Parametric Estimation Of Linear Model Under Uniformly Distributed Covariate

Linear regression is widely used in medicine, biology, survival analysis, economics, reliability analysis and industrial analysis. Sometimes, the information cannot be obtained completely, i.e. the data cannot be observed precisely, results in problems in statistical inference and hypothesis test in regression analysis. These data may be greater, or less than a particular data, or fall into an interval. The data is defined to be interval-censored when it falls into an interval.This paper focuses on parametric estimation of linear model for interval-censored covariates. By using two approximation methods of the interval-censored covariates:Discretization method and Large sample normal approximation, we can get more simpler expression for Likelihood function and reduce the complexity of calculation.Estimation method aforementioned is explored to investigate the performance of the proposed methods. Using the maximum likelihood estimation method, numerical simulations are studied by utilizing Matlab function’"fminsearch", when the minimum value corresponding to the value of the parameter estimate is derived.Through analyzing and comparing the numerical simulation results in Matlab, we get results as follows:In the linear model with an interval censor-data covariates, by using the discretization method, we can get a higher accuracy of estimation of unknown parameters, and the error is small, when compared with the traditional methods. While in the case of large sample,we can also obtain a good estimation of parameter, the result is satisfactory.