ABSTRACT
This chapter discusses the analysis and derivation of methods for estimating the parameters from random samples of the model, paying particular attention to how accurate these estimates remain in different sampling realizations. It describes the two basic approaches. Common in both approaches is the description of a loss function, also called a risk function, which is associated with an estimator that measures the estimation error as a function of both the sample value and the parameters. The chapter discusses four typical examples of statistical models and suggests optimal estimators based on various criteria. They are: estimation of the width of the uniform PDF; estimation of a Gaussian signal; estimation of the size of a Gaussian signal; and estimation of a binary signal with Gaussian noise.
