In one-dimensional regression models, we establish a rate for the r th
moment convergence (r  1) of the ordinary least-squares estimator involving explic-
itly the regressors, answering to an open question raised lately by Afendras and
Markatou (Test 25:775–784, 2016). An extension of the classic Theorem 2.6.1 of
Anderson (The statistical analysis of time series, Wiley, New York, 1971) is also
presented.

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