A Note on Wald's Type Chi-squared Tests of Fit

The Wald's method for constructing chi-squared tests of fit has been formulated more accurately. It is shown that Wald's type statistics will follow the central chi-squared distribution if and only if the limit covariance matrix of standardized frequencies will not depend on unknown parameters. Several examples that illustrate this important fact are presented. In particular, it is shown that the goodness-of-fit statistic developed by Moore and Stubblebine does not follow the chi-squared limit distribution, and, hence, cannot be used for testing multivariate normality.     

Upper Bound for p-Value of the Test of Multivariate Normal Ordered Mean Vectors Against all Alternatives

Consider the problem of testing the isotonic of several p-variate normal mean vectors against all alternatives. It is difficult to compute the exact p-value for this problem of testing with the classical method when the covariance matrices are completely unknown. In the present paper, a test statistic is proposed for this problem of testing. A reformulation of the test statistic is given based on the orthogonal projections on the closed convex cones and then the upper bound for p-value of the test statistic is computed.     

An Investigation of Agreement Between the Item Difficulty Coefficient Calculated in Accordance With Classical Test Theory and Item Response Theory With Bland–Altman Method

The purpose of this study is to investigate agreement between item difficulty coefficients calculated relying on classical test theory and item response theory with Bland–Altman method. According to results, although there is a high correlation between Pj and b coefficient estimated with HGLM (hierarchical generalized linear model), 1P, and 3P models, it can be said that there is no agreement between two methods and cannot be used interchangeably. It is observed that the confidence limit is wide according to Bland–Altman graphics. Therefore, it can be said that there is no agreement between item difficulty values obtained from two methods. Bland–Altman method which is used in clinical studies mostly is suggested to be used in the comparison of methods used especially in the evaluation of student performance in education, in agreement studies among specialist considerations especially in terms of providing additional information to the studies in which correlation coefficient is calculated.     

Binomial Mixture Modeling of University Credits

The paper reviews finite mixture models for binomial counts with concomitant variables. These models are well known in theory, but they are rarely applied. We use a binomial finite mixture to model the number of credits gained by freshmen during the first year at the School of Economics of the University of Florence. The finite mixture approach allows us to appropriately account for the large number of zeroes and the multimodality of the observed distribution. Moreover, we rely on a concomitant variable specification to investigate the role of student background characteristics and of a compulsory pre-enrollment test in predicting gained credits. In the paper, we deal with model selection, including the choice of the number of components, and we devise numerical and graphical summaries of the model results in order to exploit the information content of the concomitant variable specification. The main finding is that the introduction of the pre-enrollment test gives additional information for student tutoring, even if the predictive power is modest.     

Generalized Analysis-of-variance-type Test for the Single-index Quantile Model

In this paper, we are concerned with a test for the index parameter and index function in the single-index model. Based on the estimates obtained by the quantile regression, we extend the generalized analysis-of-variance-type test to the single-index model. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows an asymptotically χ²-distribution. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.     

Non parametric portmanteau tests for detecting non linearities in high dimensions

ABSTRACT

We propose two non parametric portmanteau test statistics for serial dependence in high dimensions using the correlation integral. One test depends on a cutoff threshold value, while the other test is freed of this dependence. Although these tests may each be viewed as variants of the classical Brock, Dechert, and Scheinkman (BDS) test statistic, they avoid some of the major weaknesses of this test. We establish consistency and asymptotic normality of both portmanteau tests. Using Monte Carlo simulations, we investigate the small sample properties of the tests for a variety of data generating processes with normally and uniformly distributed innovations. We show that asymptotic theory provides accurate inference in finite samples and for relatively high dimensions. This is followed by a power comparison with the BDS test, and with several rank-based extensions of the BDS tests that have recently been proposed in the literature. Two real data examples are provided to illustrate the use of the test procedure.     

Quasi-maximum exponential likelihood estimation for a non stationary GARCH(1,1) model

ABSTRACT

This article investigates a quasi-maximum exponential likelihood estimator(QMELE) for a non stationary generalized autoregressive conditional heteroscedastic (GARCH(1,1)) model. Asymptotic normality of this estimator is derived under a non stationary condition. A simulation study and a real example are given to evaluate the performance of QMELE for this model.     

Diagnostic tests for the distribution of random effects in multivariate mixed effects models

Abstract

Fourier methods are proposed for testing the distribution of random effects in classical and robust multivariate mixed effects models. The test statistics involve estimation of the characteristic function of random effects. Theoretical and computational issues are addressed while Monte Carlo results show that the new procedures compare favorably with other methods.     

On an ad hoc test for order restricted multivariate normal means

Abstract

For several normal mean vectors restricted by a simple ordering with respect to a multivariate order, this article derives sufficient and necessary conditions for the restricted MLEs for both mean vectors and covariance matrix, and develops an ad hoc test. It establishes conditions for the bounds of the p-values. One example of such bound is given with some comments.