POINT ESTIMATION

in statistics, the process of finding an approximate value of some parameter (mean, standard deviation, proportion) of a population from corresponding functions of random samples of the population. The accuracy of the approximation is not known, though probabilistic statements concerning such numbers as found over many experiments can be constructed. It is desirable for an estimate to be: (1) Consistent. The larger the sample size, the more accurate the estimate. (2) Unbiased. The expectation of the observed values of a function of many samples is the corresponding population parameter. (3) Most efficient or best unbiasedof all consistent, unbiased estimates, the one possessing the smallest variance. Several methods are used to calculate the estimator. The most often used, the maximum likelihood method, uses differential calculus to determine the maximum of the probability function of a number of sample parameters. The moments method equates values of sample moments (functions describing the parameter) to population moments. The solution of the equation gives the desired estimate. The Bayesian method, named for the 18th-century English mathematician Thomas Bayes, differs from the traditional methods by introducing a frequency function for the parameter being estimated. The drawback to the Bayesian method is that sufficient information on the distribution of the parameter is usually not available. One advantage is that the estimation can be easily adjusted as additional information becomes available.