The Consistency Of The Quantile And Density Function Estimator For WOD Random Samples

As we know, there are difference in independent and dependent random vari-able sequence of probability theory. The progress of the property of independent random variable sequences has been satisfactory in the middle of the 20th cen-tury. On this basis, many probabilities devote to solve the more general samples with a certain correlation according to the needs of many practical problems, and they have put forward and studied various kinds properties of the limit theorems of dependent random variables. As time goes on, there are many good results and relative achievements promote the further development in reliability theory, permeability theories, time series analysis, multi-variate statistical analysis, et al, which have been widely used in various areas such as many engineering and financial risks.Wide Orthant Dependent (WOD) sequence was proposed in 2011 by Wang kaiyong et al, they also raised some examples of specific WOD random variable to explain WOD random variable include all the generalized negative dependent random variables, some positive dependent random variables and other dependent random variable. So you can see it has very important significance to generalize the large sample properties of independent sequences to WOD sequence.Based on this good qualities of WOD sequence, this paper want to study quantile estimates convergence properties under WOD samples, and to study consistency problems under the action of recursive density function. We get the strong consistency and Bahadur representation of quantile estimates under WOD samples, and the pointwise strong consistency of the recursive density function kernel estimator for WOD samples.The specific research content as follows:In Chapter One, we introduced the research background of quantile estimates, WOD sequence, Bahadur representation and Recursive density function kernel estimator, and we also introduced research situation at home and abroad, research significance and results of this paper.In Chapter Two, we studied the strong consistency of quantile estimates and Bahadur representation by the property of WOD sequence and Markov inequality.In Chapter Three, we gave a kind of recursive density function kernel esti-mators for WOD sequence, and we also proved the pointwise strong consistency of recursive density function kernel estimators.