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In probability theory, Le Cam's theorem, named after Lucien Le Cam, states the following. Suppose: ,,, … are independent random variables, each with a Bernoulli distribution (i.e., equal to either 0 or 1), not necessarily identically distributed.
- Hájek–Le Cam convolution theorem
In statistics, the Hájek–Le Cam convolution theorem states...
- Hájek–Le Cam convolution theorem
Le Cams drittes Lemma. Das dritte Lemma von Le Cam ist eine Version des Satzes von Radon-Nikodým, in dem die absolute Stetigkeit durch Kontiguität ersetzt wird. Es wird wie folgt formuliert: Theorem
In statistics, the Hájek–Le Cam convolution theorem states that any regular estimator in a parametric model is asymptotically equivalent to a sum of two independent random variables, one of which is normal with asymptotic variance equal to the inverse of Fisher information, and the other having arbitrary distribution.
class. Then, we will introduce the concept of hypothesis testing, along with the theorem of reduction from estimation to testing. Finally, we will introduce the Le Cam methods, which are fundamental tools in establishing minimax lower bounds. 1 From Estimation to Testing
Le Cam was the major figure during the period 1950 – 1990 in the development of abstract general asymptotic theory in mathematical statistics. He is best known for the general concepts of local asymptotic normality and contiguity , and for developing a metric theory of statistical experiments, recounted in his 1986 magnum opus ...
17. Nov. 2020 · In this note we give a relatively simple but detailed proof of Le Cam’s first lemma. Our proof allows us to grasp the central idea by making analogies between contiguity and absolute continuity, and is particularly attractive when teaching this lemma in a classroom setting.
Theorem (Le Cam; Theorem 6.6 in van der Vaart) Let P n;Q n be distributions on a X n 2Xand L n = dQn dPn. If Q n /P n and (X n;L n)!d Pn (X;L) where (X;L) has joint measure M on X R +. Then X n!d Qn Z where P(Z 2B) = E M[1fX 2BgL] i.e. P(Z 2B) = R B R+ r dM(x;r) Contiguity and Asymptotics 13{11
