A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is the point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not an inner product space and conventional Bayes estimators therefore stand without their usual decision theoretic foundation. W...

A relationship between well-known estimator-correlator results from detection theory and the detection of signals in spherically invariant random noise is described. This relationship gives a general result concerning the structure of the likelihood ratio for this detection problem. Furthermore, an alternate formulation of both the likelihood ratio and the optimal estimator that arises in the e...

In this invited contribution a brief review will be presented of the integer estimation theory as developed by the author over the last decade and which started with the introduction of the LAMBDA method in 1993. The review discusses three different, but closely related classes of ambiguity estimators. They are the integer estimators, the integer aperture estimators and the integer equivariant ...

This paper reviews minimax best equivariant estimation in these invariant problems: a location parameter, scale parameter and (Wishart) covariance matrix. We briefly review development of the estimator as generalized Bayes relative to right Haar measure each case. Then we prove minimaxity procedure by giving least favorable prior sequence based on non-truncated Gaussian distributions. The resul...

Many multi-channel dereverberation and noise reduction techniques such as the multi-channel Wiener filter (MWF) require an estimate of the late reverberation and noise power spectral densities (PSDs). State-of-the-art multi-channel methods for estimating the late reverberation PSD typically assume that the noise PSD matrix is known. Instead of assuming that the noise PSD matrix is known, in thi...

The two-stage least-squares (2SLS) estimator is known to be biased when its first-stage fit is poor. I show that better first-stage prediction can alleviate this bias. In a two-stage linear regression model with Normal noise, I consider shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I...

In this paper we generalize and extend BrosowskiMeinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(19...

In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...