Hi,
the statistical model is as follows:
$Y_i = \exp(sx_i) p(x_i) + \epsilon_i$
where $x$ is the independent variable (real, assuming arbitrarily large values), $s$ is a parameter and $p$ is some unknown real-valued periodic function with reasonably short period. Given the observations $y_i$, I want to construct an estimator for $s$ and the average value
$\bar p := \lim_{T\to\infty} \frac{1}{T} \int_0^T p(x)dx$
of $p$.
Is it possible to find assumptions on the errors $\epsilon_i$ so that one can construct such estimators which are weakly consistent?
Any opinion is greatly appreciated.
