  We present an extensive frequentist analysis of the one-point statistics
(number, mean, variance, skewness and kurtosis) and two-point correlation
functions determined for the local extrema of the cosmic microwave background
temperature field observed in five-years of Wilkinson Microwave Anisotropy
Probe (WMAP) data. Application of a hypothesis test on the one-point statistics
indicates a low-variance of hot and cold spots in all frequency bands of the
WMAP data. The consistency of the observations with Gaussian simulations of the
the best-fitting cosmological model is rejected at the 95% C.L. outside the
WMAP KQ75 mask and the northern hemispheres in the Galactic and ecliptic
coordinate frames. We demonstrate that it is unlikely that residual Galactic
foreground emission contributes to the observed non-Gaussianities. However, the
application of a high-pass filter that removes large angular scale power does
improve the consistency with the best-fitting cosmological model. Two-point
correlation functions of the local extrema are calculated for both the
temperature pair product (T-T) and spatial pair-counting (P-P). The T-T
observations demonstrate weak correlation on scales below 20 degree and lie
completely below the lower 3-sigma confidence region once various temperature
thresholds are applied to the extrema determined for the KQ75 mask and northern
sky partitions. The P-P correlation structure corresponds to the clustering
properties of the temperature extrema, and provides evidence that it is the
large angular-scale structures, and some unusual properties thereof, that are
intimately connected to the properties of the hot and cold-spots observed in
the WMAP five-year data.

Cosmology and Nongalactic Astrophysics