此篇論文中我們先導出滿足內部平穩性之一維高斯隨機場樣本半偏差聯合分佈的二階動差‧進而根據大部分常用半偏差模型皆滿足的極限條件下，推導樣本半偏差聯合分佈之共變量極限結構‧我們將此結果應用於三種常用的模型：(1)the pure nugget effect model；(2)線性半偏差模型；(3)半偏差在一固定距離後維持一常數(finite range process)‧第一種模型相當於所謂的white noise process，第二種相當於Wiener process，而第三種則為finite-range transition phenomena. 論文中我們分別探討在此三種模型下，樣本半偏差共變量極限結構不同的特點。
The second-order moments of the joint distribution of the sample semivariogram are derived, assuming an underlying intrinsically stationary, Gaussian, one-dimensional random field. In addition, the asymptotic covariance structure of the sample semivariogram is derived under a certain asymptotic regime. The results are specialized to three important cases: (1) the pure nugget effect model; (2) the linear semivariogram model; and (3) a semivariogram whose sill is equal to the process variance and is attained at a finite distance. The first case corresponds to a white noise process, the second case corresponds to a Wiener process (possibly plus independent white noise), and the third case corresponds to processes called finite-range transition phenomena. Some salient differences in the sample semivariogram’s asymptotic covariance structure are noted for these processes.
