Diagonal correction for a quadratic density derivative estimate
= Diagonal correction for a quadratic density derivative estimate
{title2=$\widehat J_{2,b}=\frac1{n(n-1)b^5}\sum_{i\ne j}A((X_i-X_j)/b)$}
For $A(v)=\int L^{\prime\prime}(t)L^{\prime\prime}(t+v)\,dt$, this <U-statistic> has <expectation> $\|L_b*f^{\prime\prime}\|_2^2$. It removes the diagonal term $\|L^{\prime\prime}\|_2^2/(nb^5)$ from the integral of a squared <second derivative kernel density estimator>, but leaves smoothing <bias of an estimator>.