 The mean, variance, and bias of the OLS based estimator of the extremum of a quadratic regression model for small samplesAndreas Karlsson Rosenblad Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 9, 2870-2886 Abstract: Many economic theories suggest that the relation between two variables y and x follow a function forming a convex or concave curve. In the classical linear model (CLM) framework, this function is usually modeled using a quadratic regression model, with the interest being to find the extremum value or turning point of this function. In the CLM framework, this point is estimated from the ratio of ordinary least squares (OLS) estimators of coefficients in the quadratic regression model. We derive an analytical formula for the expected value of this estimator, from which formulas for its variance and bias follow easily. It is shown that the estimator is biased without the assumption of normality of the error term, and if the normality assumption is strictly applied, the bias does not exist. A simulation study of the performance of this estimator for small samples show that the bias decreases as the sample size increases. Date: 2022 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:51:y:2022:i:9:p:2870-2886 Ordering information: This journal article can be ordered from DOI: 10.1080/03610926.2020.1782936 Access Statistics for this article Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals |
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