کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1147956 957810 2012 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spline confidence bands for functional derivatives
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Spline confidence bands for functional derivatives
چکیده انگلیسی

We develop in this paper a new procedure to construct simultaneous confidence bands for derivatives of mean curves in functional data analysis. The technique involves polynomial splines that provide an approximation to the derivatives of the mean functions, the covariance functions and the associated eigenfunctions. We show that the proposed procedure has desirable statistical properties. In particular, we first show that the proposed estimators of derivatives of the mean curves are semiparametrically efficient. Second, we establish consistency results for derivatives of covariance functions and their eigenfunctions. Most importantly, we show that the proposed spline confidence bands are asymptotically efficient as if all random trajectories were observed with no error. Finally, the confidence band procedure is illustrated through numerical simulation studies and a real life example.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 142, Issue 6, June 2012, Pages 1557–1570
نویسندگان
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