Î¸. Relative e ciency (Def 9.1) Suppose ^ 1 and ^ 2 are two unbi-ased estimators for , with variances, V( ^ 1) and V(^ 2), respectively. Example: Suppose X 1;X 2; ;X n is an i.i.d. â¢ In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data â¢ Example- i. X follows a normal distribution, but we do not know the parameters of our distribution, namely mean (Î¼) and variance (Ï2 ) ii. The small-sample properties of the estimator Î²Ë j are defined in terms of the mean ( ) Abbott 2. Indeed, any statistic is an estimator. Properties of estimators. Some of the properties are defined relative to a class of candidate estimators, a set of possible T(") that we will denote by T. The density of an estimator T(") will be denoted (t, o), or when it is necessary to index the estimator, T(t, o). Point estimators. Only once weâve analyzed the sample minimum can we say for certain if it is a good estimator or not, but it is certainly a natural ï¬rst choice. Ë= T (X) be an estimator where . Relative e ciency: If ^ 1 and ^ 2 are both unbiased estimators of a parameter we say that ^ 1 is relatively more e cient if var(^ 1) `.
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