The Estimated Deviation In The Linear EV Model And Part Of The Linear Model

The linear EV model,also known as the measurement error model,which is both independent and dependent variables with measurement error.This model was proposed as early as the 20th century and has been studied and applied extensively.It is an impor-tant extension of simple linear model.Partially linear model was proposed in 1980s and developed rapidly.Because of its containing both parameter part and the nonparametric parts,they are more flexible in explaining variables.Now they have become an impor-tant regression model in statistical analysis.Both models have excellent characteristics of their own,and they are more in line with the actual situation than simple parametric models and nonparametric models.In addition,these models are widely used in biology,medicine,finance and other fields.Therefore,it is necessary and practical to study linear EV model and partially linear model.Large deviation and moderate deviation principles have become an important branch of probability limit theory,providing a better method for calculating the probability of rare events.Compared with the classical law of large numbers and central limit theorem,it gives the rate function,and gives more accurate results for the limit behavior of random sequences and the parameter estimation in the model.In this paper,we discuss the moderate deviations of parameter estimators and non-parameter estimator in linear EV model and partially linear model respectively,and the exponential convergence rate is given.This paper is divided into three chapters,the main contents are as follows:In the first chapter,the background and significance of this study are discussed firstly,and the two models used in this paper are listed.Then we introduce the concepts of large deviations,moderate deviations and martingale difference sequence.Finally,the main work of this paper is listed.In the second chapter,we mainly discuss the moderate deviations of least squares estimators of two unknown parameters in linear EV model when the errors are sequences of martingale difference.In the third chapter,we mainly study the moderate deviations for the least square esti-mators of unknown parameters and the estimator of nonparametric component in partially linear model when the estimation of nonparametric component is general nonparametric estimation.