• Corpus ID: 5083614

Minimum phi divergence estimator and hierarchical testing in loglinear models

@inproceedings{Cressie2000MinimumPD,
  title={Minimum phi divergence estimator and hierarchical testing in loglinear models},
  author={Noel Cressie and Leandro Pardo},
  year={2000}
}
In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum phi-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a phi-divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the problem of testing a nested sequence of loglinear models. 

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References

SHOWING 1-10 OF 23 REFERENCES

Some new statistics for testing hypotheses in parametric models

The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by a finite measures and parametrized by vector-valued

Estimation of parameters for a mixture of normal distributions on the basis of the cressie and read divergence

The estimation of the five parameters of the mixture of two normal components is studied, with emphasis on the estimation of mixing proportion. The method proposed is based on the power-divergence

Goodness-Of-Fit Statistics for Discrete Multivariate Data

1 Introduction to the Power-Divergence Statistic.- 1.1 A Unified Approach to Model Testing.- 1.2 The Power-Divergence Statistic.- 1.3 Outline of the Chapters.- 2 Defining and Testing Models: Concepts

An introduction to categorical data analysis

Two--Way Contingency Tables. Three--Way Contingency Tables. Generalized Linear Models. Logistic Regression. Loglinear Models for Contingency Tables. Building and Applying Logit and Loglinear Models.

Modelling Survival Data in Medical Research

TLDR
This paper discusses the design of clinical trials, use of computer software in survival analysis, and some non-parametric procedures for modelling survival data.

Joint dependence of risk of coronary heart disease on serum cholesterol and systolic blood pressure: a discriminant function analysis.

The association between increased risk of coronary heart disease and elevated levels of serum cholesterol and systolic blood pressure is well known. Several questions about the magnitude of this

Multinomial goodness-of-fit tests