Jackknife Estimate The Theory And Application Of Bootstrap Estimated

Jackknife and Bootstrap are two important estimators in statistics. Quenouille firstly gave the Jackknife estimator in 1949. Efron suggested the Bootstrap estimator firstly in 1979. In 1992,Efron used Jackknife-after-Bootstrap(JAB) estimator to a single statistical problem. There are many research work abroad but unfortunly there are not too much work in our country.Chapter Two discussed the basic idea of the estimators;meanwhile, the basic properties are obtained. Numerical examples illustrate that these estimators are available.The linear regression models have been wildly-used in many fields, such as agriculture, industry, meteorology, geology, economics, management and so on. In Chapter Three, Jackknife estimator, Bootstrap estimator and JAB estimator are applied to linear regression models .Numerical results illustrate that these estimators are also available.Chapter Four discussed linear models with Error-in-variable .The model is as following:where Y is an n×1vector of observations yi , Z is an n×p matrix with z iTas it i ? th row , I nis an n×n identity matrix ,andσ2is unknown common variance. X is also an n×pmatrix with xi Tas iti ? th row,εis independent ofξ,andΛis a positive definite matrix,X is observed variable,Z is unknown. Then we can get the Jackknife estimator ofβis Numerical results illustrate that Jackknife estimator, Bootstrap estimator and JAB estimator are available.Chapter Five discussed exponential family nonlinear mixed models. The model is following:We get the Jackknife estimator ofβisAccording to our discussion, the conclusions are that Jackknife estimator, Bootstrap estimator and JAB estimator are available for many models.