On testing for serial correlation of unknown form using wavelet thresholding

Omnibus procedures for testing serial correlation are developed, using spectral density estimation and wavelet shrinkage. The asymptotic distributions of the wavelet coefficients under the null hypothesis of no serial correlation are derived. Under some general conditions on the wavelet basis, the wavelet coefficients asymptotically follow a normal distribution. Furthermore, they are asymptotically uncorrelated. Adopting a spectral approach and using results on wavelet shrinkage, new one-sided test statistics are proposed. As a spatially adaptive estimation method, wavelets can effectively detect fine features in the spectral density, such as sharp peaks and high frequency alternations. Using an appropriate thresholding parameter, shrinkage rules are applied to the empirical wavelet coefficients, resulting in a non-linear wavelet-based spectral density estimator. Consequently, the advocated approach avoids the need to select the finest scale J, since the noise in the wavelet coefficients is naturally suppressed. Simple data-dependent threshold parameters are also considered. In general, the convergence of the spectral test statistics toward their respective asymptotic distributions appears to be relatively slow. In view of that, Monte Carlo methods are investigated. In a small simulation study, several spectral test statistics are compared, with respect to level and power, including versions of these test statistics using Monte Carlo simulations.     

Decision theoretic approach to real-time robust identification

A decision-theoretic approach to the estimation of unknown parameters from a linear discrete-time dynamic measurement model in the presence of disturbance uncertainty is considered. The unknown disturbance statistics are characterized by a certain class of distributions to which the real disturbance distribution is confined. Using game theory and the asymptotic estimation error covariance matrix as the criteria of how good an estimator is, the stochastic gradient-type algorithm is shown to be optimal in the min-max sense. Since the optimal solution is not tractable in practice, several suboptimal procedures are derived on the basis of suitable approximations. The convergence of the derived algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the algorithms.     

A parallel decision tree-based method for user authentication based on keystroke patterns

We propose a Monte Carlo approach to attain sufficient training data, a splitting method to improve effectiveness, and a system composed of parallel decision trees (DTs) to authenticate users based on keystroke patterns. For each user, approximately 19 times as much simulated data was generated to complement the 387 vectors of raw data. The training set, including raw and simulated data, is split into four subsets. For each subset, wavelet transforms are performed to obtain a total of eight training subsets for each user. Eight DTs are thus trained using the eight subsets. A parallel DT is constructed for each user, which contains all eight DTs with a criterion for its output that it authenticates the user if at least three DTs do so; otherwise it rejects the user. Training and testing data were collected from 43 users who typed the exact same string of length 37 nine consecutive times to provide data for training purposes. The users typed the same string at various times over a period from November through December 2002 to provide test data. The average false reject rate was 9.62% and the average false accept rate was 0.88%.     

An event-triggered approach to state estimation with multiple point- and set-valued measurements

In this work, we consider state estimation based on the information from multiple sensors that provide their measurement updates according to separate event-triggering conditions. An optimal sensor fusion problem based on the hybrid measurement information (namely, point- and set-valued measurements) is formulated and explored. We show that under a commonly-accepted Gaussian assumption, the optimal estimator depends on the conditional mean and covariance of the measurement innovations, which applies to general event-triggering schemes. For the case that each channel of the sensors has its own event-triggering condition, closed-form representations are derived for the optimal estimate and the corresponding error covariance matrix, and it is proved that the exploration of the set-valued information provided by the event-triggering sets guarantees the improvement of estimation performance. The effectiveness of the proposed event-based estimator is demonstrated by extensive Monte Carlo simulation experiments for different categories of systems and comparative simulation with the classical Kalman filter.     

Hierarchical multiresolution approaches for dense point-level breast cancer treatment data

The analysis of point-level (geostatistical) data has historically been plagued by computational difficulties, owing to the high dimension of the nondiagonal spatial covariance matrices that need to be inverted. This problem is greatly compounded in hierarchical Bayesian settings, since these inversions need to take place at every iteration of the associated Markov chain Monte Carlo (MCMC) algorithm. This paper offers an approach for modeling the spatial correlation at two separate scales. This reduces the computational problem to a collection of lower-dimensional inversions that remain feasible within the MCMC framework. The approach yields full posterior inference for the model parameters of interest, as well as the fitted spatial response surface itself. We illustrate the importance and applicability of our methods using a collection of dense point-referenced breast cancer data collected over the mostly rural northern part of the state of Minnesota. Substantively, we wish to discover whether women who live more than a 60-mile drive from the nearest radiation treatment facility tend to opt for mastectomy over breast conserving surgery (BCS, or “lumpectomy”), which is less disfiguring but requires 6 weeks of follow-up radiation therapy. Our hierarchical multiresolution approach resolves this question while still properly accounting for all sources of spatial association in the data.     

点云模型的多分辨率简化算法

为了有效地多分辨率简化点云模型,首先,采用均匀栅格法建立点云模型的拓扑关系,计算每个数据点的k邻域;然后,通过建立点云模型中数据点的协方差矩阵求得这些点的法向量,并且进行法向重定向,使所有法向量的方向都指向点云模型的外部;最后,通过衡量数据点对Laplace-Beltrami算子特征值频谱的影响,得到与数据点k邻域及其法向量相关的量化该点重要性的度量公式,随后调节控制因子的取值,实现点云模型的多分辨率简化。实验结果表明,该算法具有简化率高、保留点云模型的微小细节特征信息、简化速度快、稳定性强的特点。     

Applying wavelets transform and support vector machine for copper clad laminate defects classification

In this paper, we present a multi-resolution approach for the inspection local defects embedded in homogeneous copper clad laminate (CCL) surfaces. The proposed method does not rely on the extraction of local textural features in a spatial basis. It is based mainly on the wavelet transform and inverse wavelet transform on the smooth subimage and detail subimages by properly selecting the adequate decomposition levels. The restored image will remove regular, repetitive texture patterns and enhance only local anomalies. Based on these local anomalies, feature extraction methods can then be used to discriminate between the defective regions and homogeneous regions in the restored image. Real samples with five classes of defects have been classified using this novel multi-classifier, namely, support vector machine. The experimental results show the efficacy of the proposed method.     

Multi-stage Monte Carlo and non-linear test problems

The multi-stage Monte Carlo approach is similar to the regular Monte Carlo or random search approach that is frequently used on difficult multivariate problems. However, with multi-stage, the regular Monte Carlo search is considered to be stage one. This is followed by several more stages in an ever narrowing and re-positioning region following the best answers so far, hopefully on a trail to the optimal or a close approximation. The element of risk is certainly present in multi-stage Monte Carlo. Therefore to compare it with other algorithms for effectiveness, six test problems from the literature are selected and ‘ solved ’ with multistage. The results with multi-stage and other approaches are similar for the first five problems. However, in the last test problem, multi-stage finds many lower values than the stated ‘ minimum ’ and fourteen of them are presented here along with computer programs and a discussion of multi-stage Monte Carlo     

On wavelet-based testing for serial correlation of unknown form using Fan’s adaptive Neyman method

Test procedures for serial correlation of unknown form with wavelet methods are investigated. A new test statistic is motivated using a canonical multivariate normal hypothesis testing model. It relies on empirical wavelet coefficients of a wavelet-based spectral density estimator. The choice of the Haar wavelet function is advocated, since evidence demonstrates that the choice of the wavelet function is not critical. Under the null hypothesis of no serial correlation, the asymptotic distribution of a vector of empirical wavelet coefficients is derived, which is asymptotically a multivariate normal distribution. A test statistic is proposed based on that asymptotic result, which presents the serious advantage to be completely data-driven or adaptive, avoiding the selection of any smoothing parameters. Furthermore, under a suitable class of fixed alternatives, the wavelet-based method is consistent against serial correlation of unknown form. The test statistic is expected to exhibit good power properties when the true spectral density displays significant spatial inhomogeneity, such as seasonal or business cycle periodicities. However, the convergence of the test statistic towards its asymptotic distribution is relatively slow. Thus, Monte Carlo methods based on random samples are suggested to determine the corresponding critical values. In a simulation study, the new methodology is compared with several test statistics, with respect to their exact levels and powers. The robustness properties of the spectral methods based on Monte Carlo critical values are also investigated empirically, when the error terms are weak white noises.     

Vibration modelling with fast Gaussian wavelet algorithm

Vibration signals are considered as nonstationary signals with transients. Conventional harmonic Fourier analysis finds it difficult to model the vibration signals. In this paper, a novel approach using the global Fourier transforms and local wavelet analysis is presented for vibration analysis and modelling. Time–frequency wavelet analysis has been proven a useful tool for the detection of vibration transients. However, current algorithms with discrete or continuous wavelet transforms for vibration analysis are either low resolution of features or very time consuming. We developed a fast Gaussian wavelet algorithm with very narrow band-pass filtering technique. The time–frequency maps with high frequency resolution enable us to observe the evolution in time of significant frequencies identified by global Fourier analysis, so that the transients and the regular signals can be distinguished. These regular significant frequencies are selected to be the basis of vibration modelling. The coefficients of the model are identified by a least-squares algorithm, which ensures that the error is minimised. To demonstrate this approach a machine spindle vibration signal is analysed, and the main features of the vibration signal are extracted, which are useful for system monitoring and further analysis.