Theory of parameter estimation
0. Introduction and summary. The analysis of data from the gravitational-wave detectors that are currently under construction in several countries will be a challenging problem. The reason is that gravitational-vawe signals are expected to be extremely weak and often very rare. Therefore it will be of great importance to implement optimal statistical methods to extract all possible information about the signals from the noisy data sets. Careful statistical analysis based on correct application of statistical methods will be essential. The aim of this series of lectures is to introduce the reader to the contemporary theory of parameter estimation. Principles of main estimation methods are reviewed and the properties of the estimators are discussed. The theory of estimation is considered in a general framework of an appropriate statistical model (Sec. 2). Facing a problem of estimation one can start either with a principle (like "take the value of the parameter which is the nearest to your data"), which is developed in Sec. 3.1 ("Heuristic methods") or with some postulated properties of the estimator (Sec. 3.2, "Optimal estimators"). How much can properties of the estimator chosen change under violations of the theoretical model adopted is discussed in Sec. 4, "Robustness".
- F. N. David, E. S. Pearson, (1961), Elementary Statistical Exercises, Cambridge University Press.
- T. S. Ferguson, (1967), Mathematical Statistics. A Decision Theoretic Approach, Academic Press.
- M. Hollander, D. A. Wolfe, (1973), Nonparametric Statistics Methods, Wiley.
- E. L. Lehmann, (1986), Theory of Point Estimation, Wiley.
- R. Zieliński, (1983), Robust Statistical Procedures: a General Approach. In: Stability Problems for Stochastic Models, Lecture Notes in Mathematics 982, Springer Verlag.