Kyriacos Mattheou

On Distributional Properties and Goodness-of-Fit Tests for Generalized Measures of Divergence

The aim of this work is the investigation of a generalized family of measures of divergence which includes the well-known Csiszárs, Cressie and Reads, and the Basu–Harris–Hjort–Jones (Basu et al., 1998) measures. A weakly consistent estimator of the generalized measure of divergence is proposed and its sampling properties and the corresponding asymptotic distribution are obtained. Finally, tests for multinomial populations are constructed and simulations are performed.

Forecasting ARMA models: a comparative study of information criteria focusing on MDIC

This paper deals with the implementation of model selection criteria to data generated by ARMA processes. The recently introduced modified divergence information criterion is used and compared with traditional selection criteria like the Akaike information criterion (AIC) and the Schwarz information criterion (SIC). The appropriateness of the selected model is tested for one- and five-step ahead predictions with the use of the normalized mean squared forecast errors (NMSFE).

Measures of Divergence in Model Selection

In this chapter a number of measures of divergence are presented and the way model selection criteria are constructed via measures of divergence is discussed. The construction of the divergence information criterion based on a new family of measures of divergence is presented and the lower bound of the mean squared error of prediction is established. Some illustrative simulation results are also given.

Vector autoregressive order selection and forecasting via the modified divergence information criterion

This paper examines the problem of order selection in connection to the forecasting performance for vector autoregressive (VAR) processes. For this purpose we present a generalisation of the modified divergence information criterion (MDIC) for VAR models and compare it with traditional information criteria by Monte Carlo methods for different data generating processes for small, medium, and large sample sizes. The VAR modified divergence information criterion (VAR/MDIC) shows remarkable good results by choosing the correct model more frequently than the known traditional information criteria with the smallest mean squared forecast error.

On Generalized Tests of Fit for Multinomial Populations

The aim of this work is the investigation of tests of fit for multinomial distributions based on the Φ-family of test statistics for goodness of fit (gof) tests [Mattheou and Karagrigoriou, Aust. New Zeal. J. Statist. 52(2), 187–200 (2010)]. For comparing the various goodness of fit tests the asymptotic distribution, which is known to be chi-square, [Cressie and Read, JRSSB, 5, 440–454 (1984); Zografos et al. Comm. Statist. Theor. Meth., 19(5), 1785–1802 (1990); Mattheou and Karagrigoriou, Australian and New Zealand Journal of Statistics 52(2), 187–200 (2010)] and the empirical distribution of all test statistics under investigation are obtained and at the same time the appropriate critical values are evaluated. For the comparison, samples from trinomial distributions are used and both the size and the power of each test for various alternative hypotheses are calculated.