Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.

Efficient Centralized Cooperative Spectrum Sensing Techniques for Cognitive Networks

Wireless Communication is a system for communicating information from one point to other,without utilizing any connections like wire,cable,or other physical medium.Cognitive Radio(CR)based systems and networks are a revolutionary new perception in wireless communications.Spectrum sensing is a vital task of CR to avert destructive intrusion with licensed primary or main users and discover the accessible spectrum for the efficient utilization of the spectrum.Centralized Cooperative Spectrum Sensing(CSS)is a kind of spectrum sensing.Most of the test metrics designed till now for sensing the spectrum is produced by using the Sample Covariance Matrix(SCM)of the received signal.Some of the methods that use the SCM for the process of detection are Pietra-Ricci Index Detector(PRIDe),Hadamard Ratio(HR)detector,Gini Index Detector(GID),etc.This paper presents the simulation and comparative perfor-mance analysis of PRIDe with various other detectors like GID,HR,Arithmetic to Geometric Mean(AGM),Volume-based Detector number 1(VD1),Maximum-to-Minimum Eigenvalue Detection(MMED),and Generalized Likelihood Ratio Test(GLRT)using the MATLAB software.The PRIDe provides better performance in the presence of variations in the power of the signal and the noise power with less computational complexity.

Comparison of six generalized linear models for occurrence of lightning-induced fires in northern Daxing'an Mountains,China

The occurrence of lightning-induced forest fires during a time period is count data featuring over-dispersion （i.e., variance is larger than mean） and a high frequency of zero counts. In this study, we used six generalized linear models to examine the relationship between the occurrence of lightning-induced forest fires and meteorological factors in the Northern Daxing＇an Mountains of China. The six models included Poisson, negative binomial （NB）, zero- inflated Poisson （ZIP）, zero-inflated negative binomial （ZINB）, Poisson hurdle （PH）, and negative binomial hurdle （NBH） models. Goodness-of-fit was compared and tested among the six models using Akaike information criterion （AIC）, sum of squared errors, likelihood ratio test, and Vuong test. The predictive performance of the models was assessed and compared using independent validation data by the data-splitting method. Based on the model AIC, the ZINB model best fitted the fire occurrence data, followed by （in order of smaller AIC） NBH, ZIP, NB, PH, and Poisson models. The ZINB model was also best for pre- dicting either zero counts or positive counts （〉1）. The two Hurdle models （PH and NBH） were better than ZIP, Poisson, and NB models for predicting positive counts, but worse than these three models for predicting zero counts. Thus, the ZINB model was the first choice for modeling the occurrence of lightning-induced forest fires in this study, which implied that the excessive zero counts of lightning- induced fires came from both structure and sampling zeros.

Location Verification Systems in Emerging Wireless Networks

As location-based techniques and applications have become ubiquitous in emerging wireless networks, the verification of location information has become more important. In recent years, there has been an explosion of activity related to lo- cation-verification techniques in wireless networks. In particular, there has been a specific focus on intelligent transport systems because of the mission-critical nature of vehicle location verification. In this paper, we review recent research on wireless location verification related to vehicular networks. We focus on location verification systems that rely on for- mal mathematical classification frameworks and show how many systems are either partially or fully encompassed by such frameworks.

Optimal decision fusion given sensor rules

When all the rules of sensor decision are known, the optimal distributeddecision fusion, which relies only on the joint conditional probability densities, can be derivedfor very general decision systems. They include those systems with interdependent sensorobservations and any network structure. It is also valid for m-ary Bayesian decision problems andbinary problems under the Neyman-Pearson criterion. Local decision rules of a sensor withcommunication from other sensors that are optimal for the sensor itself are also presented, whichtake the form of a generalized likelihood ratio test. Numerical examples are given to reveal someinteresting phenomena that communication between sensors can improve performance of a senordecision, but cannot guarantee to improve the global fusion performance when sensor rules were givenbefore fusing.

Distribution-based CFAR detectors in SAR images

As traditional two-parameter constant false alarm rate （CFAR） target detec-tion algorithms in SAR images ignore target distribution, their performances are not the best or near best. As the resolution of SAR images increases, small targets present more pixels in SAR images. So the target distribution is of much significance. Distribution-based CFAR detection algorithm is presented. We unite the pixels around the test cell, and estimate the distribution of test cell by them. Generalized Likelihood Ratio Test （GLRT） is used to deduce the detectors. The performance of the distribution-based CFAR （DBCFAR） detectors is analyzed theoretically. False alarms of DBCFAR detection are fewer than those of CFAR at the same detection rate. Finally experiments are done and the results show the performance of DBCFAR is out of conventional CFAR. False alarms of DBCFAR detection are concentrated while those of CFAR detection are dispersive.

Adaptive detector design of MIMO radar with unknown covariance matrix

The problem of detecting signal with multiple input mul-tiple output （MIMO） radar in correlated Gaussian clutter dominated scenario with unknown covariance matrix is dealt with. The gen-eral MIMO model, with widely separated sub-arrays and co-located antennas at each sub-array, is adopted. Firstly, the generalized likelihood ratio test （GLRT） with known covariance matrix is ob-tained, and then the Rao and Wald detectors are devised, which have proved that the Rao and Wald test coincide with GLRT detec-tor. To make the detectors fully adaptive, the secondary data with signal-free will be collected to estimate the covariance. The per-formance of the proposed detector is analyzed, however, it is just ancillary. A thorough performance assessment by several numer-ical examples is also given, which has considered the sense with co-located antennas configure of transmitters and receivers array. The results show that the performance the proposed adaptive de-tector is better than LJ-GLRT, and the loss can be acceptable in comparison to their non-adaptive counterparts.

Adaptive detection in the presence of signal mismatch

The problem of adaptive detection in the situation of signal mismatch is considered; that is, the actual signal steering vector is not aligned with the nominal one. Two novel tunable detectors are proposed. They can control the degree to which the mismatched signals are rejected. Remarkably, it is found that they both cover existing famous detectors as their special cases. More importantly, they possess the constant false alarm rate（CFAR）property and achieve enhanced mismatched signal rejection or improved robustness than their natural competitors. Besides, they can provide slightly better matched signals detection performance than the existing detectors.

Entropy-based multipath detection model for MIMO radar

An optimized detection model based on weighted entropy for multiple input multiple output (MIMO) radar in multipath environment is presented. After defining the multipath distance difference (MDD), the multipath received signal model with four paths is built systematically. Both the variance and correlation coefficient of multipath scattering coefficient with MDD are analyzed, which indicates that the multipath variable can decrease the detection performance by reducing the echo power. By making use of the likelihood ratio test (LRT), a new method based on weighted entropy is introduced to use the positive multipath echo power and suppress the negative echo power, which results in better performance. Simulation results show that, compared with non-multipath environment or other recently developed methods, the proposed method can achieve detection performance improvement with the increase of sensors.

Improved AR-Based GLRT Detector for Range-Spread Targets in Compound-Gaussian Clutter without Secondary Data

The problem of adaptive radar detection in compound-Gaussian clutter without secondary data is considered in this paper.In most practical applications,the number of training data is limited.To overcome the lack of training data,an autoregressive（AR）-process-based covariance matrix estimator is proposed.Then,with the estimated covariance matrix the one-step generalized likelihood ratio test（GLRT） detector is designed without training data.Finally,detection performance of our proposed detector is assessed.

Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

Sammon Quadratic Recurrent Multilayer Deep Classifier for Legal Document Analytics

In recent years,machine learning algorithms and in particular deep learning has shown promising results when used in the field of legal domain.The legal field is strongly affected by the problem of information overload,due to the large amount of legal material stored in textual form.Legal text processing is essential in the legal domain to analyze the texts of the court events to automatically predict smart decisions.With an increasing number of digitally available documents,legal text processing is essential to analyze documents which helps to automate various legal domain tasks.Legal document classification is a valuable tool in legal services for enhancing the quality and efficiency of legal document review.In this paper,we propose Sammon Keyword Mapping-based Quadratic Discriminant Recurrent Multilayer Perceptive Deep Neural Classifier(SKM-QDRMPDNC),a system that applies deep neural methods to the problem of legal document classification.The SKM-QDRMPDNC technique consists of many layers to perform the keyword extraction and classification.First,the set of legal documents are collected from the dataset.Then the keyword extraction is performed using SammonMapping technique based on the distance measure.With the extracted features,Quadratic Discriminant analysis is applied to performthe document classification based on the likelihood ratio test.Finally,the classified legal documents are obtained at the output layer.This process is repeated until minimum error is attained.The experimental assessment is carried out using various performance metrics such as accuracy,precision,recall,F-measure,and computational time based on several legal documents collected from the dataset.The observed results validated that the proposed SKM-QDRMPDNC technique provides improved performance in terms of achieving higher accuracy,precision,recall,and F-measure with minimum computation time when compared to existing methods.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

一类高维组内相关结构的检验

The paper considers a high-dimensional likelihood ratio(LR)test on the intraclass correlation structure of the multivariate normal population.When the dimension p and sample size N satisfy N−1>p→∞,it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution,and the explicit expressions of the mean and the variance are also obtained.The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method,and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data.

On Testing Equality of K Multiple Correlation Matrices

Coutsourides derived an ad hoc nuisance paratmeter removal test for testing equality of two multiple correlation matrices of two independent p variate normal populations under the assumption that a sample of size n is available from each population. This paper presents a likelihood ratio test criterion for testing equality of K multiple correlation matrices and extends the results to the testing of equality of K partial correlation matrices.

A Problem of Testing Homogeneity Against Order Constraints on Risk Differences

Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, where △i’s are to be of interest and P0i’s are nuisance parameters. The null hypothesis of homogeneity on the risk difference can be written as

Shrinkage Estimation in the Random Parameters Logit Model

In this paper, we explore the properties of a positive-part Stein-like estimator which is a stochastically weighted convex combination of a fully correlated parameter model estimator and uncorrelated parameter model estimator in the Random Parameters Logit (RPL) model. The results of our Monte Carlo experiments show that the positive-part Stein-like estimator provides smaller MSE than the pretest estimator in the fully correlated RPL model. Both of them outperform the fully correlated RPL model estimator and provide more accurate information on the share of population putting a positive or negative value on the alternative attributes than the fully correlated RPL model estimates. The Monte Carlo mean estimates of direct elasticity with pretest and positive-part Stein-like estimators are closer to the true value and have smaller standard errors than those with fully correlated RPL model estimator.

Statistical inference for the nonparametric and semiparametric hidden Markov model via the composite likelihood approach

In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization(EM) algorithm is developed to compute the maximum composite likelihood.We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk’s phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange(CBOE) are conducted to demonstrate the effectiveness of the proposed methods.

A novel target detection approach based on adaptive radar waveform design

To resolve problems of complicated clutter, fast-varying scenes, and low signal-clutterratio （SCR） in application of target detection on sea for space-based radar （SBR）, a target detection approach based on adaptive waveform design is proposed in this paper. Firstly, complicated sea clutter is modeled as compound Gaussian process, and a target is modeled as some scatterers with Gaussian reflectivity. Secondly, every dwell duration of radar is divided into several sub-dwells. Regular linear frequency modulated pulses are transmitted at Sub-dwell 1, and the received signal at this sub-dwell is used to estimate clutter covariance matrices and pre-detection. Estimated matrices are updated at every following sub-dwell by multiple particle filtering to cope with fast-varying clutter scenes of SBR. Furthermore, waveform of every following sub-dwell is designed adaptively according to mean square optimization technique. Finally, principal component analysis and generalized likelihood ratio test is used for mitigation of colored interference and property of constant false alarm rate, respectively. Simulation results show that, considering configuration of SBR and condition of complicated clutter, 9 dB is reduced for SCR which reliable detection requires by this target detection approach. Therefore, the work in this paper can markedly improve radar detection performance for weak targets.

GLRT Detectors for Aircraft Wake Vortices in Clear Air

In this article, radar echoes of aircraft wake vortices are modeled as weighted sums of the frequency components of the echoes with a special covariance matrix for the weighted coefficients. With a proposed detection scheme, two generalized likelihood ratio test (GLRT) detectors are derived respectively for aircraft wake vortices with time-varying and time-invariant Doppler spectra. Then the analytical expressions for detection and false alarm probabilities of the detectors are derived and three factors are investigated which mainly influence the detection performance, i.e., the Doppler extension and uncertainty of the aircraft wake vortex, and the number of the detection cells. The results indicate that, the signal-to-noise ratio (SNR) loss induced by Doppler extension is generally several decibels. The SNR loss due to Doppler uncertainty is approximately proportional to the logarithm of the number of spectrum lines in the uncertain Doppler spectrum intervals. For a large number of detection cells, the SNR gain is approximately proportional to the square root of the number of the detection cells.