We develop a needlet approach to estimate the amplitude of general (including
non-separable) bispectra and trispectra in the cosmic microwave background, and
apply this to the WMAP 9-year data. We obtain estimates for the `orthogonal'
bispectrum mode, yielding results which are consistent with the WMAP 7-year
data. We do not observe the frequency-dependence suggested by the WMAP team's
analysis of the 9-year data. We present 1-σ constraints on the `local'
trispectrum shape \gnl/10^5= -4.1\pm 2.3, the `c1' equilateral model
\gnl^{c_1}/10^6= -0.8\pm 2.9, and the constant model \gnl^{\rm{const}}/10^6=
-0.2\pm 1.8, together with a 95% confidence-level upper bound on the
multifield local parameter \taunl<22000. We estimate the bias on these
parameters produced by point sources. The techniques developed in this paper
should prove useful for other datasets such as Planck.Comment: 21 pages - matches published versio
