Functional linear regression with derivatives

By André Mas, Besnik Pumo. 2006

49 citations recorded by the source corpus.

We introduce a new model of linear regression for random functional inputs taking into account the first-order derivative of the data. We propose an estimation method that comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronised penalisation. An asymptotic expansion of the mean square prevision error is given. The model and the method are applied to a benchmark dataset of spectrometric curves and compared with other functional models.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3468bdef263c46cccb4776a2dffea19f7b34aff8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Shahid Ullah
2. Han Lin Shang
3. Caroline F. Finch

In Control and Systems Engineering

1. Shahid Ullah
2. Han Lin Shang
3. Caroline F. Finch

In Numerical Analysis

1. Shahid Ullah
2. Han Lin Shang
3. Caroline F. Finch

Citations in the corpus

• Functional time series approach for forecasting very short-term electricity demand (2013, background): “Although not demonstrated in this paper, the continuous nature of our functional methods allows us to analyse the derivatives of curves [28,29].”
• Applications of functional data analysis: A systematic review (2013, methodology): “In particular, FDA methods can often extract additional information contained in the function and its derivatives [6,7] that is not normally available from application of traditional statistical methods [1].”