Hypothesis Testing Methods Based Extropy And Multiple Hypothesis Testing Problems

One of the must-do preparation before data analysis is the hypothesis testing for distributions.In chemistry,biology,finance or economics,the symmetry and exponen-tial assumptions are frequently used in model building.For example,in finance,the positive and negative shocks in stock price are non-symmetric.Stock prices are heavy-tailed,and better fitted by exponential family at the tail.As the complementary dual of Shannon's Entropy,Extropy attracts the attention of researchers since its birth.Similar to Entropy,Extropy measures the uncertainty of random variables.With the Extropy of record values,one can characterize certain properties of different probability distribu-tions.Based on this idea,we proved the sufficient and necessary condition of symmetry and exponentiality,and proposed two new test statistics.By the means of Monte Carlo simulation and real data examples,we showed that our tests have certain advantages.Furthermore,after testing multiple samples of multiple alternative hypothesis,the resulting p-values have to be combined in a reasonable way to be one single conclustion.Obviously,the more alternative hypothesis,the more likely that the null hypothesis been rejected.But the significance level has to be lower.The Simes test is one of the mulitiple testing procedure can be easily computed without knowing of probability distribution.Yet the Simes test does not always control for the Type 1 error.We constructed a series of p-value models and discuss the conservativeness of Simes procedure under different dependence structures.Hypothesis testing for distributional characteristics and multiple hypothesis testing procedure are the two main focus of our research.This thesis is organized as follows.Chapter 1 is the background and literature review of our study.We introduced the re-lated work on Extropy,symmetry test,exponentiality test and multiple hypothesis test.We also gave a brief introduction of our research direction and novelty.In Chapter 2,we showed the necessary and sufficient condition of symmetry with the Extropy of record values and proposed a new test statistic.Using order statistics,we gave a sample estimator of the new test.Through Monte Carlo simulation and two real data exam-ples,we showed our test's advantages and practicality.In Chapter 3,we characterized the exponential distribution using the same innovation,and proposed a new test statis-tic.By Monte Carlo simulation,we showed our test's applicable scope and advantage against the existing 58 tests on the alternative distribution with 4 types of hazard rate function.We also showed the practicality and robustness with real examples.Chapter 4 turns from single hypothesis testing to multiple hypothesis testing.We constructed a se-ries of p-value models and showed the conservativeness or non-conservativeness under Simes procedure.With the observation on the dependence structure of these models,we gave a conjecture on conservativeness.Chapter 5 concludes the thesis.We discussed some problems of this thesis and proposed future research plans.