Abstract
In this study, we look at the wavelet basis for the nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We employ a martingale approach to obtain the asymptotic properties of these wavelet estimators. These findings are established under rather broad assumptions. All we assume about the data is that they are ergodic, but beyond that, we make no assumptions. In this paper, the mean integrated squared error findings in the independence or mixing setting were generalized to the ergodic setting. The theoretical results presented in this study are (or will be) valuable resources for various cutting-edge functional data analysis applications. Applications include conditional distribution, conditional quantile, entropy, and curve discrimination.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference102 articles.
1. Bosq, D. (2000). Lecture Notes in Statistics, Springer.
2. Ramsay, J.O., and Silverman, B.W. (2005). Functional Data Analysis, Springer. [2nd ed.].
3. Ferraty, F., and Vieu, P. (2006). Nonparametric Functional Data Analysis, Springer.
4. Horváth, L., and Kokoszka, P. (2012). Inference for Functional Data with Applications, Springer.
5. Zhang, J.T. (2014). Monographs on Statistics and Applied Probability, CRC Press.
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献