Correction to: A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics
نویسندگان
چکیده
منابع مشابه
The Glivenko Cantelli Theorem and its Generalizations
In this note we will study upper bounds of random variables of the type sup A∈A |ν n (A) − ν(A)| , where A is a class of sets that needs to fulll certain assumptions. These bounds are important tools in the analysis of learning processes and probabilistic theories of pattern recognition. The presentation given here is based on [DGL96].
متن کاملLaws of Large Numbers for Random Linear
The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...
متن کاملasymptotic property of order statistics and sample quntile
چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...
15 صفحه اولPreservation Theorems for Glivenko-Cantelli and Uniform Glivenko-Cantelli Classes
We show that the P−Glivenko property of classes of functions F1, . . . ,Fk is preserved by a continuous function φ from R to R in the sense that the new class of functions x → φ(f1(x), . . . , fk(x)), fi ∈ Fi, i = 1, . . . , k is again a Glivenko-Cantelli class of functions if it has an integrable envelope. We also prove an analogous result for preservation of the uniform Glivenko-Cantelli prop...
متن کاملUniform Glivenko–Cantelli Classes
A class of sets, or functions, is said to be P–Glivenko–Cantelli if the empirical measure Pn converges in some sense to the true measure, P , as n → ∞, uniformly over the class of sets or functions. Thus, the notions of Glivenko–Cantelli, and likewise uniform Glivenko–Cantelli are for the most part qualitative assessments of how “well–behaved” a collection of sets or functions is, in the sense ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1978
ISSN: 0090-5364
DOI: 10.1214/aos/1176344384