Two geometric representations of confidence intervals for ratios of linear combinations of regression parameters: An application to the NAIRU

2010 ◽  
Vol 108 (1) ◽  
pp. 73-76 ◽  
Author(s):  
J.G. Hirschberg ◽  
J.N. Lye
Keyword(s):  
Confidence Intervals ◽  
Linear Combinations ◽  
Regression Parameters ◽  
Geometric Representations

Confidence intervals on linear combinations of variance components that are unrestricted in sign

1990 ◽  
Vol 35 (3-4) ◽  
pp. 135-143 ◽  
Author(s):  
Naitee Ting ◽  
Richard K. Burdick ◽  
Franklin A. Graybill ◽  
S. Jeyaratnam ◽  
Tai-Fang C. Lu
Keyword(s):  
Confidence Intervals ◽  
Variance Components ◽  
Linear Combinations

Confidence Intervals on Linear Combinations of K Variances

1994 ◽  
Vol 36 (7) ◽  
pp. 873-883
Author(s):  
T. Anbupalam ◽  
K. N. Ponnuswamy ◽  
M. R. Srinivasan
Keyword(s):  
Confidence Intervals ◽  
Linear Combinations

scholarly journals Analysis of Nonlinear Regression Models: A Cautionary Note

Dose-Response ◽  
2005 ◽  
Vol 3 (3) ◽  
pp. dose-response.0 ◽  
Author(s):  
Shyamal D. Peddada ◽  
Joseph K. Haseman
Keyword(s):  
Confidence Intervals ◽  
Regression Models ◽  
Nonlinear Models ◽  
Nonlinear Function ◽  
Standard Errors ◽  
True Parameter ◽  
Nonlinear Regression Models ◽  
Confidence Levels ◽  
Regression Parameters ◽  
Large Sample Theory

Regression models are routinely used in many applied sciences for describing the relationship between a response variable and an independent variable. Statistical inferences on the regression parameters are often performed using the maximum likelihood estimators (MLE). In the case of nonlinear models the standard errors of MLE are often obtained by linearizing the nonlinear function around the true parameter and by appealing to large sample theory. In this article we demonstrate, through computer simulations, that the resulting asymptotic Wald confidence intervals cannot be trusted to achieve the desired confidence levels. Sometimes they could underestimate the true nominal level and are thus liberal. Hence one needs to be cautious in using the usual linearized standard errors of MLE and the associated confidence intervals.

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