Change-Point Detection in a High-Dimensional Multinomial Sequence Based on Mutual Information

Time-series data often have an abrupt structure change at an unknown location. This paper proposes a new statistic to test the existence of a change-point in a multinomial sequence, where the number of categories is comparable with the sample size as it tends to infinity. To construct this statistic, the pre-classification is implemented first; then, it is given based on the mutual information between the data and the locations from the pre-classification. Note that this statistic can also be used to estimate the position of the change-point. Under certain conditions, the proposed statistic is asymptotically normally distributed under the null hypothesis and consistent under the alternative hypothesis. Simulation results show the high power of the test based on the proposed statistic and the high accuracy of the estimate. The proposed method is also illustrated with a real example of physical examination data

Evaluation of the Canadian government policies on controlling the COVID-19 outbreaks

In this paper, we investigate the COVID-19 pandemic in Canada and evaluate the Canadian government policies on controlling COVID-19 outbreaks. The first case of COVID-19 was reported in Ontario on 25 January 2020. Since then, there have been over million cases by now. During this time period, the federal, provincial and local governments have implemented regulations and policies in order to control the pandemic. To evaluate these government policies, which may be done by analysing the infection rate, infection period and reproductive number of COVID-19, we approach the problem by introducing an extended susceptible-exposed-infectious-removed (SEIR) model and conduct the model inference by using the iterated filter ensemble adjustment Kalman filter (IF-EAKF) algorithm. We first divide the time period into phases according to the policy intensities in each province by segmenting the time period from 4 March 2020 to 31 October 2020 into three time phases: the exploding phase, the strict policy implementation phase, and the provincial reopening phase. We then use IF-EAKF algorithm to obtain the estimates of the model parameters. We show that the infection rate in the second phase is lower than that in both first and third phases. We also discuss the number of new COVID-19 cases under different policy intensities and different policy durations in the third wave of the pandemic

Central limit theorem of random quadratics forms involving random matrices

Let and S=(s1,s2,...,sK) where random variables are i.i.d. with . The central limit theorem of the random quadratic forms is established, which arises from the application in wireless communications.Central limit theorem Large dimensional matrix Quadratic forms

On limit theorem for the eigenvalues of product of two random matrices

The existence of limiting spectral distribution (LSD) of the product of two random matrices is proved. One of the random matrices is a sample covariance matrix and the other is an arbitrary Hermitian matrix. Specially, the density function of LSD of SnWn is established, where Sn is a sample covariance matrix and Wn is Wigner matrix.Limiting spectral distribution Product of random matrices Large dimensional random matrices

Some limiting theorems of some random quadratic forms

In this paper, the random quadratic form is considered. The main motivation comes from the application to wireless communication. For [tau]>0, it is shown that converges to a fixed quantity with convergence rate oa.s(N1/2-[tau]). Also, convergence in probability is established.Convergence rate Large dimensional matrix Martingale Quadratic forms

Testing for variance changes in autoregressive models with unknown order

The problem of change point in autoregressive process is studied in this article. We propose a Bayesian information criterion-iterated cumulative sums of squares algorithm to detect the variance changes in an autoregressive series with unknown order. Simulation results and two examples are presented, where it is shown to have good performances when the sample size is relatively small.