Optimal bandwidth selection for multivariate kernel deconvolution density estimation

Assume we have i.i.d. replications from the mismeasured random vector Y=X+ε, where X and ε are mutually independent. We consider a data-driven bandwidth, based on a cross-validation ideas, for multivariate kernel deconvolution estimator of the density of X. The proposed data-driven bandwidth selection method is shown to be asymptotically optimal. As a by-product of the proof of this result, we show that the average squared error, the integrated squared error, and the mean integrated squared error are asymptotically equivalent error measures.      

Minimum-entropy, PDF approximation, and kernel selection for measurement estimation

The purpose of this paper is to investigate the selection of an appropriate kernel to be used in a recent robust approach called minimum-entropy estimator (MEE). This MEE estimator is extended to measurement estimation and pdf approximation when /spl rho/(e) is unknown. The entropy criterion is constructed on the basis of a symmetrized kernel estimate /spl rho//sub n,h/(e) of /spl rho/(e). The MEE performance is generally better than the Maximum Likelihood (ML) estimator. The bandwidth selection procedure is a crucial task to assure consistency of kernel estimates. Moreover, recent proposed Hilbert kernels avoid the use of bandwidth, improving the consistency of the kernel estimate. A comparison between results obtained with normal, cosine and Hilbert kernels is presented.     

A simple segmentation method for DNA microarray spots by kernel density estimation

The DNA microarray analysis is one of the most important areas in biomedical research. For the accurate analysis of microarray data the process of segmentation, classification of pixels as foreground or background, should be done accurately. In this paper we suggest a kernel density estimation approach for the segmentation of the microarray spot. We estimate the density of n pixel intensities for a given target area by the kernel density estimation, and the resulting kernel density estimate gives bimodal density by appropriate choice of the smoothing parameter. We suggest two modes of the kernel density estimate for n pixel intensities as estimates of the foreground (mode with larger value) and the background (mode with smaller value) intensity, respectively. The segmentation method proposed in this paper is easy and simple to use, robust to the shape of spot, and very accurate. This research was supported by Korea Science and Engineering Foundation grant (R14-2003-002-01000-0).     

Bandwidth estimation for ultra-high-speed lithium niobate modulators

The effects of velocity matching, impedance matching, conductor loss, and dielectric loss on the optical bandwidth of an ultra-high-speed lithium niobate modulator are reported. It is shown that both dielectric loss and impedance matching play a key role for velocity-matched high-speed modulators with low conductor loss. The effects of etch depth, buffer thickness, electrode width, and thegap between the electrodes on device performance are also illustrated.     

Universal smoothing factor selection in density estimation: theory and practice

In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, forall densities in all dimensions, theL ₁ error of the corresponding kernel estimate is not larger than 3+∈ times the error of the estimate with the optimal smoothing factor plus a constant times $\sqrt {\log n/n}$ , wheren is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for eachn. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method.     

Universal smoothing factor selection in density estimation: theory and practice

In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, forall densities in all dimensions, theL ₁ error of the corresponding kernel estimate is not larger than 3+∈ times the error of the estimate with the optimal smoothing factor plus a constant times , wheren is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for eachn. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method. The author's work was supported by NSERC A3456 and by FCAR Grant 90-ER-0291     

多维性能极限状态下概率地震需求分析的多元相关核密度估计法

本文不对工程需求参数（EDP）的分布类型进行人为假定,提出基于多元相关核密度估计的概率地震需求分析法。在带宽矩阵和多元高斯核函数中分别引入相关系数,并分别采用三种相关系数描述相关性,将传统核密度估计拓展到可以考虑随机变量相关性的多元核密度估计。基于SAP2000建立某钢筋混凝土框剪结构,选择最大层间位移角、最大层加速度衡量多维性能极限状态。在不同峰值地面加速度（PGA）下建立基于多元相关核密度估计的概率地震需求模型,并给出基于蒙特卡洛（MC）模拟的地震需求公式,得到结构需求的年平均超越概率。采用传统基于多维对数正态分布假定的地震风险概率法和不考虑EDP相关性的核密度估计进行对比,研究表明：与传统的多维对数正态分布假定相比,基于相关多元核密度估计的结构需求年平均超越概率偏大,而不考虑相关性的多元核密度估计所得年平均超越概率偏小;不同相关系数会影响到年平均超越概率的大小,其中Pearson相关系数影响最大,Spearman相关系数次之,Kendall相关系数最小。     

Identification of hazardous road locations of traffic accidents by means of kernel density estimation and cluster significance evaluation

This paper proposes a procedure which evaluates clusters of traffic accident and organizes them according to their significance. The standard kernel density estimation was extended by statistical significance testing of the resulting clusters of the traffic accidents. This allowed us to identify the most important clusters within each section. They represent places where the kernel density function exceeds the significance level corresponding to the 95th percentile level, which is estimated using the Monte Carlo simulations. To show only the most important clusters within a set of sections, we introduced the cluster strength and cluster stability evaluation procedures. The method was applied in the Southern Moravia Region of the Czech Republic.     

NA相依样本的非参数核估计

假设非参数衰退模型Yi=g(Xi)+iε,其中残差{iε}是一个具有未知公共密度函数f(x)的NA相依样本,g(x)=E(Y+X=x)是未知衰退函数.今首先在残差基础上定义了非参数估计gn(x)和^fn(x),并在适当条件下证明了gn(x)和^fn(x)分别是g(x)和f(x)的强一致相合估计,同时给出了相应的收敛速度.     

Product-limit estimation for length-biased censored data

Length-biased and censored data may appear when analyzing times of duration In this work, a new empirical curve $\tilde F$ for approximating a distribution functionF under right-censoring and length-bias is introduced. The proposed estimate is (not equal to but) closely related to the product-limit Kaplan-Meier estimator. Strong consistency and distributional convergence is established for a general empirical parameter $\tilde \gamma = g\left( {\int {\varphi _1 d\tilde F} ,...,\int {\varphi _\tau d\tilde F} } \right)$ . As applications, one can obtain the corresponding large sample results for estimates of the distribution function, the cumulative harard function, and the mean residual time function. The new method is illustrated with real data concerning unempoloyment duration.     

The utility of less-common statistical methods for analyzing agricultural systems: focus on kernel density estimation,copula modeling and extreme value theory

Behaviormetrika - A variety of statistical methods have been developed for multivariate analysis of agricultural systems. Some statistical methods are rarely used to study these systems, although...     

Bandwidth estimation for multimode optical fibers using the frequency correlation function of speckle patterns

In this paper we present a new method for estimating the bandwidth of multimode optical fibers based on the frequency correlation function of the speckle patterns generated by the interference of fiber modes. This technique, which does not require a pulse or signal generator, can be utilized to estimate the bandwidth of a multimode fiber using a relatively short length of fiber. By applying this method to a test fiber we obtained a bandwidth of approximately 36 MHz km which is in relatively good agreement with the approximately 44-MHz x km bandwidth measured by a conventional pulsed technique.     

Simulation-based cost estimation under economic uncertainty using kernel estimators

To simplify the process of cost estimation in many engineering applications, deterministic cost models are often used. Single value cost estimates are invariably the output of these models. It has been recognized by the cost estimating community that estimates should more appropriately be given in terms of probability distribution functions (PDFs) and that simulation methods are superior to analytical methods for determining these cost distributions. In this paper, a simulation approach employing non-parametric estimation techniques and their asymptotic properties in the development of the PDFs of cost estimates is proposed. To illustrate the approach, it is applied to the problem of project bidding.     

FRF-based structural parameters estimation using strain data: sensitivity equation,measurement and excitation selection

In this paper, a structural model updating technique is presented using frequency domain representation of incomplete strain data to identify the location and severity of structural damages. The most important challenges of model updating methods such as selection of excitation, measurement locations and interested frequency ranges are addressed. Distribution of strain energy in all structural elements and norms of the derived sensitivity equation are utilized for the selection of measurement and excitation locations. The important effect of different level of noise in measurement data and modelling error on the accuracy and robustness of the proposed method are investigated. A bowstring truss and a two-storey single-bay frame are used to evaluate the numerical ability of proposed method. The results prove the potentials of the proposed method in identifying the location and severity of damage in the presence of different errors.     

Peak clipping algorithms for background estimation in spectroscopic data

In this paper we present sensitive nonlinear iterative peak (SNIP) clipping algorithms to estimate background in various kinds of spectra. We have proposed several improvements of the SNIP algorithm. Moreover, we have extended and generalized the SNIP algorithm for multidimensional coincidence gamma-ray spectra. In addition to the continuous background, the so-called lower-order coincidences, i.e., coincidences peak-background in different dimensions, must also be included into the estimated background. Further, we have derived a set of modifications of the algorithm that allow estimation of specific shapes of background and ridges as well.     

Bayesian inference for parameters estimation using experimental data

A finite element (FE) model is developed for a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy) which accounts for uncertainties in geometry, material properties, and boundary conditions as well as limited knowledge on the behavior of connections and other components. Ambient vibration tests (AVTs) are carried out to identify the main dynamic parameters which are used for model updating in the Bayesian framework. Sensitivity analysis is performed to identify the main mechanical parameters affecting natural frequencies and mode shapes to be used as updating parameters. Finally, the posterior probability distributions of the selected updating parameters is estimated and used to assess the accuracy of the FE-based model. The importance of using a proper informative reference data set in the updating framework is assessed using different observations together with the importance of reliable surrogate models able to reduce the computational costs related to the whole framework.     

数据网格资源选择优化模型

为了满足网格数据服务的可靠性和传输时间约束,同时兼顾网络负载及节点资源的有效利用,提出了一种网格数据资源选择优化模型,该模型以网络负载和资源代价为优化目标函数,以节点的传输速度、可靠性、传输距离、网络状态、客户端带宽和容忍度阈值为输入,进而决策出参与服务的最优节点集合,同时模型中设定了权重因子来均衡网络负载与资源代价....     

Nanodomain manipulation for ultrahigh density ferroelectric data storage

Nanosized inverted domain dots in ferroelectric materials have potential application in ultrahigh density rewritable data storage systems. Herein, a data storage system is presented based on scanning non-linear dielectric microscopy and a thin film of ferroelectric single-crystal lithium tantalite. Through domain engineering, we succeeded in forming our smallest artificial nanodomain single dot at 5.1?nm diameter and an artificial nanodomain dot array with a memory density of 10.1?Tbit?inch(-2) and a bit spacing of 8.0?nm, representing the highest memory density for rewritable data storage reported to date. Subnanosecond (500?ps) domain switching speed has also been achieved. Next, actual information storage with a low bit error and high memory density was performed. A bit error ratio of less than 1 × 10(-4) was achieved at an areal density of 258?Gbit?inch(-2). Moreover, actual information storage is demonstrated at a density of 1?Tbit?inch(-2).     

The truncated Hausdorff moment problem solved by using kernel density functions

In this work, the problem of an efficient representation and its exploitation to the approximate determination of a compactly supported, continuous probability density function (pdf) from a finite number of its moments is addressed. The representation used is a finite superposition of kernel density functions. This representation preserves positivity and can approximate any continuous pdf as closely as it is required. The classical theory of the Hausdorff moment problem is reviewed in order to make clear how the theoretical results as, e.g. the moment bounds, can be exploited in the numerical procedure. Various difficulties arising from the well-known ill-posedness of the numerical moment problem have been identified and solved. The kernel coefficients of the pdf expansion are calculated by solving a constrained, non-negative least-square problem. The consistency, numerical convergence and robustness of the solution algorithm have been illustrated by numerical examples with unimodal and bimodal pdfs. Although this paper is restricted to univariate, compactly supported pdfs, the method can be extended to general pdfs either univariate or multivariate, with finite or infinite support.