Abstract: A sequential shrinkage estimation method was developed to determine a minimum sample size under which both of the variable selection and the parameter estimation with a pre-specified accuracy were achieved for the generalized linear model with measurement errors. Asymptotic properties of the proposed sequential estimation method, such as the coverage probability of the sequential confidence set and the efficiency of the minimum sample size, were studied. Simulation studies were conducted and the results show that the proposed method can save a large number of samples compared to the traditional sequential sampling method. Finally a diabetes data set was used as an example.

Key words: generalized linear model, sequential sampling, adaptive shrinkage estimate, stopping rule, confidence set