Large Sample Properties Of NOD Sequence And Risk Measure

In recent years, scholars have made some achievements in the research of NOD sequence inequality, For example. Bernstein-inequality. Rosenthal type. etc. The development of the theory will promote the development of NOD sequence in the field of statistics, in the field of statistics.it is a hot topic to study the large sample properties of a sequence. For example. PA sequence. NA sequence and other large sample properties have a large number of results, but on the NOD sequence, the research results about the large sample properties are few.With increasingly complex financial markets, The evaluation and measure-ment of risk has been highly concerned by scholars. Risk is a key consideration in the investment decision. How to scientifically and effectively measure the risk of the industry is an urgent problem to overcome. Since the 90 s, the extreme value theory has been gradually applied in the field of financial risk managemen-t. The existing research results have no systematic comparison of the Pros and cons of various risk measures, incorrect metrics can lead to mistakes in financial decisions.This master's thesis research is divided into four chapters:The first chapter is preface to introduce emphatically NOD sequence large; sample properties of the research background and the development of risk mea-surement.The second chapter mainly studies the Bahadur representation and strong consistency of VaR sample quantile estimates under NOD. Using the properties of NOD samples and related inequalities are studied under the NOD sequence, the nature of the risk measure VaR nonparametric estimator. Prove the strong consistency of VaR sample quantile estimates, at the same time it also gives the quantile estimates of VaR sample Bahadur representation.The third chapter mainly studies Asymptotic normality of the wavelet esti-mator of NOD sequence regression function. The article fixed design for nonpara-metric regression model Yi= g(xi)+?i,i< i< n, where [xi] is the fixed desigred point, g(x) is a regression function,{?i} is random error of NOD sequences, un-der the right conditions, studied asymptotic normality about unknown regression function g(x) Wavelet estimation.The fourth chapter mainly studies the CVaR measure in the application of extreme value theory. For nearly half a century, along with the economic glob-alization and diversification, the financial risk measure of financial and economic have be attention by scholars. After 90 s, the new risk management tool of VaR (value at risk) measurement method is gradually developed. With its scientific, accurate and comprehensive measurement of risk, VaR has been favored by the in-ternational financial community, but in extreme events occur, VaR measurement accuracy is not as good as CVaR (conditional value at risk).