On the asymptotic null distribution of theF-statistic for testing a partial null hypothesis in a randomized PBIB design withmassociate classes under the Neyman model

1973 ◽  
Vol 1 (1-2) ◽  
pp. 1-23
Author(s):  
Junjiro Ogawa ◽  
Sadao Ikeda
Keyword(s):  
Null Hypothesis ◽  
Null Distribution ◽  
Asymptotic Null Distribution ◽  
Pbib Design

Revisiting Tests for Neglected Nonlinearity Using Artificial Neural Networks

2011 ◽  
Vol 23 (5) ◽  
pp. 1133-1186 ◽  
Author(s):  
Jin Seo Cho ◽  
Isao Ishida ◽  
Halbert White
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Likelihood Ratio Statistic ◽  
Null Distribution ◽  
Regularity Conditions ◽  
Asymptotic Null Distribution ◽  
Monte Carlo Experiments ◽  
Artificial Neural ◽  
Open Question

Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity, paying careful attention to both components of the null. We derive the asymptotic null distribution under each component separately and analyze their interaction. Somewhat remarkably, it turns out that the previously known asymptotic null distribution for the type 1 case still applies, but under somewhat stronger conditions than previously recognized. We present Monte Carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new, stronger regularity conditions are violated.

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