Composite kernel quantile regression

The composite quantile regression (CQR) has been developed for the robust and efficient estimation of regression coefficients in a liner regression model. By employing the idea of the CQR, we propose a new regression method, called composite kernel quantile regression (CKQR), which uses the sum of multiple check functions as a loss in reproducing kernel Hilbert spaces for the robust estimation of a nonlinear regression function. The numerical results demonstrate the usefulness of the proposed CKQR in estimating both conditional nonlinear mean and quantile functions.     

Convergence rate of wavelet density estimator with data missing randomly when covariables are present

In this article, we study global L₂ error of non linear wavelet estimator of density in the Besov space B^s_pq for missing data model when covariables are present and prove that the estimator can achieve the optimal rate of convergence, which is similar to the result studied by Donoho et al. (1996) Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D. (1996). Density estimation by wavelet thresholding. Ann. Stat. 24:508–539.[Crossref], [Web of Science ®] , [Google Scholar] in complete independent data case with term-by-term thresholding of the empirical wavelet coefficients. Finite-sample behavior of the proposed estimator is explored via simulations.     

The influence function of the optimal bandwidth for kernel density estimation

Theories about the bandwidth of kernel density estimation have been well established by many statisticians. However, the influence function of the bandwidth has not been well investigated. The influence function of the optimal bandwidth that minimizes the mean integrated square error is derived and the asymptotic property of the bandwidth selectors based on the influence function is provided.     

基于多指标正交试验设计的SLS快速成型工艺参数优化

为提高SLS成型系统堆积方向微细结构的制作质量,以过度烧结深度、烧结密度和Z向尺寸偏差为优化指标,采用多指标的正交试验设计方法,通过极差分析法,讨论激光功率、预热温度、激光扫描速度、分层厚度等成型工艺参数对试件质量的影响,利用综合平衡法确定了最优工艺参数组合。试验结果表明：激光功率选取16 W,预热温度选取98℃,激光扫描速度选取3 m/s,分层厚度选取0.15 mm时,试件的制作质量为最优。试验结果有助于SLS快速成型系统提高堆积方向微细结构的制作质量。     

Relationships Between Population Density and the Perceived Quality of Neighbourhood

Two overseas survey-based scales measuring perceived quality of neighbourhood were adapted and replicated in a New Zealand context. An Italian study (Bonaiuto, Fornara, and Bonnes. (2003). Landscape and Urban Planning, 65, 41–52) measuring Perceived Residential Environmental Quality (PREQ) and an American study (Carp and Carp. (1982). Journal of Environmental Psychology, 2, 295–312) using the Perceived Environmental Quality Indices (PEQI) were applied to a sample of Auckland residents, separated into low, medium, and high population density areas. The surveys measured attitudes towards subjects such as noise, neighbours, accessibility, green areas, welfare services, recreational services, safety, maintenance, environmental health, transport services, and characteristics of an ideal neighbourhood, and were completed by 369 respondents. Primary analyses examined differences in perception across the three density groups. The factor structures of both scales were replicated with the Auckland sample, and differences across densities were found for subscales of the PREQ. The results are discussed in relation to the cross-cultural similarities of perceived environmental quality, and the concept that environmental satisfaction is based on balancing aspects of the residential environment is proposed. This research was conducted for the Foundation for Research, Science, and Technology under contract OPSX401.     

在坐标空间中原子波包的几率密度

本文首先推导出原子波包在坐标空间中几率密度的一般表达式,然后,以方形波包为例计算了其几率密度,并用计算机绘出了几率波密度随坐标和时间变化的三维曲线图。     

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。     

中国人口老龄化的地区差异分析

本文基于1990—2013年省际面板数据,以老年人口比重作为老龄化指标,采用基尼系数分解方法和Kernel密度估计方法,实证分析了中国人口老龄化的地区差异及其动态演进过程。研究结果表明：中国人口老龄化在地区分布上呈现出明显的非均衡特征;基尼系数测算及其分解结果表明,人口老龄化的地区差异总体上呈现波动缩小趋势;2004年以前,地区间差距和超变密度交替成为总体地区差异的主要来源,2004年以后,超变密度成为总体差异的主要来源。 Kernel密度估计显示,老龄化程度不断加深,地区差异呈波动趋势。     

Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model

The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.     

A note on the non-negativity of continuous-time ARMA and GARCH processes

A general approach for modeling the volatility process in continuous-time is based on the convolution of a kernel with a non-decreasing Lévy process, which is non-negative if the kernel is non-negative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary condition for the kernel to be non-negative, and propose a numerical method for checking the non-negativity of a kernel function. These results can be lifted to solving a similar problem with another approach to modeling volatility via the COntinuous-time Generalized Auto-Regressive Conditional Heteroscedastic (COGARCH) processes.