The Estimation Of Random Ratio Models And Its Application To Change-point Detection

The theory of change point testing is an important research branch of mathematical statistics.It is widely used in engineering,economics,biology,medicine and other fields.At present,many scholars pay attention on the research of CUSUM type estimator for the change point testing.Many good results of estimator have been obtained such as the convergence,the conver-gence rate and the limit distribution under the null hypothesis.In this thesis,we will use a new method named inverse moment model to study the CUSUM type estimator of the change point testing,and obtain the limit distribution under the null hypothesis.In the following,we give our structures.First,inspired by the existing models such as inverse moment model and nonpara-metric regression model,we give a more general model,where numerator and denominator of ratio contain random variables.Based on the dependent se-quence such as ?-mixing sequence,we use the technologies of Jensen inequality,moment inequality,inverse moment model theory and Taylor formula to esti-mate the first and second moments of random ratio,and obtain some results of asymptotic approximation and convergence rate.Some simulations are il-lustrated to verify our results.Secondly,as an important application to the random ratio,we carry out the study of the CUSUM type estimator for the change point testing.With some conditions,we have a limit distribution of Brownian bridge motion for the estimat,or under the null hypothesis.Similar-ly,we do some simulations and the real data analysis to check the results we obtained.