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Centering a Basic Concepts of Point Estimation. Literally, any statistic can be used as a point estimate. Note: Point estimator is random, and point estimate is fixed single value. It is just a matter of whether it is a good or bad estimate. We will use the generic Greek letter θ for the parameter of interest Point Estimation Theory. Process: Obtain sample data from each population under study Based on the sample data, estimate θ Conclusions based on sample estimates point estimate is the value of point estimator given a specific sample. Statistical inference:directed toward conclusions about one or more parameters. The first four chapters deal with exact (small-sample) theory, and their approach and organization Point Estimation. An Here in the theory of point estimation, we consider that the population under study is described by a probability density function (pdf) or probability mass function (pmf), say, 6 Classic Theory of Point Estimation Point estimation is usually a starting point for more elaborate inference, such as construc-tion of confidence intervals. Example Sensible estimations for the population mean include: sample We want to discuss parameters and estimators using a general language. Estimation theory is a branch of statistics that deals with estimating interested parameters from random observations (or sampled data). We will use the generic Greek letter θ for the parameter of interest. Statistical inference:directed toward conclusions about one or more parameters. Let q be a parameter, and q ˆ is an estimator for q. Often the notation q ˆ refers to both a random variable and a specific point esti-mateWe call q ˆ a point estimator for q; we use the point estimator to compute a point estimate, a single plausible value for q ChapterProperties of Point Estimators and Methods of Estimation Introduction Relative E ciency Consistency Su ciency The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation The Method of Moments The Method of Maximum Likelihood 1 A point estimate of a parameter denoted by ^ ; ; is a single number that can be considered as a possible value for: Since it is computed from the sample X = (X1; ; Xn); it is a function of X; that is, ^ = ^(X): Some simple examples are: If X1; ; Xn is from B(1; p) (Bernoulli data), then p ^ =Pn Point Estimation. This book is concerned with point estimation in Euclidean sample spaces.