Titlebook: Lectures on Probability Theory and Statistics; Ecole d‘Eté de Proba Erwin Bolthausen,Aad Vaart,Edwin Perkins,Pierre Be Book 2002 Springer-V

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On the construction of the three-dimensional polymer measureAn outstanding open problem in probability theory is the determination of the mean end to end distance of a standard self-avoiding random walk on the .-dimensional lattice ℤ .for . = 2,3 (and 4).

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macular-edema

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Lecture: Lower BoundsIn this lecture we state a number of theorems giving lower bounds on the asymptotic performance of estimators and tests, and make these concrete for the estimation of a parameter θ in a strict semiparametric model. Some of the proofs are deferred to Lecture 4.

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Lecture: Calculus of ScoresIn this lecture we introduce a “calculus of scores”, which is a useful way of finding efficient influence functions in models that are parametrized.

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Lecture: Gaussian ApproximationsIn this lecture we give proofs of the lower bound theorems stated in Lecture 2, in a more general setting. For completeness we start by a crash course on contiguity.

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Erwin Bolthausen,Aad Vaart,Edwin Perkins,Pierre BeIncludes supplementary material:

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Lecture Notes in Mathematicshttp://image.papertrans.cn/l/image/583572.jpg

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Lecture: Empirical Processes and Consistency of Z-Estimatorsmptotic properties of estimators in semiparametric models. In this first lecture we discuss entropy numbers, Glivenko—Cantelli classes and their application to proving consistency of .- and .-estimators.