On a crossroad of resampling plans : bootstrapping elementary symmetric polynomials

We investigate the validity of the bootstrap method for the elementary symmetric polynomials S_n^{(k)={nchoose k^{-1sumsb {1leq i_1 < ...< i_k leq n X_{i_1...X_{i_k of i.i.d. random variables $X_1,dots,X_n$. For both fixed and increasing order $k$, as $ntoinfty$ the cases where mu= {rm E X_1 neq0, the nondegenerate case, and where mu= {rm E X_1=0, the degenerate case, are considered