In statistics books least squares method is placed among other methods for distribution parameters estimation methods (like method of moments, maximum likelihood method). However in none of the books I've read there is a single example on how to estimate distribution parameters using LSM. Only linear and non linear regression examples are given. Could anybody give an example of PDF estimation using LSM?
EDIT: The least squares error function is
Where $x_i$ are the sample elements, and $\theta$ are the estimated parameters and $h(\theta_1,\theta_2,...,\theta_k)$ is some arbitrarily chosen function. How would this function look like when estimating the parameters of let's say normal distribution? Would this be:
where $f_i$ are the empirical probability density values? But then I would need to make some estimate of $f_i$ what is a different problem itself.