Lord and Wingersky have developed a method for computing the asymptotic variance-covariance matrix of maximum likelihood estimates for item and person parameters under some restrictions on the estimates which are needed in order to fix the latent scale. The method is tedious, but can be simplified for the Rasch model when one is only interested in the item parameters. This is demonstrated here under a suitable restriction on the item parameter estimates.

This paper analyzes the sum score based (SSB) formulation of the Rasch model, where items and sum scores of persons are considered as factors in a logit model. After reviewing the evolution leading to the equality between their maximum likelihood estimates, the SSB model is then discussed from the point of view of pseudo-likelihood and of misspecified models. This is then employed to provide new insights into the origin of the known inconsistency of the difficulty parameter estimates in the Rasch model. The main results consist of exact relationships between the estimated standard errors for both models; and, for the ability parameters, an upper bound for the estimated standard errors of the Rasch model in terms of those for the SSB model, which are more easily available.

Concise formulas for the asymptotic standard errors of component loading estimates were derived. The formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations. The formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances/correlations is available. The estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices.

The method of finding the maximum likelihood estimates of the parameters in a multivariate normal model with some of the component variables observable only in polytomous form is developed. The main stratagem used is a reparameterization which converts the corresponding log likelihood function to an easily handled one. The maximum likelihood estimates are found by a Fletcher-Powell algorithm, and their standard error estimates are obtained from the information matrix. When the dimension of the random vector observable only in polytomous form is large, obtaining the maximum likelihood estimates is computationally rather labor expensive. Therefore, a more efficient method, the partition maximum likelihood method, is proposed. These estimation methods are demonstrated by real and simulated data, and are compared by means of a simulation study.

Jansen (1984) gave explicit formulas for the computation of the second-order derivatives of the elementary symmetric functions. But they are only applicable to those pairs of items which have unequal parameters. It is shown here that for equal parameters similar explicit formulas do exist, too, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle.

This paper proposes a map-based localization system for autonomous vehicle self-localization in urban environments, which is composed of a pose graph mapping method and 3D curvature feature points – Monte Carlo Localization algorithm (3DCF-MCL). The advantage of 3DCF-MCL is that it combines the high accuracy of the 3D feature points registration and the robustness of particle filter. Experimental results show that 3DCF-MCL can provide an accurate localization for autonomous vehicles with the 3D point cloud map that generated by our mapping method. Compared with other map-based localization algorithms, it demonstrates that 3DCF-MCL outperforms them.