Minimum Chi-Square, not Maximum Likelihood!

Relative Precision of Minimum Chi-square and Maximum Likelihood Estimates of Regression Coefficients

Professor Doob [5], in the charming introduction to his paper delivered at the last Berkeley Symposium, remarked that physicists write like physicists, while mathematicians write like mathematicians and only for posterity. I have been given to wonder at times, for whom it is that mathematical statisticians write, and specifically whether it is for statisticians. The mathematician, we know from ...

On Empirical Likelihood and Non-parametric Pearson's Chi-square Statistic

Owen (1988) showed that the non-parametric empirical likelihood ratio under a linear constrain has an asymptotic chi-square distribution, same as in the paramet-ric case. This fact can be used to form (non-parametric, asymptotic) conndence intervals. We suggest here to use the non-parametric version of the Pearson's chi-square statistic instead of the likelihood ratio to form conndence interval...

A VARIATION ON THE MINIMUM CHI - SQUARE TEST by Paul

Maximum Likelihood and Minimum Classi cation

Hidden Markov models (HMMs) for automatic speech recognition rely on high dimensional feature vectors to summarize the short-time properties of speech. Correlations between features can arise when the speech signal is non-stationary or corrupted by noise. We investigate how to model these correlations using factor analysis, a statistical method for dimensionality reduction. Factor analysis uses...

Mean Square Convergence Rates for Maximum Quasi-likelihood Estimators

In this note we study the behavior of maximum quasilikelihood estimators (MQLEs) for a class of statistical models, in which only knowledge about the first two moments of the response variable is assumed. This class includes, but is not restricted to, generalized linear models with general link function. Our main results are related to guarantees on existence, strong consistency and mean square...