کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1146491 957513 2008 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern
چکیده انگلیسی

For a {0, 1}-pattern of finite length, an empirical process is introduced in order to describe the number of overlapping occurrences of the pattern at each level t∈[0,1]t∈[0,1] in a sequence of the corresponding indicators of i.i.d. [0, 1]-valued observations of length nn. A method for obtaining the exact finite-dimensional distributions of the empirical process is given. The weak convergence of the process to a Gaussian process in D[0,1]D[0,1] as nn tends to infinity is also established. The limiting process depends on the given pattern. The exact covariance function is compared with the asymptotic covariance function in a numerical example.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 99, Issue 7, August 2008, Pages 1460–1473
نویسندگان
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