Goodness-of-Fit Tests For Error Distribution In Linear Regression Model

Normality test of error distribution in linear regression model has been a hot research topic in the field of statistics. Linear model starts theory of statistical inference also under the hypothesis of observations following specific distribution. Failure of the population distribution means failure of the model, the conclusions according to the model are then invalid. Consequently, the importance of model checking, which is the essence of goodness-of-fit test is self-evident.In the existing literature about error distribution in linear model, the normality test, autocorrelation diagnosis, Heteroscedasticity diagnosis, the problem how to put forward a suitable model in order to fit the actual data better and reflect the characteristics of the actual data of various aspects of the research and formulation is still relatively rough, and the power of test statistics is not high. Therefore, on the previous work, we further studied the error distribution model, and put forward a more effective test method on error distribution normality test.In this paper, we introduce the EDF test statistics, which are often used in the test of goodness of fit of the sample distribution. When the distribution function contains one or two unknown parameters, the unknown parameters should be estimated, the corresponding EDF test can be called a revised EDF test, we also conducted the power simulation of single probability distribution. The main conclusions are as follows:(1)The modified EDF test procedures for testing the normal and exponential distributions with unknown parameters are suggested. The Monte Carlo algorithms are given to approximate the critical values of the EDF test statistics for a wide range of sample sizes. The power simulations show that the AD test is on the whole better than other EDF tests considered, in particular when the alternative departs from the true distribution in the tails. The modified AD test serves as the test statistic of normality test of error distribution in this paper.(2)The test procedures of goodness-of-fit test of error distribution in linear regression model are proposed, and the algorithm to estimate the critical values is given. The test procedures are based on the modified AD test. We obtain the asymptotic mull distribution of the transformed sample.(3) The test procedures of goodness-of-fit test of AR(1) error distribution in linear regression model are proposed, and the algorithm to estimate the critical values is given. The test procedures are based on the modified AD test. We obtain the asymptotic mull distribution of the transformed sample.