Theil€“Nagar ρ estimate based on d statistic. Theil and Nagar have suggested that, in small samples, instead of estimating ρ as (1 ˆ’ d/2), it should be estimated as

where n = total number of observations, d = Durbin€“Watson d, and k = number of coefficients (including the intercept) to be estimated. Show that for large n, this estimate of ρ is equal to the one obtained by the simpler formula (1 ˆ’ d/2).

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n2(1 – d/2) + k2 p = n² – k2 %3D