Identification in Parametric Models

Identification of parameters by the distribution of the minimum: The tri-variate normal case with negative correlations

“…Let us point out that when is identified in the sense of the present paper, is globally (and therefore, locally) identified in the sense of [7]. It may be noted that local identification, as remarked in the middle of p. 147 in [7], is difficult to apply in practice and, as such, not very useful.…”

“…If N( ) happens to be all of S, then is called globally identified in [7]. Let us point out that when is identified in the sense of the present paper, is globally (and therefore, locally) identified in the sense of [7].…”

“…Let f (x) be the value of the density of min {X 1 , X 2 , X 3 }, when the unknown tri-variate normal has zero means and parameter vector ≡ 2 1 , 2 2 , 2 3 , 12 , 13 , 23 . Then, according to Definition 2 in [7], the parameter vector is locally identified if there is an open set N( ) containing in 1) such that the following holds:…”

“…It is relevant to mention the (statistical) identification of the parameters defined in [7]. Let f (x) be the value of the density of min {X 1 , X 2 , X 3 }, when the unknown tri-variate normal has zero means and parameter vector ≡ 2 1 , 2 2 , 2 3 , 12 , 13 , 23 .…”

Logistic response models with item interactions

“…Identifiability of the parameters depends on the rank of I . A point in parameter space is locally identifiable if I is non‐singular (Rothenberg, 1971; Wansbeek & Meijer, 2000; Bekker & Wansbeek, 2003). A necessary identifiability condition is that the vector 1 is not in the column space of A and B .…”