We propose a new sequential procedure for estimating multivariate distributions in cases when conventional maximum likelihood has too many parameters and is therefore inaccurate or non-operational. The procedure constructs a multivariate distribution and its pseudo-likelihood sequentially, in...

Optimal GMM is known to dominate Gaussian QMLE in terms of asymptotic efficiency [Chamberlain, G., 1984. Panel data. In: Griliches, Z., Intriligator, M.D. (Eds.), Handbook of Econometrics, vol. II, pp. 1248-1313]. I derive a new condition under which QMLE is as efficient as GMM for a general...

For covariance structure models, the QMLE second-order bias is derived and compared with EL and GMM. Surprisingly, QMLE and EL have the same second-order bias if QMLE and GMM(EL) are equally first-order efficient. Other examples favoring QMLE are given.

When there are more moment conditions than observations, the usual GMM weighting matrix is singular. We show that using the generalized inverse is not a good idea. With continuous updating, the criterion function equals one for every parameter value.