Sequential L_q-Likelihood-Ratio-Type Test And Confidence Interval

Since Wald proposed the sequential probability ratio test(SPRT)in 1947,it is still an important research field in sequential analysis with fruitful results.Qin and Priebe proposed a robust hypothesis testing method in 2017:L_q-likelihood-ratio-type test,it is an important generalization of the likelihood ratio test.Therefore,it is of great significance to study the sequential L_q-likelihood-ratio-type test and its closely related confidence intervals.The main contents of this paper are as follows:In Chapter 2,a sequential L_q-likelihood-ratio-type test method is proposed and its properties are studied.The q value selection problem is studied under the condition of minimum average sample size,and some applications are given.The robustness of the sequential L_q-likelihood-ratio-type test is proved theoretically,and some simulation examples are given to verify the robustness of the test method.The average subsample capacity of SPRT and SL_qRT under the gross error model is also calculated.In Chapter 3,based on the sequential L_q-likelihood-ratio-type test,the sequential L_q maximum likelihood estimators of the parameters θ in the normal distribution N(θ,θ)are obtained.The asymptotic normality and the sequential confidence interval of the sequential L_q maximum likelihood estimators of the parameters θ and the modified parameters θ are obtained by using the random central limit theorem.The asymptotic normality and sequential confidence interval of the parameter θ are obtained after adding the variance inflating factors j(N).Finally,some simulation examples are given,and the results show that the sequential confidence interval has good coverage.