Can someone provide me hints as to where to attack part (c) from? I tried using results from U-statistics, but having trouble for connecting distribution of $$L_n(\hat{\theta}_n) - E[1\{Y_i > Y_j\} \log P_\theta (Y_i > Y_j|X_i,X_j)]$$ to distribution of $$ \hat{\theta}_n. $$ Others were straightforward.