan׳s (1995) delta hedge. Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of non-Gaussian driven models. Furthermore, we analyze these methods for non-Gaussian GARCH diffusion limit processes and link them to the corresponding discrete time counterparts. A detailed numerical analysis based on S&P 500 European call options is provided to assess the empirical performance of the proposed schemes. We also test the sensitivity of the hedging strategies with respect to the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel.     

Further developments in estimation of the largest mean ofK normal populations

We revisit the bounded maximal risk point estimation problem as well as the fixed-width confidence interval estimation problem for the largest mean amongk(≥2) independent normal populations having unknown means and unknown but equal variance. In the point estimation setup, we devise appropriate two-stage and modified two-stage methodologies so that the associatedmaximal risk can bebounded from aboveexactly by a preassigned positive number. Kuo and Mukhopadhyay (1990), however, emphasized only the asymptotics in this context. We have also introduced, in both point and interval estimation problems,accelerated sequential methodologies thereby saving sampling operations tremendously over the purely sequential schemes considered in Kuo and Mukhopadhyay (1990), but enjoying at the same time asymptotic second-order characteristics, fairly similar to those of the purely sequential ones.     

大型车辆前方路况识别显示系统

随着社会的发展,大型车辆在公路交通中占的比重越来越大。由于大型车辆车身尺寸大、视线高,会大大影响后车司机的行车视线,与小型车辆相比,大型车辆造成重大交通事故的概率更大。论文提出一种大型车辆前方路况识别显示系统,对紧随的后车进行提醒,对提高道路交通安全程度、降低交通事故发生率具有重要的现实意义。     

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators. We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes.