The general consensus of opinion, however, is that, thus far, two-stage least squares is the cheapest, easiest, and most efficient estimator
in most situations .
Overall, the geometric average is the most efficient estimator, and the overlapping average is the least efficient.
Although the overlapping average is still the least biased, it is also the least efficient estimator.
The sample 10 percent trimmed mean is clearly the most efficient estimator, with an RMSE that is more than 15 percent below that of the sample mean, with a 30 percent lower variance
After examining alternatives to the standard measures, I conclude that limited-influence estimators are more efficient estimators of the central tendency of the price-change distribution than is the overall mean.
The proposal is divided into three research projects whose goals are: (1) Obtain upper and lower bounds for the density of the solution to the two types of SPDEs (i) and (ii), by means of the Malliavin Calculus; (2) Use these bounds in order to prove the local asymptotic normality (LAN) for the models (i) and (ii), and then apply Hajek-Lecam s theorem to obtain asymptotically efficient estimators
for the parameter of the equations; (3) Study Monte Carlo methods and exact simulation of the SDE model with jumps (i), and apply these computational methods to the following financial problems: jump volatility models and numerical computations of greeks.
Using the knowledge on the behavior of the estimators we were able to design efficient estimators
of surface area using spatial grids of shifted line probes and estimators of length of fibre like objects using spatial grids of touching spheres.
Such a model depends on the independence of the variables to gain unbiased, efficient estimators
Darrell Duffie and Peter Glynn have developed efficient estimators
for complex financial applications.