Functional Wavelet-Based Modelling of Dependence Between Lupus and Stress

Abstract

The power of functional linear regression to estimate a set of curves from others involved is studied in this work in the context of life sciences. The objective is to determine the relationship between the degree of lupus and the level of stress for patients suffering this autoimmune disease. Daily stress and lupus curves have a strong local behavior with missing data those days that a patient does not answer the corresponding test. Because of this, wavelet smoothing with an appropriate thresholding rule is considered. Then, functional principal component analysis of the response and predictor variables is used to reduce the dimension and solve the multicollinearity problem that affects the estimation of the functional linear regression model with functional response. Model selection is solved by using a criterion that selects those pairs of response/predictor components that explain the highest proportions of response variability. The performance of the proposed functional model is tested on simulated and real data.