Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time‐varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white‐noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous‐time and discrete‐time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non‐parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.     

Faster Convergence to the Estimation of Quadratic Variation with Microstructure Noise

The continuous quadratic variation of asset return plays a critical role for high-frequency trading. However, the microstructure noise could bias the estimation of the continuous quadratic variation. Zhang et al. (2005 Zhang, L., Mykland, P., Ait-Sahalia, Y. (2005). A tale of two time scales: determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 100(472):1394–1411.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a batch estimator for the continuous quadratic variation of high-frequency data in the presence of microstructure noise. It gives the estimates after all the data arrive. This article proposes a recursive version of their estimator that outputs variation estimates as the data arrive. Our estimator gives excellent estimates well before all the data arrive. Both real high-frequency futures data and simulation data confirm the performance of the recursive estimator.     

Optimum Designs for Estimation of Parameters in a Quadratic Mixture-Amount Model

The authors propose a mixture-amount model, which is quadratic both in the proportions of mixing components and the amount of mixture. They attempt to find the A- and D-optimal designs for the estimation of the model parameters within a subclass of designs. The optimality of the derived designs in the entire class of competing designs has been investigated through equivalence theorem.     

Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

In this article, four bivariate exponential (BVE) distributions with subject to right censoring samples are presented. Bayesian estimates of the parameters of BVE are obtained through Linex and quadratic loss functions. Gamma prior distribution has been suggested to reforming the posterior function. The estimations and standard errors of parameters have also been obtained through simulation method. Markov chain Monte Carlo (MCMC) method is employed for the case of Block-Buse bivariate distribution because there was no closed form for estimator criteria. Simulation studies have been conducted to show that the computation parts can be implemented easily and comparing the estimated values due to two methods and with the true values as well.     

Testing for Unit Roots and the Impact of Quadratic Trends,with an Application to Relative Primary Commodity Prices

In practice a degree of uncertainty will always exist concerning what specification to adopt for the deterministic trend function when running unit root tests. While most macroeconomic time series appear to display an underlying trend, it is often far from clear whether this component is best modeled as a simple linear trend (so that long-run growth rates are constant) or by a more complicated nonlinear trend function which may, for instance, allow the deterministic trend component to evolve gradually over time. In this article, we consider the effects on unit root testing of allowing for a local quadratic trend, a simple yet very flexible example of the latter. Where a local quadratic trend is present but not modeled, we show that the quasi-differenced detrended Dickey–Fuller-type test of Elliott et al. (1996 Elliott , G. , Rothenberg , T. J. , Stock , J. H. ( 1996 ). Efficient tests for an autoregressive unit root . Econometrica 64 : 813 – 836 .[Crossref], [Web of Science ®] , [Google Scholar]) has both size and power which tend to zero asymptotically. An extension of the Elliott et al. (1996 Elliott , G. , Rothenberg , T. J. , Stock , J. H. ( 1996 ). Efficient tests for an autoregressive unit root . Econometrica 64 : 813 – 836 .[Crossref], [Web of Science ®] , [Google Scholar]) approach to allow for a quadratic trend resolves this problem but is shown to result in large power losses relative to the standard detrended test when no quadratic trend is present. We consequently propose a simple and practical approach to dealing with this form of uncertainty based on a union of rejections-based decision rule whereby the unit root is rejected whenever either of the detrended or quadratic detrended unit root tests rejects. A modification of this basic strategy is also suggested which further improves on the properties of the procedure. An application to relative primary commodity price data highlights the empirical relevance of the methods outlined in this article. A by-product of our analysis is the development of a test for the presence of a quadratic trend which is robust to whether the data admit a unit root.     

On the Estimation of Integrated Volatility With Jumps and Microstructure Noise

In this article, we propose a nonparametric procedure to estimate the integrated volatility of an Itô semimartingale in the presence of jumps and microstructure noise. The estimator is based on a combination of the preaveraging method and threshold technique, which serves to remove microstructure noise and jumps, respectively. The estimator is shown to work for both finite and infinite activity jumps. Furthermore, asymptotic properties of the proposed estimator, such as consistency and a central limit theorem, are established. Simulations results are given to evaluate the performance of the proposed method in comparison with other alternative methods.     

Goodness of Fit Test and Latent Distribution Estimation in the Mixed Rasch Model

The Cramér-von Mises test methodology is applied to build a goodness-of fit test for the mixed Rasch model. The Mixed Rasch Model is a probability model of a multivariate discrete random variable driven by an unknown latent continuous variable. The problem of estimation of the unknown fixed difficulty parameters and the latent density function is also considered. The theoretical results are illustrated through simulations and an application to real Quality of Life data.     

An optimization interpretation of integration and back-fitting estimators for separable nonparametric models

We provide an optimization interpretation of both back-fitting and integration estimators for additive nonparametric regression. We find that the integration estimator is a projection with respect to a product measure. We also provide further understanding of the back-fitting method.     

Bootstrap and Other Resampling Methodologies in Statistics of Extremes

In Statistics of Extremes, the estimation of parameters of extreme or even rare events is usually done under a semi-parametric framework. The estimators are based on the largest k-ordered statistics in the sample or on the excesses over a high level u. Although showing good asymptotic properties, most of those estimators present a strong dependence on k or u with high bias when the k increases or the level u decreases. The use of resampling methodologies has revealed to be promising in the reduction of the bias and in the choice of k or u. Different approaches for resampling need to be considered depending on whether we are in an independent or in a dependent setup. A great amount of investigation has been performed for the independent situation. The main objective of this article is to use bootstrap and jackknife methods in the context of dependence to obtain more stable estimators of a parameter that appears characterizing the degree of local dependence on extremes, the so-called extremal index. A simulation study illustrates the application of those methods.     

中国教育收益率统计估计与分析 ——基于参数和半参数估计方法的比较

 本文分别运用参数和半参数估计方法,就如何更准确有效测度中国教育收益率作深入探讨。利用CHNS数据对我国1989年至2006年的教育收益率进行估计,并采用Hausman检验法对两种估计方法结果进行检验。结果表明,从估计效率看,前者比后者的效率更高;但从估计效果看,后者才是一致性估计。而且我们发现虽然教育收益率整体呈逐渐增加趋势,但与实物资本收益率相比仍偏低。中国的教育和劳动力市场亟需加大投资和改革力度。     

中国城镇化的地域非均衡及其动态演进——来自基尼系数及核密度估计的经验证据

基于中国1995-2013年省域数据,采用基尼系数及其分解、核密度估计方法,从人口和土地城镇化入手,系统分析了中国城镇化的地域非均衡及其动态演化规律。结果发现,1.中国人口和土地城镇化分布均呈现出由东往西逐渐降低的规律,城镇化非均衡主要体现在土地城镇化,而人口城镇化则未出现明显分异。2.全国尺度人口城镇化基尼系数随时间不断下降,城镇化非均衡逐渐减小;土地城镇化基尼系数则呈倒"U"型,城镇化非均衡先增后减。3.东中西三大区域内人口城镇化基尼系数均呈直线下降,区域间非均衡东部最大,西部次之,中部最小;土地城镇化非均衡则是东部大于中部和西部,但近年来西部已超过东部。4.人口城镇化非均衡在1995-2001年间主要来自地区间重叠,而后2002-2013年主要由地区间差异驱动;土地城镇化非均衡则主要来源于地区间差异。5.核密度估计显示人口城镇化增速较快,波动较小,而土地城镇化则极化趋势明显,波动较大。新型城镇化的协调推进宜从人口和土地城镇化两方面着手,特别要注意土地城镇化的失衡发展问题。