Density Unbiased Point Estimates

A new concept of unbiasedness (density unbiasedness) for point estimates is introduced and the "best" density unbiased point estimate for the mean of any normal distribution is proved to be the ordinary sample mean $\bar{x} = \sum^n_{i = 1} x_i/n$. Under certain conditions on the form of the characteristic function of a family of probability density functions involving an unknown location parameter, $\bar{x}$ is shown to be a density unbiased point estimate of the location parameter.