A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACT

In this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990 Nakamura, T. (1990). Corrected score function for errors in variables models: methodology and application to generalized linear models. Biometrika 77:127–137.[Crossref], [Web of Science ®] , [Google Scholar]). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.     

PMSE performance of two different types of preliminary test estimators under a multivariate t error term

Abstract

In this paper, assuming that the error terms follow a multivariate t distribution, we derive the exact formula for the predictive mean squared error (PMSE) of two different types of pretest estimators. It is shown analytically that one of the pretest estimator dominates the SR estimator if a critical value of the pretest is chosen appropriately. Also, we compare the PMSE of the pretest estimators with the MMSE, AMMSE, SR and PSR estimators by numerical evaluations. Our results show that the pretest estimators dominate the OLS estimator for all combinations when the degrees of freedom is not more than 5.     

Testing for abrupt breaks in variance structures with smooth changes

Abstract

We investigate the problem of testing for variance breaks in the case where the variance structure is assumed to be smoothly time-varying under the null. Since the classical tests are aimed to detect any change in the variance, they are not able to distinguish between smooth non constant variance and abrupt breaks. In this paper a new procedure for detecting variance breaks taking into account for smooth changes in the variance under the null is proposed. The finite sample properties of the test we introduce are investigated by Monte Carlo experiments. The theoretical outputs are illustrated using U.S. macroeconomic data.     

More on the Preliminary Test Estimator in Almost Unbiased Liu Regression

This article is concerned with the parameter estimation in linear regression model when it is suspected that the regression coefficients are the subspace of the equality restrictions. The objective of this article is to introduce the preliminary test almost unbiased Liu estimators (PTAULE) based on the Wald (W), the likelihood ratio (LR), and the Lagrangian multiplier (LM) tests and compare the proposed estimators in the sense of the quadratic bias and mean square error (MSE) criterion.     

Tests for Equality of Inflation Parameters of Two Zero-Inflated Power Series Distributions

In this article, we consider two independent zero-inflated power series distributions and provide likelihood ratio test for equality of inflation parameters of the same. As an illustration, testing equality of inflation parameters of two zero inflated Poisson distributions is provided. Further, simulation study to investigate power of likelihood ratio tests has been carried out.     

A Test for Constant Hazard Against a Change-Point Alternative

In this article, we consider the change-point hazard rate model which arises quite commonly in mechanical or biological systems, which experience a high hazard rate early in their lifetime due to infant mortality and then a constant or steady hazard rate after the threshold time. We first derive the corresponding mean residual life function (MRLF) and observe that the MRLF is initially increasing and then constant. Here, we derive a test statistic for exponentiality against Increasing Initially then Constant Mean Residual Life (ICMRL). We also derive the asymptotic distribution of the test statistic and compare the power of the test with other existing tests such as likelihood ratio, Weibull, and Log gamma tests considered in the literature. The test performs quite well as compared to other alternatives studied.     

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.