Nonparametric estimation in ? ? -series processes
A counting process { N ( t ) , t ? 0 } with the interoccurrence times X1,X2, X 1 , X 2 ,  is an ? ? -series process if there exists a real number ? ? such that (k?Xk)k=1,2, ( k ? X k ) k = 1 , 2 ,  forms a renewal process. The nonparametric inference problem in an ? ? -series process is taken into consideration. The Mann test is applied for trend analysis and a graphical technique is presented in order to test whether the data come from an ? ? -series process. Some nonparametric estimators for three important parameters of the ? ? -series process are obtained by using a linear regression method. The consistency and asymptotic normality properties are investigated. The performances of the estimators are evaluated by a simulation study. Some suggestions on the choice of the estimators are made based on the theoretical and simulation results. Further, the method is illustrated through a real-life example.
trend linear regression ? ? -series process ? ? ? ? ?