  For a wide class of monotonic functions $f$, we develop a Chernoff-style
concentration inequality for quadratic forms $Q_f \sim \sum\limits_{i=1}^n
f(\eta_i) (Z_i + \delta_i)^2$, where $Z_i \sim N(0,1)$. The inequality is
expressed in terms of traces that are rapid to compute, making it useful for
bounding p-values in high-dimensional screening applications. The bounds we
obtain are significantly tighter than those that have been previously
developed, which we illustrate with numerical examples.
