基于渐近优化检测器的数字水印最佳检测阈值的确定

数字水印系统中检测阈值的大小会影响到检测器的检测效果。渐近优化检测器是一种采用Rao检验方式的盲水印检测算法,但其检测阈值是完全凭经验人为设定的,为了使渐近优化检测器阈值的确定客观与精确,利用最小差错概率准则对检测阈值进行了理论分析,并具体给出了一个水印检测系统错误率达到最小的最佳检测阈值的计算公式。实验结果表明,该方法能使水印检测系统的错误率在理论上达到最小,同时检测阈值的大小具有自适应性和客观性。     

A robust estimator for the tail index of Pareto-type distributions

In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric models which are fitted to excesses over large thresholds. Maximum likelihood estimators however are often not very robust, which makes them sensitive to few particular observations. Even in extreme value statistics, where the most extreme data usually receive most attention, this can constitute a serious problem. The problem is illustrated on a real data set from geopedology, in which a few abnormal soil measurements highly influence the estimates of the tail index. In order to overcome this problem, a robust estimator of the tail index is proposed, by combining a refinement of the Pareto approximation for the conditional distribution of relative excesses over a large threshold with an integrated squared error approach on partial density component estimation. It is shown that the influence function of this newly proposed estimator is bounded and through several simulations it is illustrated that it performs reasonably well at contaminated as well as uncontaminated data.     

A robust estimator for the tail index of Pareto-type distributions

In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric models which are fitted to excesses over large thresholds. Maximum likelihood estimators however are often not very robust, which makes them sensitive to few particular observations. Even in extreme value statistics, where the most extreme data usually receive most attention, this can constitute a serious problem. The problem is illustrated on a real data set from geopedology, in which a few abnormal soil measurements highly influence the estimates of the tail index. In order to overcome this problem, a robust estimator of the tail index is proposed, by combining a refinement of the Pareto approximation for the conditional distribution of relative excesses over a large threshold with an integrated squared error approach on partial density component estimation. It is shown that the influence function of this newly proposed estimator is bounded and through several simulations it is illustrated that it performs reasonably well at contaminated as well as uncontaminated data.     

粒子群优化在极值分布模型研究中的应用

由于灾难等极端事故发生的随机性以及数据之间的差异性,在运用极值理论计算风险时,必然面临模型的不确定性。为避免极值分布模型选择不当所引起的拟合误差,在介绍了极值理论相关概念的基础上,采用通用的广义极值分布模型,通过粒子群算法对复杂模型参数进行优化。以飞行安全为例进行仿真,实现了不同分布类型的统一优化处理,算法寻优速度较快、拟合效果理想,为准确选择极值分布模型提供了一条有效的途径。     

Estimation of probabilities using the logistic model in retrospective studies

Methods for estimating the parameters of the logistic regression model when the data are collected using a case-control (retrospective) scheme are compared. The regression coefficients are estimated by maximum likelihood methodology. This leaves the constant term parameter to be estimated. Four methods for estimating this parameter are proposed. The comparison of the four estimators is in two parts. First, they are compared for large samples. This is accomplished via the asymptotic distribution of the estimators. Second, the estimators are compared for small samples. This is conducted via stimulation using 11 logistic models. The estimation of the posterior probability of the response variable being a success (Px), as given by the logistic regression model, when the constant parameter is estimated by each of the four proposed methods is the main focus of this paper. A third concern is the comparison of the logistic discriminant procedures when each of the four methods of estimating the constant parameters is used. In addition, the linear discriminant function procedure is included. This comparison is executed only for small samples via simulation. It was found that when estimating Px, method 1 (which is essentially the MLE) minimizes the expected mean square error. The results were not as clear when the parameter of interest was the constant term itself. The results from the classification comparisons implied that when the logistic model contains mostly (or all) binary regression variables the logistic discriminant procedure using method 1 to estimate the constant term gives minimum expected error rate; otherwise the linear discriminant function gives minimum expected error rate. In the latter case the logistic discriminant procedure (method 1 estimator of the constant term) is approximately as good.     

A flexible extreme value mixture model

Extreme value theory is used to derive asymptotically motivated models for unusual or rare events, e.g. the upper or lower tails of a distribution. A new flexible extreme value mixture model is proposed combining a non-parametric kernel density estimator for the bulk of the distribution with an appropriate tail model. The complex uncertainties associated with threshold choice are accounted for and new insights into the impact of threshold choice on density and quantile estimates are obtained. Bayesian inference is used to account for all uncertainties and enables inclusion of expert prior information, potentially overcoming the inherent sparsity of extremal data. A simulation study and empirical application for determining normal ranges for physiological measurements for pre-term infants is used to demonstrate the performance of the proposed mixture model. The potential of the proposed model for overcoming the lack of consistency of likelihood based kernel bandwidth estimators when faced with heavy tailed distributions is also demonstrated.     

Identification of the minimum effective dose for right-censored survival data

In this paper, we consider identifying the minimum effective dose (MED) in a dose-response study when survival data are subject to random right-censorship, where the MED is defined to be the smallest dose level under study that has survival advantage over the zero-dose control. To this end, we suggest single-step-down testing procedures based on three different types of weighted logrank statistics, respectively. The comparative results of a Monte Carlo error rate and power/bias study for a variety of survival and censoring distributions are then presented and discussed. The application of the testing procedures for identifying the MED is finally illustrated by using a numerical example of prostate cancer data.     

基于极限学习机的结构健康监测数据恢复

为解决桥梁结构健康监测系统中数据丢失问题,引入格兰杰因果关系分析各传感器变量数据间的关系,选择与传感器丢失数据格兰杰因果关系大的变量作为极限学习机的输入向量,实现丢失数据的恢复。通过实际桥梁监测丢失数据的仿真实验,以均方根误差和最大误差绝对值作为评估指标,并与反向传播网络和最小二乘支持向量机算法对比,结果表明该方法在理论和实践上是正确和可行的。     

鲁棒Luenberger观测器设计

观测器控制系统中的观测器条件是系统的状态观测值渐近收敛于系统真实状态的根本条件.本文首先提出了Luenberger观测器设计的一种参数方法,然后根据使观测器条件误差为最小的准则,考虑了具有参数摄动的系统的鲁棒Luenberget观测器设计问题,给出了简单、有效的算法.仿真结果说明了本文方法的有效性.     

Asymptotically efficient parameter estimation using quantized output observations

This paper studies identification of systems in which only quantized output observations are available. An identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations. Strong convergence of the algorithm is first derived. The algorithm is then extended to a scenario of system identification with communication constraints, in which the sensor output is transmitted through a noisy communication channel and observed after transmission. The main results of this paper demonstrate that these algorithms achieve the Cramér-Rao lower bounds asymptotically, and hence are asymptotically efficient algorithms. Furthermore, under some mild regularity conditions, these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large. These results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank.     

On test horizon for model validation by output error

We derive necessary and sufficient conditions under which the parameters of the model are identical to those of the true system which is supposed to be linear and of finite dimension. These conditions are that the cross-correlations between the output error and the input as well as the model output should be asymptotically null in a finite horizon. This horizon may be used as a minimum necessary test horizon in model validation     

An extreme value problem in a linear sampled-data feedback system

When an uncorrelated, wide-band Markov noise process contaminates the input signal to a linear sampled-data feedback system, the extreme values of the mean-square true error and the mean-square apparent error are shown to occur for most practical purposes at the same value of the scalar loop gain. The gain parameter in an adaptive system may therefore be adjusted for minimum mean-square true error by minimizing the corresponding apparent error. An actual practical example is used to illustrate the result.     

New robust forecasting models for exchange rates prediction

This paper introduces two robust forecasting models for efficient prediction of different exchange rates for future months ahead. These models employ Wilcoxon artificial neural network (WANN) and Wilcoxon functional link artificial neural network (WFLANN). The learning algorithms required to train the weights of these models are derived by minimizing a robust norm called Wilcoxon norm. These models offer robust exchange rate predictions in the sense that the training of weight parameters of these models are not influenced by outliers present in the training samples. The Wilcoxon norm considers the rank or position of an error value rather than its amplitude. Simulation based experiments have been conducted using real life data and the results indicate that both models, unlike conventional models, demonstrate consistently superior prediction performance under different densities of outliers present in the training samples. Further, comparison of performance between the two proposed models reveals that both provide almost identical performance but the later involved low computational complexity and hence is preferable over the WANN model.     

Logistic map neural modelling: A theoretical foundation

The aim of this paper is to establish a theoretical framework for the modelling and simulation of chaotic attractors using neural networks. The attractor paradigm in this paper is the logistic map, which is modelled via neural networks in the convergence, periodic and chaotic regions. It is proved that, under certain conditions, the function simulated by the neural model is actually the logistic map with a different value of the λ parameter from the theoretical value. A two-dimensional system is defined and studied, facilitating the generation of the theoretical time series and the associated simulation error. The fixed points of periods p = 1 and p = 2 are identified and studied with respect to their stability. For higher period values, a theorem concerning the periodicity of the simulation error is postulated and proved. The minimum simulation error value is calculated using analytical methods, and the chaotic nature of the system with respect to Lyapunov exponents is described. Conclusions are discussed with respect to the experimental results obtained by the simulation models.     

Estimation of the autoregression parameter with infinite dispersion of noise

To estimate the unknown autoregression parameter in the case when noise has an infinite dispersion, the weighted estimate by the least-squares method is suggested. The limit distribution of the error of estimation is obtained. It is shown that the weighted estimate is asymptotically more exact in comparison with the common estimate by the least-squares method.     

A quantile estimation for massive data with generalized Pareto distribution

This paper proposes a new method of estimating extreme quantiles of heavy-tailed distributions for massive data. The method utilizes the Peak Over Threshold (POT) method with generalized Pareto distribution (GPD) that is commonly used to estimate extreme quantiles and the parameter estimation of GPD using the empirical distribution function (EDF) and nonlinear least squares (NLS). We first estimate the parameters of GPD using EDF and NLS and then, estimate multiple high quantiles for massive data based on observations over a certain threshold value using the conventional POT. The simulation results demonstrate that our parameter estimation method has a smaller Mean square error (MSE) than other common methods when the shape parameter of GPD is at least 0. The estimated quantiles also show the best performance in terms of root MSE (RMSE) and absolute relative bias (ARB) for heavy-tailed distributions.     

改进搜索机制的单纯形法引导麻雀搜索算法

为了改善基本麻雀搜索算法在处理优化问题时存在的收敛精度不高、速度慢和易陷入局部极小值的问题,提出一种改进搜索机制的单纯形法引导麻雀搜索算法。首先,针对发现者搜索过程随机性过高的问题,改进发现者搜索机制,提高算法收敛速度和稳定性;其次,改进麻雀搜索算法侦察机制,提高算法跳出局部极小值能力;最后,对每一次迭代适应度较差的部分个体采用单纯形法的相关操作,提高算法搜索能力。在8个基准测试函数以及部分CEC2014测试函数上的性能对比,同时结合Wilcoxon秩和检测分析,验证了改进算法的鲁棒性。     

On wavelet-based testing for serial correlation of unknown form using Fan’s adaptive Neyman method

Test procedures for serial correlation of unknown form with wavelet methods are investigated. A new test statistic is motivated using a canonical multivariate normal hypothesis testing model. It relies on empirical wavelet coefficients of a wavelet-based spectral density estimator. The choice of the Haar wavelet function is advocated, since evidence demonstrates that the choice of the wavelet function is not critical. Under the null hypothesis of no serial correlation, the asymptotic distribution of a vector of empirical wavelet coefficients is derived, which is asymptotically a multivariate normal distribution. A test statistic is proposed based on that asymptotic result, which presents the serious advantage to be completely data-driven or adaptive, avoiding the selection of any smoothing parameters. Furthermore, under a suitable class of fixed alternatives, the wavelet-based method is consistent against serial correlation of unknown form. The test statistic is expected to exhibit good power properties when the true spectral density displays significant spatial inhomogeneity, such as seasonal or business cycle periodicities. However, the convergence of the test statistic towards its asymptotic distribution is relatively slow. Thus, Monte Carlo methods based on random samples are suggested to determine the corresponding critical values. In a simulation study, the new methodology is compared with several test statistics, with respect to their exact levels and powers. The robustness properties of the spectral methods based on Monte Carlo critical values are also investigated empirically, when the error terms are weak white noises.     

基于分组方法的软件可靠性极值数据统计分析

提出了分组失效数据极值统计分析的方法。首先用相关系数法对分组失效数据的母体分布警行了假设检验;然后对母体分布的参数分别进行了点估计和区间估计，最后通过仿真验证了方法的可行性并给出了一实例。     

基于奇异值分解的压缩感知观测矩阵优化算法

针对压缩感知（CS）中从优化后的Gram矩阵求解观测矩阵时会出现较大相关系数的问题,在利用现有算法得到优化后的Gram矩阵的基础上,通过求解等价变换后的目标函数对观测矩阵行向量的导数得到目标函数取极值时行向量的值,并通过对误差矩阵进行奇异值分解（SVD）在上述行向量的值中选出使得目标函数取最值时行向量的解析式,在此基础上给出了观测矩阵的优化算法：通过借鉴K-SVD算法中逐行优化目标矩阵的思想,对观测矩阵进行逐行迭代优化,并将相邻两轮迭代产生的观测矩阵所对应的相关性之差作为衡量迭代是否结束的条件。仿真结果表明：该算法在观测矩阵与稀疏基的相关性方面优于改进前的算法,从而提高了重构精度。