Peiwen Jia, Xiaojun Song, Haoyu Wei
arXiv 10 Oct 2021 · Econometrics
arXiv:2110.04849 · PDF · DOI · OpenAlex · Extracted main text
The normality assumption for random errors is fundamental in the analysis of variance (ANOVA) models, yet it is seldom subjected to formal testing in practice. In this paper, we develop Neyman's smooth tests for assessing normality in a broad class of ANOVA models. The proposed test statistics are constructed via the Gaussian probability integral transformation of ANOVA residuals and are shown to follow an asymptotic Chi-square distribution under the null hypothesis, with degrees of freedom determined by the dimension of the smooth model. We further propose a data-driven selection of the model dimension based on a modified Schwarz's criterion. Monte Carlo simulations demonstrate that the tests maintain the nominal size and achieve high power against a wide range of alternatives. Our framework thus provides a systematic and effective tool for formally validating the normality assumption in ANOVA models.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Janic-Wróblewska, Alicja and Ledwina, Teresa (2000) Data driven rank test for two-sample problem | 0.950 | 7 | 3 | 86% |
| 2 | Duchesne, Pierre and Lafaye De Micheaux, Pierre and Tagne Tatsinkou,… (2016) Estimating the mean and its effects on Neyman smooth tests of normality for ARMA models | 0.941 | 6 | 3 | 83% |
| 3 | Neyman, Jerzy (1937) Smooth Test for Goodness of Fit | 0.843 | 3 | 3 | 100% |
| 4 | Kallenberg, Wilbert CM and Ledwina, Teresa (1999) Data-driven rank tests for independence | 0.822 | 6 | 2 | 83% |
| 5 | Kallenberg, Willibrordes Cornelis Maria and Ledwina, Teresa (1995) On data driven Neyman's tests | 0.781 | 7 | 2 | 71% |
| 6 | Kraus, David (2007) Data-driven smooth tests of the proportional hazards assumption | 0.763 | 6 | 2 | 67% |
| 7 | Ducharme, Gilles R and Lafaye de Micheaux, Pierre (2004) Goodness-of-fit tests of normality for the innovations in ARMA models | 0.737 | 4 | 2 | 75% |
| 8 | Bera, Anil K and Ghosh, Aurobindo and Xiao, Zhijie (2013) A smooth test for the equality of distributions | 0.737 | 3 | 2 | 100% |
| 9 | Inglot, Tadeusz and Kallenberg, Wilbert CM and Ledwina, Teresa (1997) Data driven smooth tests for composite hypotheses | 0.693 | 5 | 1 | 100% |
| 10 | Kallenberg, Wilbert CM and Ledwina, Teresa (1997) Data-driven smooth tests when the hypothesis is composite | 0.693 | 5 | 1 | 100% |
Showing the top 10 of 55 scored citations.