  Local polynomial regression of order at least one often performs poorly in
regions of sparse data. Local constant regression is exceptional in this
regard, though it is the least accurate method in general, especially at the
boundaries of the data. Incorporating information from differential equations
which may approximately or exactly hold is one way of extending the sparse
design capacity of local constant regression while reducing bias and variance.
A nonparametric regression method that exploits first order differential
equations is introduced in this paper and applied to noisy mouse tumour growth
data. Asymptotic biases and variances of kernel estimators using Taylor
polynomials with different degrees are discussed. Model comparison is performed
for different estimators through simulation studies under various scenarios
which simulate exponential-type growth.
