A Robust Surveillance Scheme for Stochastically Ordered Alternatives

Introduction:The score statisticZ(θ)and the maximin efficient robust test statisticZMERTare commonly used in genetic association study, but according to our knowledge there is no formal comparison of them.Methods:In this report, we compare the asymptotic behavior ofZ(θ)andZMERT, by computing their Asymptotic Relative Efficiencies (AREs) relative to each other. Four commonly used ARE measures, the Pitman ARE, Chernoff ARE, Hodges-Lehmann ARE and the Bahadur ARE are considered. Some modifications of these methods are made to simplify the computations. We found that the Chernoff, Hodges-Lehmann and Bahadur AREs are suitable for our setting.Results and Conclusion:Based on our study, the efficiencies of the two test statistic varies for different criterion used, and for different parameter values under the same criterion, so each test has its advantages and dis-advantages according to the criterion used and the parameters involved, which are described in the context. Numerical examples are given to illustrate the use of the two statistics in genetic association study.

The development of tools for automated analysis of data collected for mine countermeasures (MCM) search, classify and map (SCM) has predominantly focused on automated target recognition for individual mines. As MCM target detection becomes more automated, detecting spatial patterns in the positioning of mines should follow. Natural restrictions on mine deployment such as depth and bottom contour as well as mine deployment methodology and protocol effectively create mine line patterns that are typical to coastal areas. We have developed a mine line detection algorithm that uses nonparametric spatial analysis to identify mine-like contacts (MLCs) that fit into mine line patterns dictated by standard mine laying protocol in coastal regions. In general, a set of MLCs reported from a mine detection sensor will consist of both actual mines and false alarms; the algorithm classifies every MLC in this set into one of three classes: fixed — the MLCψfits into a mine line pattern with fixed mine spacing; random -the MLCψfits into a mine line pattern with random mine spacing; or false alarm-ψ-the MLCψdoes not fit into a mine line pattern and is subsequently not considered a mine. The latest version of the algorithm utilizes nonparametric techniques and requires no knowledge of either the detection sensor's probability of detection (P d ) or probability of false alarm (P fa ). A nonparametric anomaly detector first identifies regions with unusually high MLC density for more detailed analysis. Suspected regions are subsequently analyzed for unusually regular patterns of MLCs. The probabilities that the observed target densities and target patterns could occur simply by chance are estimated by comparison with results from nearby areas using basic information about mine deployment. To ensure that a mine line's full extent is captured, the algorithm attempts to grow a line after it is detected. And a more detailed probability analysis distinguishes random mine lines from fixed-spaced mine lines. Extensive Matlab simulations characterize the algorithm's performance across a wide range of operating environments and simulated minefield configurations. In total, ten replications each of 1,367 different configurations have been evaluated. These configurations include three different water depths (10 ft., 6 ft. and 200 ft.), six false notional alarm rates (1, 2,5,10,15 and 20 false alarms per sq. NM), three false alarm distributions (uniform, sloped, and striped), three sensor probabilities of detections (0.4, 0.6 and 0.9), three target confidence scores (0.6,0.8 and 1.0) and four false alarm confidence scores (0.5, 0.6, 0.8 and 1.0). The range of simulation parameters was selected in part as an attempt to push the algorithm past its acceptable performance limits. However, the algorithm performed remarkably well even under the worst conditions. For MLC sets with false alarm rates as high as 20 per square nautical mile, the algorithm correctly classifies over 98% of the MLCs as mines and detects 97% of the mine lines. Furthermore, it reduces the false alarm rate from 20 to 0.2 per square nautical mile with a false mine line rate of 0.14 false lines per square nautical mile. The algorithm achieves even lower false alarm rates when the initial false alarm rate is less than 20. The automated mine line detection discovers many obscure lines that are virtually undetectable to the naked eye.

The random-threshold decision rule, which is an equalizer-rule in terms of probability-of-error for symmetrically distributed bounded-amplitude nonstationary noise, is compared with the sign detector and linear detector for bounded-amplitude noise via asymptotic relative efficiency (ARE). Explicit ARE expressions are derived for these detectors. The result shows that the random-threshold decision rule can be as effective as, or better than the sign detector and as effective as the linear detector, in terms of ARE, for some bounded-amplitude noise cases.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bradley (1977) has shown that the mixed normal family of distributions is an important population model in many behavioural science research contexts. Researchers engaged in studies of the type discussed by Bradley (1977) might well wonder about the relative appropriateness of various statistical techniques that might be employed in data analyses. For example, in the case of a two‐sample test for shift, should one use the parametric t test or some non‐parametric counterpart such as Wilcoxon's rank‐sum test? The primary purpose of this paper is to examine some of the characteristics of the asymptotic relative efficiency (ARE) of the Wilcoxon rank‐sum test relative to the independent means t test under various mixtures of two normal distributions. Pursuant to this goal, the equation for finding the ARE of the two tests under various mixtures of two distributions is developed, the equation is applied to various example situations, and certain limiting values of the equation are noted. As a result, it is concluded that the Wilcoxon statistic tends to have large ARE advantages over the t test in research contexts similar to those considered by Bradley (1977). It is concluded, therefore, that the Wilcoxon test is the more appropriate statistic for the research situations considered.

Two methods are considered for comparing the asymptotic efficiencies of robust detectors in the problem of detecting coherent signals in additive noise. The first of these methods considers the relative detector sample sizes for a fixed value of the detector power, while the second method considers the relative detector sample sizes for a fixed value of the local detector power, as measured by the local values of the slopes or curvatures of the detector power functions. These measures of efficiency are variations of the asymptotic relative efficiencies (AREs) of Pitman and Blomqvist, respectively, adapted to the robust detection problem. These two approaches are used to compare the performance of robust nonlinear correlators to that of robust M-detectors in both one-sided and two-sided detection problems, under an epsilon -contaminated mixture model for uncertainty in the noise statistics. Both measures of ARE, fixed-power and fixed-local-power, indicate that the robust nonlinear correlator outperforms the robust M-detector for this type of model. However, the fixed-local-power ARE is shown to be more useful in measuring the degree to which the robust nonlinear correlator is more efficient. >

Abstract.Two frequency domain tests of fit for autoregressive moving average time series models are considered. The tests are slight generalizations of those introduced by Cameron (1978) and Milhøj (1981). It is shown that according to asymptotic relative efficiency the test by Milhøj outperforms the test by Cameron. However, if asymptotic relative efficiency is used as a standard of comparison, both of these tests are extremely poor as compared to the well‐known time domain test of Box and Pierce (1970), for the asymptotic relative efficiency of the frequency domain tests as compared to the Box‐Pierce test is zero.

The relationship between distance measures and asymptotic relative efficiency is discussed. It is shown that the ratio of the Bhattacharyya distance or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> divergences of two test statistics is equivalent to asymptotic relative efficiency. Two-input systems are discussed as examples, and the performances of the polarity coincidence correlator (PCC) and the correlator are discussed in terms of the distance measures of reduced data.

It has been reported that using unlabeled data together with labeled data to construct a discriminant function works successfully in practice. However, theoretical studies have implied that unlabeled data can sometimes adversely affect the performance of discriminant functions. Therefore, it is important to know what situations call for the use of unlabeled data. In this paper, asymptotic relative efficiency is presented as the measure for comparing analyses with and without unlabeled data under the heteroscedastic normality assumption. The linear discriminant function maximizing the area under the receiver operating characteristic curve is considered. Asymptotic relative efficiency is evaluated to investigate when and how unlabeled data contribute to improving discriminant performance under several conditions. The results show that asymptotic relative efficiency depends mainly on the heteroscedasticity of the covariance matrices and the stochastic structure of observing the labels of the cases.

In order to cure the crux of low accuracy of traditional PG transient stability prediction (PGTSP) methods, a PGTSP method based on improved Convolutional Neural Network(CNN) is proposed under big data. First, the theoretical framework of state assessment of Power Grid (PG) is constructed according to analysis of historical big data in PG. Based on data source, big data classification, big data cleaning and processing, PG status assessment is realized. Then, by selecting a variety of PG traits as the multi-input trait space of CNN model. By using multi-channel idea to independently analyze and fuse various features, a multi-channel multi-trait fusion CNN(MC-MF-FCNN) model is constructed and the accurate prediction of grid transient stability is achieved. Finally, the root mean square error(RMSE), false alarm rate, false alarm rate and accuracy rate of the proposed algorithm and the other two algorithms under the same conditions are compared and analyzed through simulation experiments. The results show that RMSE, false alarm rate and miss alarm rate of the proposed algorithm are the smallest and the accuracy is the highest. The highest accuracy rate within 9 cycles after the fault is 96.83 %, and the minimum RMSE, missed alarm rate and false alarm rate are 0.196, 2.15% and 1.32%, respectively. The performance is better than the other two comparison algorithms.

This paper treats the problem of detecting a signal of known form in the presence of additive noise whose distribution function may not be known. Two detection schemes are considered, one for a signal which is known exactly and one for a signal with unknown phase. Using the criterion of asymptotic relative efficiency (ARE), the performance of each detector is compared with that of the corresponding detector which is optimum for Gaussian noise. It is shown that for detecting a known signal, the ARE of the nonparametric detector relative to the correlation detector is equal to one if the noise is Gaussian, and is strictly greater than one for any continuous non-Gaussian noise distribution. An identical result holds for the ARE of the nonparametric detector for a signal with unknown phase relative to the standard envelope detector.

Pseudo maximum likelihood estimation (PML) for the Dirich-let-multinomial distribution is proposed and examined in this pa-per. The procedure is compared to that based on moments (MM) for its asymptotic relative efficiency (ARE) relative to the maximum likelihood estimate (ML). It is found that PML, requiring much less computational effort than ML and possessing considerably higher ARE than MM, constitutes a good compromise between ML and MM. PML is also found to have very high ARE when an estimate for the scale parameter in the Dirichlet-multinomial distribution is all that is needed.

The paper presents the calculation method of an asymptotic relative efficiency of the least absolute deviations estimate with respect to the maximum likelihood estimate for the parameter presented in the first order autoregressive model with a stochastic coefficient. The method is based on approximation of its asymptotic relative efficiency by Taylor series. The paper considers an example of the asymptotic relative efficiency calculation for the case where diffusion of the innovation process has an approximate Gaussian distribution (Tukey distribution). It is found out that if the assumptions of the Gaussian process are performed approximately, the maximum likelihood estimate is more efficient than the least absolute deviation estimate

When old/new recognition memory is tested with equal numbers of studied and nonstudied items and no rewards or instructions that favour one response over the other, there is no obvious reason for response bias. In line with this, Canadian undergraduates have shown, on average, a neutral response bias when we tested them on recognition of common English words. By contrast, most subjects we have tested on recognition of richly detailed images have shown a conservative bias: they more often erred by missing a studied image than by judging a nonstudied image as studied. Here, in an effort to better understand these materials-based bias effects (MBBEs), we examined changes in hit and false alarm (FA) rates (and in sensitivity and bias) from the first to fourth quartile of a recognition memory test in eight experiments in which undergraduates studied words and/or images of paintings. Response bias for images tended to increase across quartiles, whereas bias for words showed no consistent pattern across quartiles. This pattern could be described as an increase in the MBBE over the course of the test, but the underlying patterns for hits and FAs are not easily reconciled with this interpretation. Hit rates decreased over the course of the test for both materials types, with that decline tending to be steeper for images than words. For words, FA rates tended to increase across quartiles, whereas for paintings FA rates did not increase across quartiles. We discuss implications of these findings for theoretical accounts of the MBBE.

We developed and tested the Bayesian multiple comparison correction method for Bayesian voxelwise second-level fMRI analysis with R. The performance of the developed method was tested with simulation and real image datasets. First, we compared false alarm and hit rates, which were used as proxies for selectivity and sensitivity, respectively, between Bayesian and classical inference methods. For the comparison, we created simulated images, added noise to the created images, and analyzed the noise-added images while applying Bayesian and classical multiple comparison correction methods. Second, we analyzed five real image datasets to examine how our Bayesian method worked in realistic settings. When the performance assessment was conducted, the Bayesian correction method demonstrated good sensitivity (hit rate ≥ 75%) and acceptable selectivity (false alarm rate < 10%) when N ≥ 8. Furthermore, the Bayesian correction method showed better sensitivity compared with the classical correction method while maintaining the aforementioned acceptable selectivity.

Rockburst is a serious hazard in underground engineering, and accurate prediction of rockburst risk is challenging. To construct an intelligent prediction model of rockburst risk with interpretability and high accuracy, three binary scorecards predicting different risk levels of rockburst were constructed using ChiMerge, evidence weight theory, and the logistic regression algorithm. An intelligent rockburst prediction model based on scorecard methodology (IRPSC) was obtained by integrating the three scorecards. The effects of hazard sample category weights on the missed alarm rate, false alarm rate, and accuracy of the IRPSC were analyzed. Results show that the accuracy, false alarm rate, and missed alarm rate of the IRPSC for rockburst prediction in riverside hydropower stations are 75%, 12.5%, and 12.5%, respectively. Setting higher hazard sample category weights can reduce the missed alarm rate of IRPSC, but it will lead to a higher false alarm rate. The IRPSC can adaptively adjust the threshold and weight value of the indicator and convert the abstract machine learning model into a tabular form, which overcomes the commonly black box problems of machine learning model, as well as is of great significance to the application of machine learning in rockburst risk prediction.