If E|g(X)|=∞, we say that Eg(X) does not exist. (Ross 1988 refers to this as the "law of the unconscious statistician." We do not find this amusing.) (查看原文)
Definition 1.2.4 Given a sample sapce S and an association sigma algebra B, a probability function is a function P with domain B that satisifies
1. P(A) >= 0 for all A in B.
2. P(S) = 1.
3. If A1, A2, ... in B are parwise disjoint, then P(Union(Ai)) = sum(P(Ai))
The three properties given in Definition 1.2.4 are usually referred to as the Axioms of Probability (or the Kolmogorov Axioms, after A. Kolmogorov, one of the fathers of probability theory). (查看原文)
The property of consistency is concerned with the asymptotic accuracy of an estimator: Does it converge to the parameter that it is estimating? In this section we look at a related property, efficiency, which is concerned with the asymptotic variance of an estimator. (查看原文)
The ANOVA null is the intersection of more easily understood univariate hypotheses. Most interesting inferences in an ANOVA can be expressed as contrasts or sets of contrasts. (查看原文)
