Define (as in (10)) and correspondingly ˆ k$_{P}$ for the polynomial P with estimated coefficients ˆ P ( i$_{1}$, ..., i$_{p}$, ¯ θ, A ) . Note that k$_{p}$ does not depend on A. Lemma 6.1. For ˆ θ$_{T}$ and ˆ V$_{T}$ that satisfy Assumptions 2.3 and 2.4 moreover if ¯ P ( i$_{1}$, ..., i$_{p}$, ¯ θ ) = 0 , and The result implies that for any polynomial ¯ P with probability approach- ing one the lowest order of homogeneous polynomials entering into ¯ P can be determined and also for each coefficient it can be decided whether it is zero or not with probability approaching 1; each non-zero coefficient can be consistently estimated. Pr ( ˆ P ( i$_{1}$, ..., i$_{p}$, ¯ θ ) = 0 ) → 1 Pr ( ˆ k$_{P}$ = k$_{P}$ ) → 1 . ˆ P ( i$_{1}$, ..., i$_{p}$, ¯ θ, V ) − ¯ P ( i$_{1}$, ..., i$_{p}$, ¯ θ, V ) →$_{p}$ 0 , k$_{P}$ = min 0 ≤ k ≤ $_{m$_{P}$}${ k : ¯ P ( i$_{1}$, ..., i$_{p}$, ¯ θ, A ) = 0 for i$_{1}$ + ... + i$_{p}$ = k } , (31) 36