Recall that the power can be any value in the half-open interval RowBox[{RowBox[{"(", RowBox[{"0", ",", "2"}]}], "]"}], but we restrict ourselves to as a rational fraction . Here RowBox[{"θ", ">", "0"}] is still denoted as the inverse-range parameter since SuperscriptBox["θ", RowBox[{"-", "1"}]] is the "range" (or "scale") in the autocorrelation .

As in [1], assume that one realization of the considered process is observed over the interval RowBox[{RowBox[{"(", RowBox[{"0", ",", "1"}]}], "]"}] at in the regular grid (thus is the size of each dataset). As for the Matérn (1) case, such a dataset is also simulated via fast Fourier transforms (FFTs).

The exponent is assumed known and the same three methods as in the Matérn (1) case are implemented here for estimating θ and the variance SuperscriptBox["τ", "2"], namely: Cressie's weighted least-squares method [2], the "hybrid" Zhang–Zimmerman method [3] and the recently-proposed CGEM-EV method [4], here in the case with no measurement error. For each of the three methods, the estimate of the so-called "microergodic coefficient," which is now (in the case , this coincides with the well-known expression of for the Matérn (1/2) case since the general expression for the Matérn (ν) case is ), is naturally defined as the product of the squared estimate of by the power of the estimate of θ. Recent mathematical studies [5, 6] have established that can indeed be easily estimated from one dense observation of over a finite interval (a so-called "infill" asymptotic framework). However, the separate estimation of θ or τ is more difficult.