کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1145460 1489667 2015 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonparametric functional central limit theorem for time series regression with application to self-normalized confidence interval
ترجمه فارسی عنوان
قضیه محدودیت عملکرد مرکزی غیر پارامتر برای رگرسیون سری زمانی با استفاده از بازه زمانی اطمینان خودآموزی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
چکیده انگلیسی

This paper is concerned with the inference of nonparametric mean function in a time series context. The commonly used kernel smoothing estimate is asymptotically normal and the traditional inference procedure then consistently estimates the asymptotic variance function and relies upon normal approximation. Consistent estimation of the asymptotic variance function involves another level of nonparametric smoothing. In practice, the choice of the extra bandwidth parameter can be difficult, the inference results can be sensitive to bandwidth selection and the normal approximation can be quite unsatisfactory in small samples leading to poor coverage. To alleviate the problem, we propose to extend the recently developed self-normalized approach, which is a bandwidth free inference procedure developed for parametric inference, to construct point-wise confidence interval for nonparametric mean function. To justify asymptotic validity of the self-normalized approach, we establish a functional central limit theorem for recursive nonparametric mean regression function estimates under primitive conditions and show that the limiting process is a Gaussian process with non-stationary and dependent increments. The superior finite sample performance of the new approach is demonstrated through simulation studies.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 133, January 2015, Pages 277–290
نویسندگان
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