Sequential statistical procedures for processes of the exponential class with independent increments

Abstract

In this survey paper sequential statistical procedures for the exponential class of processes with independent increments are considered. After the definition of the exponential class a characterization in terms of the LEVY-CHXNTCBXN.representation is given. Then, sequential estimation problems* and sequential testing of hypotheses with respect to the underlying parameter are studied. Finally, some possible extensions of the considered notions and methods to other classes of processes are indicated.

Keywords:

• Processes with independent increments LEVY-CHINTCHIN reriresentfltion sufficient statistic
• sequential likelihood principle
• moment relations
• WALD's fundamental identity
• sequential probability ratio test (SPRT)
• sequential estimation
• CBAMÉR-RAO-type inequality
• efficiency
• consistency

¹Paper given at the 5th International Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin (GDR), Mara/Apr 1981.

¹Paper given at the 5th International Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin (GDR), Mara/Apr 1981.

Notes

¹Paper given at the 5th International Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin (GDR), Mara/Apr 1981.