  Due to measurement noise, a common problem in in various fields is how to
estimate the ratio of two functions. We consider this problem of estimating the
ratio of two functions in a nonparametric regression model. Assuming the noise
is normally distributed, this is equivalent to estimating the ratio of the
means of two normally distributed random variables. We identified a consistent
estimator that gives the mean squared loss of order $O(1/n)$ ($n$ is the sample
size) when conditioned on a highly probable event. We also present our result
applied to both the real data from EAPS and on simulated data, confirming our
theoretical results.
