A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Entropy Drives an Attached Water Molecule from the C- to N-Terminus on Protonated Proline

Results from infrared photodissociation (IRPD) spectroscopy and kinetics of singly hydrated, protonated proline indicate that the water molecule hydrogen bonds preferentially to the formally neutral carboxylic acid at low temperatures and at higher temperatures to the protonated N-terminus, which bears the formal charge. Hydration isomer populations obtained from IRPD kinetic data as a function of temperature are used to generate a van`t Hoff plot that reveals that C-terminal binding is enthalpically favored by 4.2-6.4 kJ/mol, whereas N-terminal binding is entropically favored by 31-43 J/(mol K), consistent with a higher calculated barrier for water molecule rotation at the C-terminus.