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dard normal random variable. Further, as long as 2 θ$_{pj}$ ∈ Ω$_{εη}$ for j ≤ r, ˜ λ$_{pi}$ consid- ered as a function of λ$_{i}$ is continuous on λ$_{i}$ ∈ supp ˆ F λ p for sufficiently large p, a.s.. Hence, the empirical distribution of ˜ λ$_{i}$ converges. Moreover, ˜ λ$_{max}$ = max$_{i}$$_{=1}$$_{,...,p}$( ˜ λ$_{pi}$ ) and ˜ λ$_{min}$ = min$_{i}$$_{=1}$$_{,...,p}$( ˜ λ$_{pi}$ ) a.s. converge to finite real numbers. Now, for τ such that | τ | < √ p/ (2 ˜ λ$_{max}$ ) , we have r p 

<img src='content_image/318893.jpg'>

for sufficiently large p, a.s.. Using this inequality, we get, for sufficiently large p and any positive t such that β$_{1}$r $^{2}$M + t < √ p/ (2 ˜ λ$_{max}$ ) , 

<img src='content_image/318894.jpg'>

Setting t = M ′ 4 ˜ λ 2 max − β$_{1}$r $^{2}$M (here we assume that M and M ′ are such that t satisfies the above requirements), we get 

Replacing γ ( k,s ) p 2 by − γ ( k,s ) p 2 in the above derivations and combining the result with the above inequality, we get 

When k = s, following a similar line of arguments, we obtain 

and thus, for sufficiently large p, 

<img src='content_image/318895.jpg'>

<img src='content_image/318896.jpg'>

<img src='content_image/318897.jpg'>

<img src='content_image/318898.jpg'>

