Basic Concepts of Estimation Theory

This chapter sets the general framework for some topics of asymptotic statistics that will be covered in this and in subsequent chapters, and it includes a specific notation. Basic knowledge of mathematical statistics is helpful, but not essential. The chapter starts with introducing the basic terms parametric model, statistical space, and canonical model, and it provides several examples. We also learn about the notions estimator and sequences of estimators as well as of desirable properties of such sequences, namely asymptotic unbiasedness and consistency. The chapter concludes with (asymptotic) confidence sets or, what is synonymous, confidence regions. A confidence set is a random set that covers an unknown parameter value with at least a given minimum high probability, no matter which parameter governs the underlying distribution of the random variables in the statistical model.