非参数核密度估计在异方差模型中的应用

针对非参数核密度估计中最优窗宽的选择在实际建模中的不足,提出了一个新的最优窗宽选择的迭代方法,克服了使用传统的经验法则所带来的局限性。并在此基础上用一种新的非参数核密度估计ML方法应用到了中国股票市场,通过与极大似然估计对比论证了此方法的有效性和可行性。实证分析表明,通过与实际值的模拟对比,运用非参数估计技术得到上证指数日收益率的拟合值要优于极大似然估计的拟合值。     

人口普查中遗漏人口数的估计

研究目标:用完整遗漏估计量替代目前使用的未匹配遗漏估计量、逆记录检查遗漏估计量和平衡推算遗漏估计量。研究方法:采取文献解读、成果借鉴和移植及实地调查相结合的方法,研究完整遗漏估计量及其方差估计。研究发现:人口普查遗漏估计不只是要提供遗漏估计值,还要揭示遗漏的原因及其遗漏者的特征;构造普查遗漏估计量,既要包括登记在事后计数调查人口名单而未登记在普查名单的单重遗漏人口,还要包括同时遗漏于这两项调查名单的双重遗漏人口。研究创新:提出完整遗漏估计量。研究价值:完整遗漏估计量有望应用于中国2030年普查遗漏估计,开创世界人口普查遗漏估计应用完整遗漏估计量的先河。     

VaR样本分位数估计的偏差改进

本文指出了人们通常所使用的VaR样本分位数估计量会产生高估或低估的现象,并分析了产生这些现象的原因,提出在样本较大的情况下利用加权样本分位数估计量去估计VaR,在样本较小的情况下用基于Bootstrap方法的样本分位数估计量去估计VaR。数值模拟的结果表明,这些估计方法的估计精度得到了较好地改进。最后,运用这两种分位数估计量来估计两支股票(招商银行、中国石化)的日对数回报序列的VaR值,并比较它们的风险估计量的大小。     

组合方法视角下复杂协整关系的非参数识别

研究目标:构建对复杂协整关系进行非参数识别时有效、可操作的组合方法。研究方法:综合考虑核估计方法、窗宽选择以及协整检验三类关键因素，提出待分析的多种组合方法，通过蒙特卡洛模拟和中俄两国购买力平价理论在有限样本下对各组合方法的性质进行对比分析。研究发现:“局部线性核估计(LL)+交错验证窗宽选择(CV)+方差比检验”组合方法在识别真实协整关系时扭曲水平(Size)低，ADF检验在识别虚假协整关系时检验功效(Power)高。研究创新:扩展了E-G协整检验步骤，以非参数组合方法的视角提取最优残差序列并对复杂协整关系进行有效验证。研究价值:利用组合方法为复杂协整关系的建模探索出一条可行之路并丰富其应用场景，也为中俄两国进一步推进经贸合作提供了理论依据。     

人口普查质量评估中Logistic回归模型的应用

双系统估计量是目前估计目标总体真实人口数及人口普查净误差的主流方法,构造双系统估计量时,要求总体中的人口具有相同的登记概率。为达此目的,目前各国通行的做法是对人口总体进行抽样后分层。用Logistic回归模型取代抽样后分层是人口普查质量评估领域的前沿问题。本文系统地解读了基于Logistic回归模型的双系统估计量及其方差估计量,认为Logistic回归模型能够纳入更多的分层变量,具有很好的应用前景。     

对估计量优劣性评价标准的研究

未知总体参数的估计是数理统计学研究的重要课题。目前估计总体参数的方法很多,但无论使用何种方法,都涉及到估计量的精确度问题。为评价估计量的精确程度,统计学家根据样本容量的大小,分别提出了小样本的三条性质(无偏性、有效性和最佳线性无偏性)及大样本的三条性质(渐近无偏性,一致性和渐近有效性)作为评价估计量优劣性的标准。本     

人口普查净误差估计中的双系统估计量研究

评估普查计数的完整性已经成为五年或十年一次的人口普查不可分割的一部分。评估通常采取质量评估调查的方式。该调查建立在双系统估计量基础上。考虑到普查登记质量及人口移动因素,这三份人口登记名单可提供7个总体指标。由于质量评估调查采取抽样的方式进行,所以这些总体指标要用样本来构造其估计量。基于复杂抽样方法形成的双系统估计量没有现成的方差公式计算其方差。通常使用分层刀切方差估计量近似计算双系统估计量的方差。这需要计算第一步所有样本抽样单位的复制权数。本文将对双系统估计量构造的各个环节进行理论与实践相结合的阐述,深入解析其中深层次的理论问题,为基础理论研究做出贡献,另外也将探讨基于双系统估计量的合成估计量在区域人口数目估计中的应用问题。     

复杂样本的方差估计——基于逆抽样设计的方法

复杂样本的方差估计，通常采用的是随机组、刀切法等传统方法，本文提出采用逆抽样设计方法。基于一个实际调查数据的模拟分析，通过对抽样方法进行逆设计，构造了对应的方差估计量，并从精度、灵活性等方面将逆抽样设计方法与传统方差估计方法进行多角度对比，探讨了该方法的适用条件。     

空间动态面板模型拟极大似然估计的渐近效率改进

Lee和Yu(2008)研究了一类同时带个体与时间固定效应的空间动态面板模型的拟极大似然估计量的大样本性质.本文说明当扰动项非正态时,拟极大似然估计量的渐近效率可以被进一步提高.为此,我们构造了一组合待定矩阵且形式一般的矩条件以用来包含对数似然函数一阶条件的特殊形式.从无冗余矩条件的角度,选取最优待定矩阵得到了最佳广义矩估计量.本文证明了当扰动项正态分布时,最佳广义矩估计量和拟极大似然估计量渐近等价;当扰动项非正态分布时,广义矩估计量具有比拟极大似然估计量更高的渐近效率.Monte Carlo实验结果与本文的理论预期一致.     

非等间隔动态面板数据模型：估计方法与应用实例

非等间隔动态面板数据模型由于相邻两期观测之间的时间长度不尽相同使得传统动态面板数据模型的估计方法失效,本文提出使用非线性最小二乘、最短距离以及它们的一步估计量对该模型进行估计,证明了这四个估计量的一致性和渐进正态性,同时借助蒙特卡洛模拟的方法验证了它们在有限样本中的估计精度,并且进一步使用所提出的估计量讨论了以往文献由于缺乏相应的估计方法而没有被研究或者充分讨论的问题,得到了一些新的结论。     

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.     

On kernel nonparametric regression designed for complex survey data

In this article, we consider nonparametric regression analysis between two variables when data are sampled through a complex survey. While nonparametric regression analysis has been widely used with data that may be assumed to be generated from independently and identically distributed (iid) random variables, the methods and asymptotic analyses established for iid data need to be extended in the framework of complex survey designs. Local polynomial regression estimators are studied, which include as particular cases design-based versions of the Nadaraya–Watson estimator and of the local linear regression estimator. In this paper, special emphasis is given to the local linear regression estimator. Our estimators incorporate both the sampling weights and the kernel weights. We derive the asymptotic mean squared error (MSE) of the kernel estimators using a combined inference framework, and as a corollary consistency of the estimators is deduced. Selection of a bandwidth is necessary for the resulting estimators; an optimal bandwidth can be determined, according to the MSE criterion in the combined mode of inference. Simulation experiments are conducted to illustrate the proposed methodology and an application with the Canadian survey of labour and income dynamics is presented.     

Nonparametric estimation of conditional VaR and expected shortfall

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya–Watson estimators. Moreover, an ad hoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical study is carried out to illustrate the finite sample performance of the proposed estimators.     

Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non‐recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.     

Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution

We propose a computationally efficient and statistically principled method for kernel smoothing of point pattern data on a linear network. The point locations, and the network itself, are convolved with a two‐dimensional kernel and then combined into an intensity function on the network. This can be computed rapidly using the fast Fourier transform, even on large networks and for large bandwidths, and is robust against errors in network geometry. The estimator is consistent, and its statistical efficiency is only slightly suboptimal. We discuss bias, variance, asymptotics, bandwidth selection, variance estimation, relative risk estimation and adaptive smoothing. The methods are used to analyse spatially varying frequency of traffic accidents in Western Australia and the relative risk of different types of traffic accidents in Medellín, Colombia.     

Functional Coefficient Cointegration Models Subject to Time–Varying Volatility with an Application to the Purchasing Power Parity

This paper analyses functional coefficient cointegration models with both stationary and non‐stationary covariates, allowing time‐varying (unconditional) volatility of a general form. The conventional kernel weighted least squares (KLS) estimator is subject to potential efficiency loss, and can be improved by an adaptive kernel weighted least squares (AKLS) estimator that adapts to heteroscedasticity of unknown form. The AKLS estimator is shown to be as efficient as the oracle generalized kernel weighted least squares estimator asymptotically, and can achieve significant efficiency gain relative to the KLS estimator in finite samples. An illustrative example is provided by investigating the Purchasing Power Parity hypothesis.     

Relative efficiency and deficiency of kernel type estimators of smooth distribution functions

Abstract  The problem is investigated whether a given kernel type estimator of a distribution function at a single point has asymptotically better performance than the empirical estimator. A representation of the relative deficiency of the empirical distribution function with respect to a kernel type estimator is established which gives a complete solution to this problem. The problem of finding optimal kernels is studied in detail.     

Edgeworth approximations for semiparametric instrumental variable estimators and test statistics

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable estimator considered in Newey (Econometrica 58 (1990) 809) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and (a version of) nearest neighbor estimates as special cases. Our expansions are valid to order n^−2ε for some 0<ε<1/2, where ε depends on the smoothness and dimensionality of the data distribution and on the order of the polynomial chosen by the practitioner. We use the expansions to define optimal bandwidth selection methods for both estimation and testing problems and apply our methods to simulated data.     

Combining kernel estimators in the uniform deconvolution problem

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Initially the inversions yield two different estimators of the density and two estimators of the distribution function. We construct asymptotically optimal convex combinations of these two estimators. We also derive pointwise asymptotic normality of the resulting estimators, the pointwise asymptotic biases and an expansion of the mean integrated squared error of the density estimator. It turns out that the pointwise limit distribution of the density estimator is the same as the pointwise limit distribution of the density estimator introduced by Groeneboom and Jongbloed (Neerlandica, 57, 2003, 136), a kernel smoothed nonparametric maximum likelihood estimator of the distribution function.     

Simultaneous selection and weighting of moments in GMM using a trapezoidal kernel

This paper proposes a novel procedure to estimate linear models when the number of instruments is large. At the heart of such models is the need to balance the trade off between attaining asymptotic efficiency, which requires more instruments, and minimizing bias, which is adversely affected by the addition of instruments. Two questions are of central concern: (1) What is the optimal number of instruments to use? (2) Should the instruments receive different weights? This paper contains the following contributions toward resolving these issues. First, I propose a kernel weighted generalized method of moments (GMM) estimator that uses a trapezoidal kernel. This kernel turns out to be attractive to select and weight the number of moments. Second, I derive the higher order mean squared error of the kernel weighted GMM estimator and show that the trapezoidal kernel generates a lower asymptotic variance than regular kernels. Finally, Monte Carlo simulations show that in finite samples the kernel weighted GMM estimator performs on par with other estimators that choose optimal instruments and improves upon a GMM estimator that uses all instruments.