Change-point Detection Based On Empirical Euclidean Likelihood

Change-point problem has been a hot research field in statistics during the last few decades.For a sequential data,the point called change-point if the distribution of the data before and after that point have changes.Change-point detection is refer to finding the change-point.At the same time,other statistical problems can be consider,such as parameter estimation,the distribution properties and so on.Many statistical scholars paid attention to change-point problem and widely applied the statistical methods which are related to the change-point problem to real life in various fields,such as Economy,geology,climate,biology,medicine,image processing,signal denoising and so on.In this paper,the change point problem in mean model and linear regression model has discussed.It is significant to studying change point in mean model,because it is the groundwork in statistics.The euclidean likelihood method is proposed to detected the change point in mean model.The trimmed empirical euclidean likelihood ratio function is constructed based on the features of this model.And the explicit expression is derived.The null limit distribution of the test statistic is investigated with extreme value distribution.And the change point detection is made.If the change point exists,it's location and consistency are discussed.Simulations and real analysis of Nile River data show that our proposed method is practicable and effective.It is necessary to discussed the change point problems in linear regression model that is functional and has used to various fields widely.Based on the features of the linear regression model with change point,the trimmed empirical euclidean likelihood ratio test function is constructed.And the explicit expression is given.The null limit distribution is proved to be related to extreme value distribution.And the change point detection is made.The location and consistency of change point are discussed when the change point is exists.The practicability and effectiveness of proposed method is illustrated by simulation results and real analysis of Old Faithful geyser of yellow Stone Park.