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Titlebook: Weak Convergence and Empirical Processes; With Applications to Aad W. Vaart,Jon A. Wellner Book 19961st edition Springer Science+Business M

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發(fā)表于 2025-3-21 19:56:11 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Weak Convergence and Empirical Processes
副標(biāo)題With Applications to
編輯Aad W. Vaart,Jon A. Wellner
視頻videohttp://file.papertrans.cn/1022/1021355/1021355.mp4
叢書名稱Springer Series in Statistics
圖書封面Titlebook: Weak Convergence and Empirical Processes; With Applications to Aad W. Vaart,Jon A. Wellner Book 19961st edition Springer Science+Business M
描述This book tries to do three things. The first goal is to give an exposition of certain modes of stochastic convergence, in particular convergence in distribution. The classical theory of this subject was developed mostly in the 1950s and is well summarized in Billingsley (1968). During the last 15 years, the need for a more general theory allowing random elements that are not Borel measurable has become well established, particularly in developing the theory of empirical processes. Part 1 of the book, Stochastic Convergence, gives an exposition of such a theory following the ideas of J. Hoffmann-J!1Jrgensen and R. M. Dudley. A second goal is to use the weak convergence theory background devel- oped in Part 1 to present an account of major components of the modern theory of empirical processes indexed by classes of sets and functions. The weak convergence theory developed in Part 1 is important for this, simply because the empirical processes studied in Part 2, Empirical Processes, arenaturally viewed as taking values in nonseparable Banach spaces, even in the most elementary cases, and are typically not Borel measurable. Much of the theory presented in Part 2 has previously been sc
出版日期Book 19961st edition
關(guān)鍵詞Estimator; Mathematics; Maxima; Maximum; Minimum; Random variable; Statistics
版次1
doihttps://doi.org/10.1007/978-1-4757-2545-2
isbn_softcover978-1-4757-2547-6
isbn_ebook978-1-4757-2545-2Series ISSN 0172-7397 Series E-ISSN 2197-568X
issn_series 0172-7397
copyrightSpringer Science+Business Media New York 1996
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The Ball Sigma-Field and Measurability of Supremae two .-fields are equal for separable spaces (Problems 1.7.3 and 1.7.4). For some nonseparable spaces, it is even fairly common that maps are ball measurable even though they are not Borel measurable. Thus one may wonder about the possibility of a weak convergence theory for ball measurable maps. I
板凳
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Convergence: Almost Surely and in Probabilityhastic convergence, stronger than weak convergence. In this section we consider their nonmeasurable extensions together with the concept of almost uniform convergence, which is equivalent to outer almost sure convergence for sequences, but stronger and more useful for general nets.
地板
發(fā)表于 2025-3-22 05:37:57 | 只看該作者
Convergence: Almost Surely and in Probabilityhastic convergence, stronger than weak convergence. In this section we consider their nonmeasurable extensions together with the concept of almost uniform convergence, which is equivalent to outer almost sure convergence for sequences, but stronger and more useful for general nets.
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發(fā)表于 2025-3-22 09:54:08 | 只看該作者
Uniformity and Metrizationgence over certain subsets. These subsets can be fairly big: equicontinuity and boundedness suffice. On the other hand, there also exist small (countable) subsets such that pointwise convergence on such a subset is automatically uniform, and equivalent to pointwise convergence on the whole of ..(D),
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Uniformity and Metrizationgence over certain subsets. These subsets can be fairly big: equicontinuity and boundedness suffice. On the other hand, there also exist small (countable) subsets such that pointwise convergence on such a subset is automatically uniform, and equivalent to pointwise convergence on the whole of ..(D),
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