FREQUENCY DOMAIN TESTS OF MULTIVARIATE GAUSSIANITY AND LINEARITY

A stationary multivariate time series { X _t } is defined as linear if it can be written in the form X _t = ∑^∞ _{j =−∞} A _j e _{t − j} where A _j are square matrices and e _t are independent and identically distributed random vectors. If the e _t } are normally distributed, then { X _t is a multivariate Gaussian linear process. This paper is concerned with the testing of departures of a vector stationary process from multivariate Gaussianity and linearity using the bispectral approach. First the definition and properties of cumulants of random matrices are used to obtain the expressions for the higher-order cumulant and spectral vectors of a linear vector process as defined above. Then it is shown that linearity of a vector process implies constancy of the modulus square of its normalized higher-order spectra whereas the component of such a vector process does not necessarily have a linear representation. Finally, statistics for the testing of multivariate Gaussianity and linearity are proposed.     

A study of process monitoring based on inverse Gaussian distribution

The inverse Gaussian distribution has considerable applications in describing product life, employee service times, and so on. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and location parameters of the inverse Gaussian distribution respectively, are proposed when the in-control parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. An ARL-unbiased control chart for the shape parameter with the desired ${\mathit{ARL}}_0$, which takes the variability of the parameter estimate into account, is further developed. The performance of the proposed control charts is investigated in terms of the ARL and standard deviation of the run length. Finally, an example is used to illustrate the proposed control charts.     

Single-machine parallel-batching scheduling with family jobs to minimize weighted number of tardy jobs

We consider the problem of scheduling n jobs in batches on a single parallel-batching machine, where the jobs are partitioned into jobs families and the jobs in each family have the same due date. The objective is to minimize the weighted number of tardy jobs. We first devise an efficient pseudo-polynomial time and a fully polynomial time approximation scheme for the weighted problem. Then we present $O(n^2)$-time and $O(n\log n)$-time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time, respectively.     

Efficient data selection for speech recognition based on prior confidence estimation using speech and monophone models

This paper proposes an efficient speech data selection technique that can identify those data that will be well recognized. Conventional confidence measure techniques can also identify well-recognized speech data. However, those techniques require a lot of computation time for speech recognition processing to estimate confidence scores. Speech data with low confidence should not go through the time-consuming recognition process since they will yield erroneous spoken documents that will eventually be rejected. The proposed technique can select the speech data that will be acceptable for speech recognition applications. It rapidly selects speech data with high prior confidence based on acoustic likelihood values and using only speech and monophone models. Experiments show that the proposed confidence estimation technique is over 50 times faster than the conventional posterior confidence measure while providing equivalent data selection performance for speech recognition and spoken document retrieval.     

HIGHER ORDER MOMENTS OF SAMPLE AUTOCOVARIANCES AND SAMPLE AUTOCORRELATIONS FROM AN INDEPENDENT TIME SERIES

Abstract. Given length- n sampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, in n , that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross-moments of the non-centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovariances.     

A stochastic Kaczmarz algorithm for network tomography

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end-to-end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.     

广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

首先,通过引入拟减法算子给出K-积分模定义,并针对广义Mamdani模糊系统实施等距剖分其输入空间. 其次,应用分片线性函数（Piecewise linear function,PLF）的性质构造性地证明了广义Mamdani模糊系统在K-积分模意义下具有泛逼近性,从而将该模糊系统对连续函数空间的逼近能力扩展到一类可积函数类空间上. 最后,通过模拟实例给出该广义Mamdani模糊系统对给定可积函数的泛逼近及实现过程.     

Nonlinear time series forecasting with Bayesian neural networks

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.