Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

Vector FIGARCH process, its persistence and co-persistence in variance

In this paper, the definition of the vector FIGARCH process is established, and the stationarity and some properties of the process are discussed. According to the stationarity and the results of Du and Zhang [1], we verify the persistence in variance of the vector FIGARCH process, and finally establish the sufficient and necessary condition for the co-persistence in the variance of the process and also discuss the constant related vector FIGARCH ( p , d , q ) process as a special case.

A New Vector Markov Process for M/G/1 Queue

In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.

Inspection-replacement policy of system under predictive maintenance

In general, every system is in one of the three states： normal, abnormal, or failure state. When the system is diagnosed as abnormal state, it needs predictive maintenance, lfthe system fails, an identical new one will replace it. The predictive maintenance cannot make the system ＂as good as new＂. Under these assumptions, the reliability index and the inspection-replacement policy of a system were studied. The explicit expression of the reliability index and the average income rate （i.e., the long-run average income per unit time） are derived by using probability analysis and vector Markov process method. The criterion of feasibility for the optimal inspection-replacement policy under the maximum average income rate is obtained. The numerical example shows the optimal inspection-replacement policy can raise the average income rate when the optimal inspection-replacement policy is feasible.

Determination of reservoir induced earthquake using support vector machine and gaussian process regression

The prediction of magnitude （M） of reservoir induced earthquake is an important task in earthquake engineering. In this article, we employ a Support Vector Machine （SVM） and Gaussian Process Regression （GPR） for prediction of reservoir induced earthquake M based on reservoir parameters. Comprehensive parameter （E） and maximum reservoir depth] （H） are considered as inputs to the SVM and GPR. We give an equation for determination oil reservoir induced earthquake M. The developed SVM and GPR have been compared with] the Artificial Neural Network （ANN） method. The results show that the developed SVM and] GPR are efficient tools for prediction of reservoir induced earthquake M. /

Some Group Runs Based Multivariate Control Charts for Monitoring the Process Mean Vector

In this article, we propose two control charts namely, the “Multivariate Group Runs’ (MV-GR-M)” and the “Multivariate Modified Group Runs’ (MV-MGR-M)” control charts, based on the multivariate normal processes, for monitoring the process mean vector. Methods to obtain the design parameters and operations of these control charts are discussed. Performances of the proposed charts are compared with some existing control charts. It is verified that, the proposed charts give a significant reduction in the out-of-control “Average Time to Signal” (ATS) in the zero state, as well in the steady state compared to the Hotelling’s T2 and the synthetic T2 control charts.

Numerical investigation of dynamic characteristics of dual throat nozzle and bypass dual throat nozzle in thrust vectoring starting process

The Bypass Dual Throat Nozzle(BDTN)is a novel fluidic Thrust Vectoring(TV)nozzle,it switches to TV state by opening the valve in the bypass.To greatly manipulate the BDTN,the dynamic characteristics in the TV starting process should be analyzed.This paper conducts numerical simulations to grasp the variation processes of performances and the flow field evolution of BDTN and Dual Throat Nozzle(DTN).The dynamic responses of TV starting in typical DTN models are investigated at first.Then,the TV starting processes of BDTN in different Nozzle Pressure Ratio(NPR)conditions are simulated,and the valve opening durations(T)are also considered.Before the expected TV direction is achieved in the DTN,the jet is deflected to the opposite direction at the beginning of the dynamic process,which is called the reverse TV phenomenon.However,this phenomenon disappears in the BDTN.The larger injection width of DTN intensifies unsteady oscillations,and the reverse TV phenomenon is strengthened.In the BDTN,T determines the delay degree of performance variations compared to the static results,which is called hysteresis effect.At NPR=10,the hysteresis affects the final stable performance of BDTN.This study analyses the dynamic characteristics in DTN and BDTN,laying a foundation for further design of nozzles and control strategies.

On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises:Estimation and Testing

This paper studies a partially nonstationary vector autoregressive(VAR)model with vector GARCH noises.We study the full rank and the reduced rank quasi-maximum likelihood estimators(QMLE)of parameters in the model.It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions.Based these,the likelihood ratio(LR)test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector,asymptotically.As far as we know,our test is new in the literature.The critical values of the LR test are simulated via the Monte Carlo method.The performance of this test in finite samples is examined through Monte Carlo experiments.We apply our approach to an empirical example of three interest rates.

Common Persistence and Error-Correction Mode in Conditional Variance

We firstly define the persistence and common persistence of vector GARCH process from the point of view of the integration, and then discuss the sufficient and necessary condition of the copersistence in variance. In the end of this paper, we give the properties and the error correction model of vector GARCH process under the condition of the co-persistence.

Ruin Probabilities for a Risk Model with Two Classes of Claims

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.

Simultaneous characterization of multiple properties of solid and liquid phases in crystallization processes using NIR

Near infrared spectroscopy （NIR） is now probably the most popular process analytical technology （PAT） for pharmaceutical and some other industries. However, unlike mid-IR, NIR is known to have difficulties in monitoring crystallization or precipitation processes because the existence of solids could cause distortion of the spectra. This phenomenon, seen as unfavorable previously, is however an indication that NIR spectra contain rich information about both solids and liquids, giving the possibility of using the same instrument for multiple property characterization. In this study, transflectance NIR calibration data was obtained using solutions and slurries of varied solution concentration, particle size, solid concentration and temperature. The data was used to build calibration models for prediction of the multiple properties of both phases. Predictive models were developed for this challenging application using an approach that combines genetic algorithm （GA） and support vector machine （SVM）. GA is used for wavelength selection and SVM for mode building. The new GA-SVM approach is shown to outperform other methods including GA-PLS （partial least squares） and traditional SVM. NIR is thus successfully applied to monitoring seeded and unseeded cooling crystallization processes of L-glutamic acid.