Selected Estimated Models with Φ−divergence Statistics
نویسنده
چکیده
When testing for discriminating between two competing models, a statistical method, usually, proceeds by evaluating the measure for discrepancy between the observed data and each parametric model. The parameter model with smaller value of measure statistic is generally chosen. This paper addresses the question of testing for choosing between two estimated models using some φ−divergence type statistics.We choice for arbitrary √n -asymptotically normal estimators to be used for introducing these statistics. The results here are illustrated by a simulation study, then Large Sample theory and bootstrap methods are used to construct our φ−divergence tests in parametric models.
منابع مشابه
Minimum Φ-divergence Estimator and Hierarchical Testing in Loglinear Models
In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum φ-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a φ-divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the prob...
متن کاملLoglinear Models: An approach based on φ-Divergences
In this paper we present a review of some results about inference based on φ-divergence measures, under assumptions of multinomial sampling and loglinear models. The minimum φ-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator is considered. This estimator is used in a φdivergence measure which is the basis of new statistics for solving three importan...
متن کاملChoosing the Best Φ–divergence Goodness– Of–fit Statistic in Multinomial Sampling for Loglinear Models with Linear Constraints
Choosing the best φ-divergence goodness-of-fit statistic in multinomial sampling with linear constraints Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped wit...
متن کاملPhi-divergence Test Statistics in Multinomial Sampling for Hierarchical Sequences of Loglinear Models with Linear Constraints
We consider nested sequences of hierarchical loglinear models when expected frequencies are subject to linear constraints and we study the problem of finding the model in the the nested sequence that is able to explain more clearly the given data. It will be necessary to give a method to estimate the parameters of the loglinear models and also a procedure to choose the best model among the mode...
متن کاملObserved Diffusion Processes
In this paper we propose the use of φ-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, θ)dt + σ(Xt, θ)dWt, from discrete observations {Xti , i = 0, . . . , n} with ti = i∆n, i = 0, 1, . . . , n, under the asymptotic scheme ∆n → 0, n∆n → ∞ and n∆n → 0. The class of φ-divergences is wide and includes several special member...
متن کامل