When the nonparametric identification result is interpreted to support possible wider applicability, when estimation is in fact based on a parametric model the question arises as to which nonparametric models are close to a model misspecified as parametric. This question may be posed e.g. for the analysis of Cunha et al 2010 who use Gaussian and mixed Gaussian distri- butions in estimation. Is there some meaningful nonparametric class that includes the Gaussian where observationally close models imply closeness of latent factors? 

Define a class of generalized functions Φ( B, Λ , m, V ) ⊂ S ′ for some pos- itive constant B and matrix Λ; a generalized function b ∈ Φ( B, Λ , m, V ) if there exists a function ¯ b ( ζ ) ∈ Φ( m, V ) with support in ‖ ζ ‖ > B such that also ¯ b ( ζ ) − 1 ∈ Φ( m, V ) and b · I ( ‖ ζ ‖ > B ) = ¯ b ( ζ ) exp ( − ζ $^{′}$Λ ζ ) . Note that a lin- ear combination of functions in Φ( B, Λ , m, V ) belongs to the same class. For a sequence of b$_{n}$ ∈ Φ( B, Λ , m, V ) to converge to zero as generalized functions it is necessary that the corresponding ¯ b$_{n}$ converge to zero (a.e.). 

Assumption 4. γ ∈ Φ( B, Λ$_{γ}$ , m, V ); φ ∈ Φ( B, Λ$_{φ}$ , m, V ) . 

If this assumption holds ε$_{1}$ = γ · φ ∈ Φ( B, Λ$_{γ}$ +Λ$_{φ}$ , 2 m, V $^{2}$) and ε$_{2}$ = γ ′ k · φ also is in Φ( B, Λ$_{γ}$ + Λ$_{φ}$ , 2 m, V $^{2}$) . 

## Theorem 2 Under conditions of Theorem 1 and the Assumption 4 applying to generalized functions ε$_{i,n}$, i = 1 , 2 if ε$_{i,n}$ → ε$_{i}$ in S $^{′}$, then the corresponding solutions γ$_{n}$ given by (9) or (10) converge to γ in S $^{′}$. 

Proof. From the conditions of the theorem η$_{i,n}$ = ε$_{i,n}$ − ε$_{i}$ converges in S ′ 

