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Journal of Statistical Theory and Practice

, Volume 12, Issue 1, pp 66–81 | Cite as

The simultaneous assessment of normality and homoscedasticity in linear fixed effects models

  • Ye Yang
  • Thomas Mathew
Article

Abstract

This article investigates the problem of simultaneously testing the normality and homoscedasticity assumptions in a linear fixed effects model when we have grouped data. This has been facilitated by the assumption of a smooth alternative to the normal distribution. The smooth alternative is specified using Legendre polynomials, and the score statistic is derived under two scenarios: a common smooth alternative across the different groups, or different smooth alternatives across the different groups. A data-driven approach available in the literature is used for determining the order of the polynomials. For the null distribution of the score statistic, the accuracy of the asymptotic chi-squared distribution is numerically investigated under a one-way fixed effects model with balanced and unbalanced data. The results are illustrated with an example.

Keywords

Balanced data Legendre polynomials one-way fixed effects model score test smooth alternative unbalanced data 

AMS Subject Classification

62F03 62J20 

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Copyright information

© Grace Scientific Publishing, 20 Middlefield Ct, Greensboro, NC 27455 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Maryland Baltimore CountyBaltimoreUSA

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