As a technical supplement to Zhu and Zhang (2004), we give detailed information on how to establish asymptotic theory for both maximum likelihood estimate and maximum modified likelihood estimate in mixture regression models. Under specific and reasonable conditions, we show that the optimal convergence rate of n− 1 4 for estimating the mixing distribution is achievable for both the maximum lik...

in this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. method is tested on problems to ensure the computational eciency. we have compared numerical results with results obtained by other method in literature. we conclude that propose method is computationally ecient and eective.

We discuss tail behaviors, subexponentiality and extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. It shows that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distr...

In this paper we study the frequentist convergence rate for the Latent Dirichlet Allocation (Blei et al., 2003) topic models. We show that the maximum likelihood estimator converges to one of the finitely many equivalent parameters in Wasserstein’s distance metric at a rate of n without assuming separability or non-degeneracy of the underlying topics and/or the existence of more than three word...

The error bound in probability between the approximate maximum likelihood estimator AMLE and the continuous maximum likelihood estimator MLE is investigated for nonlinear nonhomogenous stochastic system with unknown parameter. The rates of convergence of the approximations for Itô and ordinary integral are introduced under some regular assumptions. Based on these results, the in probability rat...

The Multiple Input Multiple output (MIMO) system are considered to be the strongest candidate for the maximum utilization of available bandwidth. In this paper, the MIMO system with the combination of Multi-Carrier Code Division Multiple Access (MC-CDMA) and Space Time Coding (STC) using the Alamouti’s scheme is considered. A Genetic Algorithm (GA) based receiver with an exceptional relationshi...

The multivariate t distribution has many potential applications in applied statistics. Current computational advances will make it routinely available in practice in the near future. Here we focus on maximum likelihood estimation of the parameters of the multivariate t, with known and unknown degrees of freedom, with and without missing data, and with and without covariates. We describe EM, ECM...

We establish minimax lower bounds and maximum likelihood convergence rates of parameter estimation for mean-covariance multivariate Gaussian mixtures, shape-rate Gamma mixtures, and some variants of finite mixture models, including the setting where the number of mixing components is bounded but unknown. These models belong to what we call ”weakly identifiable” classes, which exhibit specific i...

This paper is concerned with the study of the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of parameter appearing linearly in the drift coefficient of two types of stochastic partial differential equations (SPDE’s).