In estimating logistic regression models, convergence of the maximization algorithm is critical, however, this may fail. Numerous bias correction methods for maximum likelihood estimates of the parameters have been conducted for cases of complete data sets and also longitudinal models. For binary response fixed effects panel data model, the conditional logit estimator is consistent for balanced data. When faced with missing covariates problem, researchers opt for various imputation techniques to make the data complete and without loss of generality consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique which yields the best estimates with minimum variance is still elusive. The main aim of this paper is to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector which will make the Newton-Raphson algorithm to converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through partitioning of the covariate matrix. We also confirm from the moduli of the Hessian matrices that the log likelihood of a panel data logistic model has a global maximum as the parameter estimates. Simulation results reveal that model based simulation perform better than classical imputation techniques yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models with single fixed effects.

Energy distance is used to eigenvalue distributions in this new Wishart distribution study, providing a new perspective on high-dimensional data. Multivariate statistics relies on Wishart distribution to explain covariance matrices. This analysis shows how degrees of freedom and covariance matrix configurations affect eigenvalue dispersion. We use energy distance based on eigenvalue distributions to assess Wishart distribution differences without the "curse of dimensionality" via extensive simulation simulations. This approach improves measurement accuracy and processing efficiency in distribution comparisons and enables new analytical pathways in scientific fields that need data covariance comprehension. Our results show that degrees of freedom and matrix structure considerably affect energy distances, expanding the theoretical framework and practical applications of statistical models.