Change-point detection of mean vector or covariance matrix shifts using multivariate individual observations

A preliminary control chart is given for detecting a shift in the mean vector, the covariance matrix, or both, when multivariate individual observations are available. The data are partitioned after each observation in turn, and the likelihood ratio statistic for a shift is calculated. The control chart is obtained by plotting these statistics after dividing by the expected value under the condition of no shift. This adjustment is done in order to reduce the variation in sensitivity with the location of any shift. Using generalized inverses allows the detection of a shift after as few as two of the observations, or with as few as two remaining observations, or at any intermediate point. Multiple shifts often can be detected by recursive application of the method. When a shift is detected, the plotted statistic is divided into a part due to the shift in the sample mean vector and another part attributable to a shift in the sample covariance matrix. This is done for diagnostic purposes. Using simulation, approximate values are given for the expected values of the plotted statistics and an upper control limit.     

Test on the linear combinations of mean vectors in high-dimensional data

In this study, we propose a procedure for simultaneous testing \(l (l\ge 1)\) linear relations on \(k(k\ge 2)\) high-dimensional mean vectors with heterogeneous covariance matrices, which extends the result derived by Nishiyama et al. (J Stat Plan Inference 143(11):1898–1911, 2013) and does not need the normality assumption. The newly proposed test statistic is motivated by Bai and Saranadasa (Statistica Sinica 6(2):311–329, 1996) and Chen and Qin (Ann Stat 38(2):808–835, 2010). As a special case, our result could be applied to multivariate analysis of variance, that is, testing the equality of k high-dimensional mean vectors.     

Fuzzy simultaneous measurement of two polarization vector components

The advent of quantum computers threatens the security of conventional encryption schemes (e.g., those based upon the excessive amount of computational time that might be required to guess your password). Quantum encryption is intended to restore the security by basing it instead upon the impossibility of the simultaneous measurement of two noncommuting operators. I derive a measurement associated with the angular momentum lowering operator, which describes a simultaneous (yet realizable) measurement of two noncommuting spin-vector components. Correlations between two such detectors are also discussed and compared with the conventional Stern-Gerlach results.     

Assessing mean and median filters in multiple testing for large-scale imaging data

A new multiple testing procedure, called the FDR _L procedure, was proposed by Zhang et al. (Ann Stat 39:613–642, 2011) for detecting the presence of spatial signals for large-scale 2D and 3D imaging data. In contrast to the conventional multiple testing procedure, the FDR _L procedure substitutes each p-value by a locally aggregated median filter of p-values. This paper examines the performance of another commonly used filter, mean filter, in the FDR _L procedure. It is demonstrated that when the p-values are independent and uniformly distributed under the true null hypotheses, (i) in view of estimating the resulting false discovery rate, the mean filter better alleviates the “lack of identification phenomenon” of the FDR _L procedure than the median filter; (ii) in view of signal detection, the median filter enjoys the “edge-preserving property” and lends support to its better performance in detecting sparse signals than the mean filter.     

A biplot method for multivariate normal populations with unequal covariance matrices

Some previous ideas about non-linear biplots to achieve a joint representation of multivariate normal populations and any parametric function without assumptions about the covariance matrices are extended. Usual restrictions on the covariance matrices (such as homogeneity) are avoided. Variables are represented as curves corresponding to the directions of maximum means variation. To demonstrate the versatility of the method, the representation of variances and covariances as an example of further possible interesting parametric functions have been developed. This method is illustrated with two different data sets, and these results are compared with those obtained using two other distances for the normal multivariate case: the Mahalanobis distance (assuming a common covariance matrix for all populations) and Rao’s distance, assuming a common eigenvector structure for all the covariance matrices. This work is supported by DGICYT grant (Spain), BFM2000-0801 and also 1999SGR00059.     

Occlusion invariant face recognition using mean based weight matrix and support vector machine

In this paper, a novel occlusion invariant face recognition algorithm based on Mean based weight matrix (MBWM) technique is proposed. The proposed algorithm is composed of two phases—the occlusion detection phase and the MBWM based face recognition phase. A feature based approach is used to effectively detect partial occlusions for a given input face image. The input face image is first divided into a finite number of disjointed local patches, and features are extracted for each patch, and the occlusion present is detected. Features obtained from the corresponding occlusion-free patches of training images are used for face image recognition. The SVM classifier is used for occlusion detection for each patch. In the recognition phase, the MBWM bases of occlusion-free image patches are used for face recognition. Euclidean nearest neighbour rule is applied for the matching. GTAV face database that includes many occluded face images by sunglasses and hand are used for the experiment. The experimental results demonstrate that the proposed local patch-based occlusion detection technique works well and the MBWM based method shows superior performance to other conventional approaches.     

A low-complexity adaptive beamformer for ultrasound imaging using structured covariance matrix

In recent years, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in simultaneous improvement in imaging resolution and contrast. These improvements have been achieved at the expense of higher computational complexity, with respect to the conventional non-adaptive delay-and-sum (DAS) beamformer, in which computational complexity is proportional to the number of elements, O(M). The computational overhead results from the covariance matrix inversion needed for computation of the adaptive weights, the complexity of which is cubic with the subarray size, O(L(3)). This is a computationally intensive procedure, which makes the implementation of adaptive beamformers less attractive in spite of their advantages. Considering that, in medical ultrasound applications, most of the energy is scattered from angles close to the steering angle, assuming spatial stationarity is a good approximation, allowing us to assume the Toeplitz structure for the estimated covariance matrix. Based on this idea, in this paper, we have applied the Toeplitz structure to the spatially smoothed covariance matrix by averaging the entries along all subdiagonals. Because the inverse of the resulting Toeplitz covariance matrix can be computed in O(L(2)) operations, this technique results in a greatly reduced computational complexity. By using simulated and experimental RF data-point targets as well as cyst phantoms-we show that the proposed low-complexity adaptive beamformer significantly outperforms the DAS and its performance is comparable to that of the minimum variance beamformer, with reduced computational complexity.     

Optimal designs for some stochastic processes whose covariance is a function of the mean

This paper considers optimal experimental designs for models with correlated observations through a covariance function depending on the magnitude of the responses. This suggests the use of stochastic processes whose covariance structure is a function of the mean. Covariance functions must be positive definite. This fact is nontrivial in this context and constitutes one of the challenges of the present paper. We show that there exists a huge class of functions that, composed with the mean of the process in some way, preserves positive definiteness and can be used for the purposes of modeling and computing optimal designs in more realistic situations. We offer some examples for an easy construction of such covariances and then study the problem of locally D-optimal designs through an illustrative example as well as a real radiation retention model in the human body.     

Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions

In this paper, the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the use of a suitable block-diagonalization of the hypothesis matrix, it is possible to obtain a decomposition of the main hypothesis into two sub-hypotheses. Using this decomposition, it is then possible to obtain the likelihood ratio test statistic as well as its exact moments in a much simpler way. The exact distribution of the likelihood ratio test statistic is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes and the approach followed allows us to extend its validity to situations where the population distributions are elliptically contoured. A real-data example is presented and a simulation study is also conducted.     

基于高维随机矩阵特征值之差的滚动轴承状态异常检测算法

针对滚动轴承异常检测准确性差、精度低及数据维度灾难造成检测困难等问题,提出一种基于随机矩阵特征值之差指标的滚动轴承状态异常检测算法.运用平移时间窗对不同时刻的轴承信息锁定,并通过分段、随机化、扩增和维度重构等方法构造出高维随机特征矩阵;利用随机矩阵理论对高维数据良好的处理能力,给出了滚动轴承特征值之差指标的构造方法及动...     

A new data reduction scheme for the fragmentation testing of polymer composites

A new reduction scheme of fragmentation data for the derivation of interfacial mechanical properties in polymer composites is proposed. The scheme is based on a theoretical model that accounts for elastic load transfer and friction at the interface, as well as for the statistical nature of fibre strength. Interface mechanical behaviour is characterized by two independent parameters, namely the interface bond strength and interface frictional resistance. Derived values of the two interface properties are computed, such that they yield the best possible agreement between experimental and theoretical results for the evolution of fibre fragment aspect ratio and debonding ratio as a function of applied strain. Results are reported for carbon fibres embedded in an epoxy matrix, with different levels of fibre surface treatment.     

Electrochemical immunosensors for the simultaneous detection of two tumor markers

The microfabrication of electrochemical immunosensors for the simultaneous detection of two protein analytes is described. The sensors consisted of two iridium oxide electrodes (1-mm diameter) patterned on a glass substrate. Capture antibodies were immobilized on the porous iridium oxide electrodes by covalent attachment using (3-aminopropyl)triethoxysilane and glutaraldehyde. The spatial separation of the electrodes (2.5 mm) enabled simultaneous electrochemical immunoassays to be conducted without cross-talk between the electrodes. Proteins were measured using electrochemical ELISA, and detection was achieved by electrochemically oxidizing alkaline phosphatase-generated hydroquinone. Sensors for the simultaneous detection of goat IgG and mouse IgG, and for the tumor markers CEA and AFP, were developed. The sensors had detection limits of 1, 2, 1.2, and 1 ng/mL for goat IgG, mouse IgG, CEA, and AFP, respectively.     

A novel technique for testing pulsed RF MSK data communicationdevices

The paper discusses a novel technique for testing Minimum Shift Keying (MSK) impulsive radio-frequency (RF) signal transmitters. This technique utilizes the acquired samples of a single shot signal to determine the trajectories of the frequency and phase, by means of a time domain analysis. The theoretical foundation of this technique is given, discussing the application to a pulsed RF MSK signal modulated with a bit-rate of 5 Mb/s, having a total duration of 6 μs and whose central frequency falls in the band going from 960 to 1206 MHz. The performance of the measurement algorithm (robustness, influence of the digitizer resolution, time base jitter, and noise on the precision of the measurement) has been evaluated by means of simulation tests. The method has been experimentally verified for the characterization of identification friend or foe (IFF) time division multiple access (TDMA) actual devices     

Bias of mean value and mean square value measurements based onquantized data

This paper investigates the imperfect fulfilment of the validity conditions of the noise model quantization. The general expressions of the deviations of the moments from Sheppard's corrections are derived. Approximate upper and lower bounds of the bias are given for the measurement of first- and second-order moments of sinusoidal, uniformly distributed, and Gaussian signals. It is shown that because of the uncontrollable mean value at the input of the ADC (offset, drift), the worst-case values have to be investigated; it is illustrated how a simple-form envelope function of the errors can be used as an upper bound. Since the worst-case relative positions of the signal and the quantization characteristics are taken into account, the results are valid for both midtread and midrise quantizers, while in the literature results are given for a selected quantizer type only     

A simultaneous confidence corridor for varying coefficient regression with sparse functional data

We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time-independent covariates with coefficients as functions of time-dependent covariates. Based on spline smoothing, we propose data-driven simultaneous confidence corridors for the coefficient functions with asymptotically correct confidence level. Such confidence corridors are useful benchmarks for statistical inference on the global shapes of coefficient functions under any hypotheses. Simulation experiments corroborate with the theoretical results. An example in CD4/HIV study is used to illustrate how inference is made with computable p values on the effects of smoking, pre-infection CD4 cell percentage and age on the CD4 cell percentage of HIV infected patients under treatment.     

A model for the transverse strain response of unidirectional ceramic matrix composites during tensile testing

A comprehensive micromechanical model relating the longitudinal stress and transverse strain of unidirectional fibre toughened ceramic matrix composites (CMCs) is presented. The model uses different cylindrical unit-cells to describe the composite throughout a tensile test and considers all relevant damage mechanisms. The proposed model takes into account the Poisson contraction of fibre and matrix, the relief of thermal residual stresses upon damage development, and the build-up of compressive radial stresses at the interface due to mismatch between fibre and matrix after debonding and sliding. Thus the modelled transverse strain response depends on a wide range of microstructural and micromechanical parameters. The approach is checked by comparing the experimentally observed and simulated response of a unidirectional SiC/CAS composite of which all constituent properties were determined experimentally. The agreement between experiment and theory is excellent.