79,330 research outputs found
Maximum Likelihood Estimation of Parameters in a Mixture Model
The estimation of parameters of the log normal distribution based on complete and censored samples are considered in the literature. In this article, the problem of estimating
the parameters of log normal mixture model is considered. The Expectation Maximization algorithm is used to obtain maximum likelihood estimators for the parameters, as
the likelihood equation does not yield closed form expression. The standard errors of
the estimates are obtained. The methodology developed here is then illustrated through
simulation studies. The confidence interval based on large-sample theory is obtained
A Multivariate Generalized Orthogonal Factor GARCH Model
The paper studies a factor GARCH model and develops test procedures which can be used to test the number of factors needed to model the conditional heteroskedasticity in the considered time series vector. Assuming normally distributed errors the parameters of the model can be straightforwardly estimated by the method of maximum likelihood. Inefficient but computationally simple preliminary estimates are first obtained and used as initial values to maximize the likelihood function. Maximum likelihood estimation with nonnormal errors is also straightforward. Motivated by the empirical application of the paper a mixture of normal distributions is considered. An interesting feature of the implied factor GARCH model is that some parameters of the conditional covariance matrix which are not identifiable in the case of normal errors become identifiable when the mixture distribution is used. As an empirical example we consider a system of four exchange rate return series.Multivariate GARCH model; mixture of normal distributions; exchange rate
A Tight Convex Upper Bound on the Likelihood of a Finite Mixture
The likelihood function of a finite mixture model is a non-convex function
with multiple local maxima and commonly used iterative algorithms such as EM
will converge to different solutions depending on initial conditions. In this
paper we ask: is it possible to assess how far we are from the global maximum
of the likelihood? Since the likelihood of a finite mixture model can grow
unboundedly by centering a Gaussian on a single datapoint and shrinking the
covariance, we constrain the problem by assuming that the parameters of the
individual models are members of a large discrete set (e.g. estimating a
mixture of two Gaussians where the means and variances of both Gaussians are
members of a set of a million possible means and variances). For this setting
we show that a simple upper bound on the likelihood can be computed using
convex optimization and we analyze conditions under which the bound is
guaranteed to be tight. This bound can then be used to assess the quality of
solutions found by EM (where the final result is projected on the discrete set)
or any other mixture estimation algorithm. For any dataset our method allows us
to find a finite mixture model together with a dataset-specific bound on how
far the likelihood of this mixture is from the global optimum of the likelihoodComment: icpr 201
Finite Impulse Response Errors-in-Variables system identification utilizing Approximated Likelihood and Gaussian Mixture Models
In this paper a Maximum likelihood estimation algorithm for Finite Impulse Response Errors-in-Variables systems is developed. We consider that the noise-free input signal is Gaussian-mixture distributed. We propose an Expectation-Maximization-based algorithm to estimate the system model parameters, the input and output noise variances, and the Gaussian mixture noise-free input parameters. The benefits of our proposal are illustrated via numerical simulation
High dimensional Sparse Gaussian Graphical Mixture Model
This paper considers the problem of networks reconstruction from
heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well
known that parameter estimation in this context is challenging due to large
numbers of variables coupled with the degeneracy of the likelihood. We propose
as a solution a penalized maximum likelihood technique by imposing an
penalty on the precision matrix. Our approach shrinks the parameters thereby
resulting in better identifiability and variable selection. We use the
Expectation Maximization (EM) algorithm which involves the graphical LASSO to
estimate the mixing coefficients and the precision matrices. We show that under
certain regularity conditions the Penalized Maximum Likelihood (PML) estimates
are consistent. We demonstrate the performance of the PML estimator through
simulations and we show the utility of our method for high dimensional data
analysis in a genomic application
A mixture logistic model for panel data with a Markov structure
In this study, we propose a mixture logistic regression model with a Markov
structure, and consider the estimation of model parameters using maximum
likelihood estimation. We also provide a forward type variable selection
algorithm to choose the important explanatory variables to reduce the number of
parameters in the proposed model.Comment: Some results of this study have been included in the report of a
research project of Professor Yu-Hsiang Cheng, and the report is now
available. Thus we add the information in this versio
- …