Statistical inference for the slope parameter in functional linear regression

In this paper, we consider the linear regression model Y=SX+ε with functional regressors and responses. We develop new inference tools to quantify deviations of true slope S from a hypothesized operator S0 respect Hilbert–Schmidt norm ~S−S0~2, as well prediction error E‖SX−S0X‖2. Our analysis is applicable time series based on asymptotically pivotal statistics. This makes it particularly user-friendly, because avoids choice tuning parameters inherent in long-run variance estimation or bootstrap dependent data. also discuss two sample problems change point detection. Finite properties are investigated by means simulation study. Mathematically, our approach sequential version popular spectral cut-off estimator SˆN for S. prove that (sequential) plug-in estimators deviation measures N-consistent satisfy weak invariance principles. These results rest smoothing effect L2-norms, exploit proof-technique, smoothness shift, which has potential applications other fields.