Maximum Likelihood Position Location with a Limited Number of

MAXIMUM LIKELIHOOD COVARIANCE ESTIMATION WITH A CONDITION NUMBER CONSTRAINT By

High dimensional covariance estimation is known to be a difficult problem, has many applications and is of current interest to the larger statistical community. We consider the problem of estimating the covariance matrix of a multivariate normal distribution in the “large p small n” setting. Several approaches to high dimensional covariance estimation have been proposed in the literature. In ma...

Breakdown Points for Maximum Likelihood Estimators of Location–scale Mixtures

ML-estimation based on mixtures of Normal distributions is a widely used tool for cluster analysis. However, a single outlier can make the parameter estimation of at least one of the mixture components break down. Among others, the estimation of mixtures of t-distributions by McLachlan and Peel [Finite Mixture Models (2000) Wiley, New York] and the addition of a further mixture component accoun...

The Limited Information Maximum Likelihood Estimator as an Angle

When an econometric structural equation includes two endogenous variables and their coefficients are normalized so that their sum of squares is 1, it is natural to express them as the sine and cosine of an angle. The Limited Information Maximum Likelihood (LIML) estimator of this angle when the error covariance matrix is known has constant variance. Of all estimators with constant variance the ...

Maximum likelihood estimation of photon number distribution from homodyne statistics

An interesting application of the homodyne detection is the measurement of phase–insensitive properties of optical fields, dependent on the photon number distribution [1]. The homodyne technique goes beyond the current limitations of direct photodetection. First, ultrafast sampling time can be achieved by using the local oscillator field in the form of a short pulse. Secondly, information on th...

The Maximum Number of Edges in a Strongly Multiplicative Graph