It is desirable that a numerical maximization algorithm monotonically increase its objective
function for the sake of its stability of convergence. It is here shown how one can adjust the …

Publisher Summary This chapter discusses stochastic approximation. It discusses basic
results on the stochastic approximation of a point of minimum of a function of k real …

We establish upper and lower bounds on the asymptotic minimax risk in estimating (1) a
density at a point when the density is known to be decreasing with a Lipschitz condition;(2) a …

It is shown that the Keifer-Wolfowitz procedure--for functions f sufficiently smooth at θ, the
point of minimum--can be modified in such a way as to be almost as speedy as the Robins …

Let H (y∣ x) be a family of distribution functions depending upon a real parameter x, and let
M (x)=∫∞-∞ y dH (y∣ x) be the corresponding regression function. It is assumed M (x) is …

These notes originate from a couple of lectures which were given in the Econometric
Workshop of the Center for Operations Research and Econometrics (CORE) at the Catholic …

In many problems of maximum likelihood estimation, it is impossible to carry out either the E‐
step or the M‐step of the EM algorithm. The present paper introduces a gradient algorithm …

For some time it has been well known among specialists in mathematical programming that
the statistical problem of fitting a linear multiple regression with the criterion of minimizing …

The course for which these notes were originally prepared was a one-semester graduate
level course at Purdue University, dealing with optimization in general and best …

For statistical estimation problems, it is typical and even desirable that several reasonable
estimators can arise for consideration. For example, the mean and median parameters of a …