Abstract: The quantile is an important concept in statistics. It has been widely used in many fields such as reliability statistical analysis, economics, finance, bioinformatics and medicine. The study of the dependent random sequences has received a lot of attention since it weakens the limitation of independence. Therefore, based on the m-dependent sequences, this paper studies the large sample properties of the sample quantile kernel estimation. Firstly, using the limit theorem of m-dependent sequences, the Cramer function is calculated, and the moderate deviation principle of sample quantile kernel estimation is proved. Secondly, by verifying the Cramer condition, large deviation results of the sample quantile kernel estimation are obtained. The proof methods and results of the independent and identically distributed samples are simplified and generalized. Also the results provide an important basis for discussing the moderate deviation and large deviation of other types of dependent sequences.

Key words: m-dependent random sequence, the sample quantile kernel estimate, moderate deviation, large deviation