content_image/305951.jpg content_image/305950.jpg content_image/305948.jpg content_image/305949.jpg
Define (as in (10)) 

<img src='content_image/305951.jpg'>

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 

<img src='content_image/305950.jpg'>

<img src='content_image/305948.jpg'>

<img src='content_image/305949.jpg'>

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. 

