Test Statistics For Detection Research Articles

Asymptotic behaviour of a test statistic for detection of change in mean of vectors

The paper gives an asymptotic distribution of a test statistic for detecting a change in a mean of random vectors with dependent components. The studied test statistic has a form of a maximum of a square Euclidean norms of vectors with components being standardized partial cumulative sums of deviations from means. The limit distribution was obtained using a result of Piterbarg [1994. High deviations for multidimensional stationary Gaussian processes with independent components. In: Zolotarev, V.M. (Ed.), Stability Problems for Stochastic Models, pp. 197–210].

Target Detection in Clutter Using Adaptive OFDM Radar

We address the problem of detecting a target moving in clutter environment using an orthogonal frequency division multiplexing (OFDM) radar. The broadband OFDM signal provides frequency diversity to improve the performance of the system. First, we develop a parametric model that accounts for the measurements at multiple frequencies including the Doppler shift. Then, we present a statistical detection test and evaluate its performance characteristics. Based on this, we propose an algorithm to adaptively design the parameters for the next transmitting waveform. Numerical examples illustrate our analytical results, demonstrating the achieved performance improvement due to the OFDM signaling method and adaptive waveform design.

Particle Filtering Based Approach for Landmine Detection Using Ground Penetrating Radar

In this paper, we present an online stochastic approach for landmine detection based on ground penetrating radar (GPR) signals using sequential Monte Carlo (SMC) methods. The processing applies to the two-dimensional B-scans or radargrams of 3-D GPR data measurements. The proposed state-space model is essentially derived from that of Zoubir et al., which relies on the Kalman filtering approach and a test statistic for landmine detection. In this paper, we propose the use of reversible jump Markov chain Monte Carlo in association with the SMC methods to enhance the efficiency and robustness of landmine detection. The proposed method, while exploring all possible model spaces, only expends expensive computations on those spaces that are more relevant. Computer simulations on real GPR measurements demonstrate the superior performance of the SMC method with our modified model. The proposed algorithm also considerably outperforms the Kalman filtering approach, and it is less sensitive to the common parameters used in both methods, as well as those specific to it.

Scattering of light by a periodic structure in the presence of randomness VII: Application of statistical detection test

Detection of periodic structures, hidden in random surfaces has been addressed by us for some time and the `extended matched filter' method,developed by us, has been shown to be effective in detecting the hidden periodic part from the light scattering data in circumstances where conventional data analysis methods cannot reveal the successive peaks due to scattering by the periodic part of the surface. It has been shown that if $r_{0}$ is the coherence length of light on scattering from the rough part and $\Lambda$ is the wavelength of the periodic part of the surface, the extended matched filter method can detect hidden periodic structures for $(r_{0}/\Lambda )\ge 0.11$, while conventional methods are limited to much higher values ($(r_{0}/\Lambda) \ge 0.33$). In the method developed till now, the detection of periodic structures involves the detection of the central peak, first peak and second peak in the scattered intensity of light, located at scattering wave vectors $v_{x} = 0$, $Q$, $2Q$,respectively, where $Q = 2\pi/\Lambda$, their distinct identities being obfuscated by the fact that the peaks have width $\Delta v_{x} = 2\pi/r_{0} \gg Q$. The relative magnitudes of these peaks and the consequent problems associated in identifying them is discussed. The Kolmogorov--Smirnov statistical goodness test is used to justify the identification of the peaks. This test is used to `reject' or `not reject' the null hypothesis which states that the successive peaks do exist. This test is repeated for various values of $r_{0}/\Lambda$, which leads to the conclusion that there is really a periodic structure hidden behind the random surface.

Generalized LRT-Based Voice Activity Detector

A robust and effective voice activity detection (VAD) algorithm is proposed for improving speech recognition performance in noisy environments. The approach is based on well-known statistical tests based on the determination of the speech/non-speech bispectra by means of third-order auto-cumulants. This algorithm differs from many others in the way the decision rule is formulated being the statistical tests built on a multiple observation (MO) window consisting of averaged bispectrum coefficients of the speech signal. Clear improvements in speech/non-speech discrimination accuracy demonstrate the effectiveness of the proposed VAD. It is shown that application of a statistical detection test leads to a better separation of the speech and noise distributions, thus allowing a more effective discrimination and a tradeoff between complexity and performance. The experimental analysis carried out on the AURORA 3 databases provides an extensive performance evaluation together with an exhaustive comparison to the standard VADs, such as ITU G.729, GSM AMR, and ETSI AFE, for distributed speech recognition (DSR) and other recently reported VADs

A Logistic Regression Mixture Model for Interval Mapping of Genetic Trait Loci Affecting Binary Phenotypes

Often in genetic research, presence or absence of a disease is affected by not only the trait locus genotypes but also some covariates. The finite logistic regression mixture models and the methods under the models are developed for detection of a binary trait locus (BTL) through an interval-mapping procedure. The maximum-likelihood estimates (MLEs) of the logistic regression parameters are asymptotically unbiased. The null asymptotic distributions of the likelihood-ratio test (LRT) statistics for detection of a BTL are found to be given by the supremum of a chi2-process. The limiting null distributions are free of the null model parameters and are determined explicitly through only four (backcross case) or nine (intercross case) independent standard normal random variables. Therefore a threshold for detecting a BTL in a flanking marker interval can be approximated easily by using a Monte Carlo method. It is pointed out that use of a threshold incorrectly determined by reading off a chi2-probability table can result in an excessive false BTL detection rate much more severely than many researchers might anticipate. Simulation results show that the BTL detection procedures based on the thresholds determined by the limiting distributions perform quite well when the sample sizes are moderately large.

TESTING FOR INDEPENDENCE AND LRT FOR VAD

In this paper we propose a simple method for Voice Activity Detection (VAD) in noisy environments based on periodogram of squares. The approach is based on a test for independence between a sequence of identically distributed random variables using the classical technique of Likelihood Ratio Test (LRT). This algorithm differs from many others in the way the decision rule is formulated (detection tests) and the domain used in this approach. Clear improvements in the speed of speech/non-speech discrimination accuracy demonstrate the effectiveness of the proposed VAD. It has been shown that application of statistical detection test leads to a better separation of the speech and noise distributions, thus allowing a more effective discrimination and a tradeoff between complexity and performance. The experimental analysis carried out on the AURORA databases and tasks provides an extensive performance evaluation together with an exhaustive comparison to the standard VADs such as ITU G.729, GSM AMR and ETSI AFE for distributed speech recognition (DSR), and other recently reported VADs based in statistical tests.

Multiple QTLs influencing triglyceride and HDL and total cholesterol levels identified in families with atherogenic dyslipidemia

We conducted a genome-wide scan using variance components linkage analysis to localize quantitative-trait loci (QTLs) influencing triglyceride (TG), high density lipoprotein-cholesterol (HDL-C), low density lipoprotein-cholesterol, and total cholesterol (TC) levels in 3,071 subjects from 459 families with atherogenic dyslipidemia. The most significant evidence for linkage to TG levels was found in a subset of Turkish families at 11q22 [logarithm of the odds ratio (LOD)=3.34] and at 17q12 (LOD=3.44). We performed sequential oligogenic linkage analysis to examine whether multiple QTLs jointly influence TG levels in the Turkish families. These analyses revealed loci at 20q13 that showed strong epistatic effects with 11q22 (conditional LOD=3.15) and at 7q36 that showed strong epistatic effects with 17q12 (conditional LOD=3.21). We also found linkage on the 8p21 region for TG in the entire group of families (LOD=3.08). For HDL-C levels, evidence of linkage was identified on chromosome 15 in the Turkish families (LOD=3.05) and on chromosome 5 in the entire group of families (LOD=2.83). Linkage to QTLs for TC was found at 8p23 in the entire group of families (LOD=4.05) and at 5q13 in a subset of Turkish and Mediterranean families (LOD=3.72). These QTLs provide important clues for the further investigation of genes responsible for these complex lipid phenotypes. These data also indicate that a large proportion of the variance of TG levels in the Turkish population is explained by the interaction of multiple genetic loci.

Statistical properties of limit of detection test statistics

There are a number of possible ways to define the instrumental limit of detection (LOD) figure of merit and in the present work we define four such sample test statistics and derive their probability density functions (PDFs). Although the derived PDFs were found to be irreducible integrals, they are easily evaluated via numerical integration and can be used to obtain expectation values, population precisions and confidence intervals. Monte Carlo simulation methods were used to prepare normalized histograms of one million LOD variates each, for homoscedastic linear calibration curve systems, and these were found to be in excellent agreement with the numerically obtained PDFs and associated statistics. The software used in all aspects of the present work is available for free, with full, commented source code, and is designed to facilitate exploration of calibration curve systems of immediate interest to the reader.

Moving object detection using adaptive subband decomposition and fractional lower-order statistics in video sequences

In this paper, a moving object detection method in video sequences is described. In the first step, the camera motion is eliminated using motion compensation. An adaptive subband decomposition structure is then used to analyze the motion compensated image. In the “low–high” and “high–low” subimages moving objects appear as outliers and they are detected using a statistical detection test based on fractional lower-order statistics. It turns out that the distribution of the subimage pixels is almost Gaussian in general. On the other hand, at the object boundaries the distribution of the pixels in the subimages deviates from Gaussianity due to the existence of outliers. By detecting the regions containing outliers the boundaries of the moving objects are estimated. Simulation examples are presented.

Adaptive resolution of mainlobe and sidelobe detections using model order determination

This paper presents the development and performance evaluation of a methodology for distinguishing between mainlobe and sidelobe detections that arise in adaptive radar systems operating in adverse environments. Various adaptive detection test statistics such as the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT) and adaptive coherence estimate (ACE), and combinations of these, have been previously analyzed with respect to their sidelobe rejection capabilities. In contrast to these methods, which are based on detecting a single target with known direction and Doppler, the present method uses model order determination techniques applied to the AMF or GLRT data observed over the range of unknown angle and Doppler parameters. The determination of model order, i.e., the number of signals present in the data, is made by using least-squares model fit error residuals and applying the Akaike information criterion. Comprehensive computer simulation results are presented which demonstrate substantial improvement in sidelobe rejection performance compared to previous methods.

The distribution of test statistics for outlier detection in heavy-tailed samples

We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of David et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our main result concerns the limiting distribution of n − 1 2 O n for the outlier statistic ▪ when the observations X i are the domain of attraction of an α-stable law. We present approximate critical values for O n for finite samples using response surface methods.

Robust adaptive threshold for control of false alarms

The thresholding of univariate test statistics for signal detection is considered for the case in which the pertinent probability distributions are not known but some training data is available. A distribution-free method for setting the threshold is derived. This threshold value maintains the average probability of false alarm (Pfa) at a fixed level and can be applied to noise/clutter data from any underlying probability distribution. Detection and false alarm performance are evaluated for the case in which the true, underlying univariate probability density is exponential for both noise and signal-plus-noise data. Performance is compared to the best adaptive detector, which is invariant to the exponential parameter governing the noise distribution, as well as the bounding case in which the exponential parameter is completely known. For this case, it is shown that the cost for a robust design is a small loss in the average probability of detection for a fixed average probability of false alarm. The study is of particular interest to radar and sonar.

Parametric adaptive matched filter for airborne radar applications

The parametric adaptive matched filter (PAMF) for space-time adaptive processing (STAP) is introduced via the matched filter (MF), multichannel linear prediction, and the multichannel LDU decomposition. Two alternative algorithmic implementations of the PAMF are discussed. Issues considered include sample training data size and constant false alarm rate (CFAR). Detection test statistics are estimated for airborne phased array radar measurements, and probability of detection is estimated using simulated phased array radar data for airborne surveillance radar scenarios. For large sample sizes, the PAMF performs close to the MF; performance degrades slightly for small sample sizes. In both sample size ranges, the PAMF is tolerant to targets present in the training set.

Statistical Tests for Detection of Misspecified Relationships by Use of Genome-Screen Data

Misspecified relationships can have serious consequences for linkage studies, resulting in either reduced power or false-positive evidence for linkage. If some individuals in the pedigree are untyped, then Mendelian errors may not be observed. Previous approaches to detection of misspecified relationships by use of genotype data were developed for sib and half-sib pairs. We extend the likelihood calculations of Göring and Ott and Boehnke and Cox to more-general relative pairs, for which identity-by-descent (IBD) status is no longer a Markov chain, and we propose a likelihood-ratio test. We also extend the identity-by-state (IBS)-based test of Ehm and Wagner to nonsib relative pairs. The likelihood-ratio test has high power, but its drawbacks include the need to construct and apply a separate Markov chain for each possible alternative relationship and the need for simulation to assess significance. The IBS-based test is simpler but has lower power. We propose two new test statistics-conditional expected IBD (EIBD) and adjusted IBS (AIBS)-designed to retain the simplicity of IBS while increasing power by taking into account chance sharing. In simulations, the power of EIBD is generally close to that of the likelihood-ratio test. The power of AIBS is higher than that of IBS, in all cases considered. We suggest a strategy of initial screening by use of EIBD and AIBS, followed by application of the likelihood-ratio test to only a subset of relative pairs, identified by use of EIBD and AIBS. We apply the methods to a Genetic Analysis Workshop 11 data set from the Collaborative Study on the Genetics of Alcoholism.

Comparison of the Performance of Fourteen Statistical Tests for Detection of Outlying Values in Geochemical Reference Material Databases

This work presents a comparison of relative efficiency of fourteen statistical tests to detect outliers in normally distributed samples. These tests include deviation/spread, Grubbs-type, Dixon-type, and high-order moment statistics. Performance for the statistical tests is evaluated using Geochemical Reference Material databases from the United States Geological Survey. Test efficiency is compared for the first application of statistics in version k = 1 and k = 2, as well as for tests in version k = 1 applied consecutively against block procedures in which k = 2, 3, or 4 values are evaluated at the same time. In both evaluations, the sensitivity of the statistical tests shows a general strong dependence on sample size. The best performance is observed for the block procedures compared to consecutive statistical tests affected by masking effects.

Detection of gross erros in data reconciliation by principal component analysis

AbstractStatistical testing provides a tool for engineers and operators to judge the valididty of process measurements and data reconciliation. Univeriate, maximum power and chisquare tests have been widely used for this purpose. Their performance, however, has not always been satisfactory. A new class of test statistics for detection and identification of gross errors is presented based on principal component analysis and is compared to the other statistics. It is shown that the new test is capable of detecting gross erros of smallmaginitudes and has substantial power to correctly identify the variables in error, when the other tests fail.

On Model Order Determination of Complex Exponential Signals

We present an algorithm for model order determination and corresponding maximum likelihood parameter estimation for complex exponential signal modeling. The algorithm exploits initial nonparametric frequency location estimates to significantly reduce the search space for the correct model order and parameter estimates. An FFT is used to obtain initial frequency region estimates. An initial overdetermined model order and initial frequency estimates are obtained using the CRB resolution limit and the FFT peaks. After iterative minimization, a post-processing step eliminates the extraneous sinusoidal modes using CRB resolution limits arii statistical detection tests. Because the algorithm searches on only a limited set of model orders and parameter regions, it is computationally tractable even for large data lengths and model orders. Simulations are provided to illustrate the performance of the proposed algorithm.

Simple test statistics for major gene detection: a numerical comparison

We compare 22 simple tests for the detection of major gene segregation in livestock populations. These tests belong to two groups: methods based on the comparison of within-family distribution and methods based on the comparison of parents' and offspring performances. The power of the 22 tests and the robustness of the two more powerful of these 22 are evaluated by simulation. Thirteen types of major loci, differing in the within-genotype means, variances or alleles frequencies, are studied. Thirty hierarchically balanced populations defined by the number of sire families (5-20), dams per sire (1-20) and progenies per dam (1-20) are simulated. The quantiles are estimated from 2000 samples, the power from 1000 samples and the robustness from 100 samples. The more powerful tests are the within family-variance heterogenity test (Bartlett test) and the within-family mean-variance regression (Fain 1978). Their robustness may be very low, in particular when the trait distribution is skewed.

Least squares collocation and statistical testing

The authors address the issue of statistical testing in least squares collocation (LSC) in two stages. The first stage concerns the extension and focusing of theLSC equations to the task of statistical testing. The second stage deals with statistical testing titself and is introduced in the second portion of the paper. The paper commences with an overview of the development ofLSC and its relationship to least squares adjustment (LSA). Expressions for the various random variables and their corresponding covariance matrices are derived and in some instances are gleaned from the literature for the following quantities: (i) corrections to the unknown parameters with a priori covariance information; (ii) estimated signal at both the observation and computation points; and (iii) the noise at the observation points. Some of the needed covariance matrices are either obscurely hidden in the literature or not available at all, but, nevertheless are given in the paper. Also given are expressions for the estimated variance factor which forms the basis of various statistical tests. The paper closes with an overview and enumeration of possible statistical tests for detection of outliers in the observations.