A paradox in least-squares estimation of linear regression models

Z. D. Bai and Meihui Guo

Statistics & Probability Letters, 1999, vol. 42, issue 2, 167-174

Abstract: This note considers a paradox arising in the least-squares estimation of linear regression models in which the error terms are assumed to be i.i.d. and possess finite rth moment, for r[set membership, variant][1,2). We give a concrete example to show that the least-squares estimator of the slope parameter is inconsistent when the intercept parameter of the model is given. However, surprisingly this estimator is consistent when the intercept parameter is intendedly assumed to be unknown and re-estimated simultaneously with the slope parameter.

Keywords: Consistency; Least-squares; estimate; rth; moment (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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