Estimation of Impact Ranges for Functional Valued Predictors

Spectroscopy plays a crucial role in various scientific and industrial applications, enabling the analysis of complex materials and their interactions with incident radiation. Hyperspectral remote sensing, also known as imaging spectroscopy, is essential for numerous Earth science applications, spanning multiple disciplines, including ecology, geology, and cryosphere research. With the abundance of current orbital imaging spectrometers, and with space agencies and commercial companies set to expand their use in the next few years, developing methodologies that maximize the utility of these data is crucial. Identifying the wavelength ranges of diagnostic absorption features in spectra is essential for understanding the relationship between spectral data and responses of interest. In this paper, we propose a statistical approach that utilizes Functional Partial Least Squares (FPLS) to model the spectral data as smooth functions and study their impact on the response variable along sub-intervals of the domain. To capture the localized relationships within specific sub-intervals, termed impact ranges, we present a novel two-stage estimation procedure to identify the midpoint and half-length of the impact ranges. Additionally, we introduce an algorithm for iteratively applying the proposed two-stage approach to estimate both the number and location of potential impact ranges. The proposed procedure is evaluated via Monte Carlo simulation and is applied to a real dataset of spectra to identify the location of the diagnostic absorption features for predicting calcium carbonate (CaCO₃) content in soil. Our methodology accurately estimates the number and location of impact ranges, corresponding to absorption features in spectral data.