Goodness-of-fit tests for type-I extreme-value and 2-parameterWeibull distributions

This study investigates the properties of the Kolmogorov-Smirnov (K-S), Cramer-von Mises (C-M) and Anderson-Darling (A-D) statistics for goodness-of-fit tests for type-I extreme-value and for 2-parameter Weibull distributions, when the population parameters are estimated from a complete sample by graphical plotting techniques (GPT). Three GPT-median ranks, mean ranks, symmetrical sample cumulative distribution (symmetrical ranks)-are combined with the least-squares method (LSM) on extreme-value and Weibull probability paper to estimate the population parameters. The critical values of the K-S, C-M, A-D statistics are calculated by Monte Carlo simulation, in which 10⁶ sets of samples for each sample size of 3(1)20, 25(5)50, and 60(10)100 are generated. The power of the K-S, C-M, A-D statistics are investigated for 3 graphical plotting techniques and for maximum likelihood estimators (MLE). A Monte Carlo simulation provided the power results using 10⁴ repetitions for each sample size of 5, 10, 25, 40. The power comparison showed that: Among 3 GPT, the symmetrical ranks give more powerful results than the median and mean ranks for the K-S, C-M, A-D statistics; Among 3 GPT and the MLE, the symmetrical ranks provide more powerful results than the MLE for the K-S and A-D statistics; for the C-M statistic, the MLE provide more powerful results than 3 GPT; Generally, the A-D statistic coupled with the symmetrical ranks and LSM is most powerful among the competitors in this study and is recommended for practical use     

Modified KS, AD, and C-vM tests for the Pareto distribution withunknown location and scale parameters

Standard goodness-of-fit tests based on the empirical CdF (Edf) require continuous underlying distributions with all parameters specified. Three modified Edf-type tests, the Kolmogorov-Smirnov (K-S), Anderson-Darling (A-D), and Cramer-von Mises (C-vM), are developed for the Pareto distribution with unknown parameters of location and scale and known shape parameter. The unknown parameters are estimated using best linear unbiased estimators. For each test, Monte Carlo techniques are used to generate critical values for sample sizes 5(5)30 and Pareto shape parameters 0.5(0.5)4.0. The powers of the modified tests are investigated under eight alterative distributions. In most cases, the powers of the modified K-S, A-D, C-vM tests are considerably higher than the chi-square test. Finally, a functional relationship is identified between the modified K-S and C-vM test statistics and the Pareto shape parameter. Powerful goodness-of-fit tests that supplement the best linear unbiased estimates are provided     

Testing exponentiality based on the Kullback-Leibler information with the type II censored data

We express the joint entropy of order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint entropy of the type II censored data. Then we establish a goodness of fit test statistic based on the Kullback-Leibler information with the type II censored data, and compare its performance with some leading test statistics. A Monte Carlo simulation study shows that the proposed test statistic shows better powers than some leading test statistics against the alternatives with monotone increasing hazard functions.     

基于空间谱的频谱感知算法及性能分析

现有的基于特征值或谱密度的频谱感知算法,多分别使用近似高斯分布和Tracy-Widom分布来分别分析求解检验统计量在信号是否存在时的分布,未能给出统一的解析表达式。该文提出均匀线阵(ULA)条件下基于空间谱密度比的频谱感知算法,并且基于顺序统计量的最新研究成果,给出检验统计量统一的闭合表达式。该算法基于离散空间谱密度最大最小值的比建立检验统计量。仿真结果表明,对于8阵元的ULA,在采样点数为1000、检测概率为0.9时,所提算法比最大最小特征值(MME)比算法有约1.7 dB的性能优势,同时也有效验证了检验统计量理论分布的准确性。     

Blind recognition of STBC-OFDM signals based on modified K-S test

Aiming at the problem that existed blind classification of STBC-OFDM in multiple input single output (MISO) communication system,an efficient method for blind classification of space-time block coded orthogonal frequency-division multiplexing (STBC-OFDM) signals based on modified Kolmogorov-Smirnov (K-S) test was proposed,when a single receiver antenna was employed at the receiver.Firstly,the model of received STBC-OFDM signals in MISO systems was given.Secondly,with the correlation of the coding matrix of STBC-OFDM signals,and the discrimination features function provided by the empirical cumulative distribution (CDFs) of the received OFDM blocks was constructed.Finally,the distance between CDFs was tested by the two-sample K-S test,which could blindly classify the STBC-OFDM signals.The proposed algorithm didn't need the estimation of channel,noise statistics and modulation type,and consequently,was well suited for non-cooperative communication context.Theoretical analysis and experimental verify its validity.     

Analysis of a simple step-stress life test with a random stress-change time

This paper studies a variation of a simple step-stress life testing in which the stress change time is random, and the test is subject to type II censoring. We assume that only two order statistics from the test are observed. The first observed order statistic is the stress change time from a low level stress to a high level stress during the testing, and the second observed order statistic is the final failure time when the test is censored. We first present the joint probability distribution of the two order statistics observed from the simple step-stress accelerated life test. Maximum likelihood estimates, and the method of moment estimates for model parameters based on the joint distribution are considered. We also present the exact confidence interval estimates for the model parameters based on various pivotal quantities, and demonstrate the estimation procedure by a simulated example.     

授权用户信号随机到达时基于双门限的多用户合作频谱感知方法

针对认知无线电系统中可能出现的授权用户信号随机到达时的频谱感知问题,提出了一种基于双门限的多用户合作频谱感知方法.首先在本地判决时采用高低双门限的方式,如果判决量大于高门限就判1,小于低门限判0,在两个门限之间就把判决量直接发送给融合中心,融合中心将直接收到的判决量进行软判决合并,软判决的结果再与其他硬判决的结果进行"OR原则"的硬判决合并,从而得到最终的判决结果.仿真表明所提方法的性能比传统"OR原则"硬判决合并方案要好,仅仅略逊于传统等增益软判决合并方案,但是能大量节省认知网络中的传输比特数.     

A generalized switching CFAR processor based on test cell statistics

In this paper, a new constant false alarm rate (CFAR) thresholding algorithm which is a generalisation of the switching CFAR (S-CFAR) that takes into account the statistics of the sample in the test cell for reference sample selection is proposed. It employs a composite approach based on the switching CFAR and the order statistic CFAR (OS-CFAR). A mathematical analysis in a homogeneous environment is provided for this detector. The results obtained show that the detection performance of the generalised S-CFAR (GS-CFAR) is improved both in homogenous background and non-homogenous environment caused by interfering targets and clutter edge.     

Two chi-square statistics for determining the orders p andq of an ARMA (p, q) process

The &thetas;, λ, and η functions have been previously proposed for use in choosing the autoregressive and moving-average orders of an ARMA (q, p) process visually. Two chi-square statistics associated with these three functions are presented and used here to determine the orders of an ARMA process statistically. It is shown that the two statistics are asymptotically equivalent to the Quenouille-Walker's goodness-of-fit test statistic, which is a Lagrange multiplier test statistic. Some numerical examples are presented to illustrate the usefulness of the two chi-square statistics as well as the three functions in ARMA modeling     

Distributed detection of narrowband signals

Distributed signal detection schemes have received significant attention, but most research has focused on cases with independent observations at the different sensors. Cases with dependent narrowband signals, which are of practical interest in communication, radar, and sonar problems, are studied. The focus is on applications where the observations consist of a weak common signal in possibly non-Gaussian additive noise which is independent from sensor to sensor. The author finds that the best (locally optimum) sensor test statistics for such cases are often different from the best test statistics for cases with isolated sensors and that these sensor test statistics may be nonsymmetric for highly symmetric problems. The possible difference between the best weak-signal distributed sensor test statistic and the best weak-signal test statistic for an isolated sensor can be shown to be due to the distributed sensors attempting to approximate the correlation terms found in the corresponding centralized tests     

Toward realistic and practical ideal observer (IO) estimation for the optimization of medical imaging systems

The ideal observer (IO) employs complete knowledge of the available data statistics and sets an upper limit on observer performance on a binary classification task. However, the IO test statistic cannot be calculated analytically, except for cases where object statistics are extremely simple. Kupinski have developed a Markov chain Monte Carlo (MCMC) based technique to compute the IO test statistic for, in principle, arbitrarily complex objects and imaging systems. In this work, we applied MCMC to estimate the IO test statistic in the context of myocardial perfusion SPECT (MPS). We modeled the imaging system using an analytic SPECT projector with attenuation, distant-dependent detector-response modeling and Poisson noise statistics. The object is a family of parameterized torso phantoms with variable geometric and organ uptake parameters. To accelerate the imaging simulation process and thus enable the MCMC IO estimation, we used discretized anatomic parameters and continuous uptake parameters in defining the objects. The imaging process simulation was modeled by precomputing projections for each organ for a finite number of discretely-parameterized anatomic parameters and taking linear combinations of the organ projections based on continuous sampling of the organ uptake parameters. The proposed method greatly reduces the computational burden and allows MCMC IO estimation for a realistic MPS imaging simulation. We validated the proposed IO estimation technique by estimating IO test statistics for a large number of input objects. The properties of the first- and second-order statistics of the IO test statistics estimated using the MCMC IO estimation technique agreed well with theoretical predictions. Further, as expected, the IO had better performance, as measured by the receiver operating characteristic (ROC) curve, than the Hotelling observer. This method is developed for SPECT imaging. However, it can be adapted to any linear imaging system.     

Blind identification of MISO-FIR channels

In this paper, we address the problem of determining the order of MISO channels by means of a series of hypothesis tests based on scalar statistics. Using estimated 4th-order output cumulants, we exploit the sensitiveness of a Chi-square test statistic to the non-Gaussianity of a stochastic process. This property enables us to detect the order of a linear finite impulse response (FIR) channel. Our approach leads to a new channel order detection method and we provide a performance analysis along with a criterion to establish a decision threshold, according to a desired level of tolerance to false alarm. Afterwards, we introduce the concept of MISO channel nested detectors based on a deflation-type procedure using the 4th-order output cumulants. The nested detector is combined with an estimation algorithm to select the order and estimate the parameters associated with different transmitters composing the MISO channel. By treating successively shorter and shorter channels, it is also possible to determine the number of sources.     

采用T2统计量和拟合优度的盲频谱感知算法

针对低信噪比和采样数少时频谱感知性能差的问题,首先利用样本检验矩阵的样本特征构造T2统计量,再结合似然比准则构造新的检验统计量,最后推导了频谱空闲时检验统计量的概率密度函数,提出基于贝塔分布的盲频谱感知算法。但此算法在采样数较少时,检测性能较差,因此结合Anderson Darling准则,提出基于贝塔分布的拟合优度检验算法。在高斯信道和瑞利衰落信道下对所提算法进行仿真,并与已有盲频谱感知算法仿真结果进行对比,所提算法具有更好的检测性能,且不需要主用户信息,不用进行特征分解,不受噪声方差影响。      

A performance study of some transient detectors

We present a simulation study of several different statistics applied to the detection of unknown transient signals in white Gaussian noise. The results suggest that relatively unsophisticated tests based on temporal localization of power, such as the Page (1954) test and a test based on a new statistic due to Nuttall (see NUWC-NPT Tech. Rep. 11123, 1996, and NUWC-NPT Tech. Rep. 10822, 1997), give reliable results     

Goodness-of-fit tests for the power-law process

The power-law process is often used as a model for reliability growth of complex systems or reliability of repairable systems. Often goodness-of-fit tests are required to check the hypothesis that failure data came from a power-law process model. Three statistics, Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling, are considered for a goodness-of-fit test of a power-law process in the case of failure-truncated data. Tables of critical values for the three statistics are presented and the results of a power study are given under the alternative hypothesis that failure data came from a nonhomogeneous Poisson process with log-linear intensity function. This power comparison is a new result, which can guide in selecting a test statistic and sample size. The power study shows that the tests have acceptable power for some parameter values and the Cramer-von Mises statistic has the highest power for a sample-size ⩾20     

Optimum quantization of order statistics

We present necessary conditions for minimum mean square error (MMSE) quantization of order statistics. These conditions are obtained by observing that in a quantize-sort cascade system, operations of quantization and sorting are interchangeable. We consider MMSE quantization of a single order statistic as well as of a group of order statistics and highlight several interesting properties. Numerical characteristics of order statistic quantizers are presented for Gaussian and uniform distributions, and detailed comparisons are made     

基于Kolmogorov—Simirnov检验统计量的OFDM识别方案

为了对OFDM信号进行识别,针对高阶矩算法的运算量大的不足,提出一种基于经验分布函数统计量法用于识别OFDM信号和单载波信号。提出单载波／OFDM信号识别模型,建立了最优经验分布函数评价准则,推导了最优经验分布函数;详细阐述了基于KS检验法的OFDM信号识别流程;理论分析及仿真结果表明,该统计量提高了对高斯分布的拟合能力,进而提高了对OFDM信号的识别能力,同时相比高阶矩法,运算量少。     

CFAR edge detector for polarimetric SAR images

Finding the edges between different regions in an image is one of the fundamental steps of image analysis, and several edge detectors suitable for the special statistics of synthetic aperture radar (SAR) intensity images have previously been developed. In this paper, a new edge detector for polarimetric SAR images is presented using a newly developed test statistic in the complex Wishart distribution to test for equality of covariance matrices. The new edge detector can be applied to a wide range of SAR data from single-channel intensity data to multifrequency and/or multitemporal polarimetric SAR data. By simply changing the parameters characterizing the test statistic according to the applied SAR data, constant false-alarm rate detection is always obtained. An adaptive filtering scheme is presented, and the distributions of the detector are verified using simulated polarimetric SAR images. Using SAR data from the Danish airborne polarimetric SAR, EMISAR, it is demonstrated that superior edge detection results are obtained using polarimetric and/or multifrequency data compared to using only intensity data.     

Lognormal Random-Field Models and Their Applications to Radar Image Synthesis

Lognormal random fields with multiplicative spatial interaction are proposed for modeling radar image intensity. Two particular classes of two-dimensional (2-D) lognormal random fields are introduced: multiplicative autoregressive (MAR), and multiplicative Mnrkov random fields (MMRF). The MAR and MMRF models are formulated as invertible point-transformations of Gaussian autoregressive and Gaussian Markov random fields (GMRF) and therefore possess many desirable properties. Least squares and maximum likelihood estimates for random-field parameters are presented, a decision rule is developed for selecting model order and transformations to normality as well, and techniques for synthesizing 2-D lognormal random fields are provided. Several Seasat synthetic aperture radar (SAR) images were tested using the decision rule developed in this paper and using the Kolmogorov-Smirnov (K-S) goodness-of-fit test. With both tests they were found to possess a good fit to lognormal statistics. MAR and MMRF models were fit to Seasat SAR images, and then the models were used to generate synthetic images that closely resemble the original SAR images both visually and in their variograms. This demonstrates the generality and appropriateness of the MAR and MMRF models for radar imagery.