We present a new exponential inequality for degenerate U-statistics. The bound of the log of the hazard is quadratic for small to medium values of the deviation and linear for larger value. We apply this bound to a family of test statistics and provide the key step in a optimality result for adaptive tests (Bickel and Ritov, 1992). ∗Research partially supported by NSA Grant MDA 904-94-H2020 and...

Distance measures between a reference signal and the autoregressive estimate are used as an objective reference for comparing autoregressive order-determining criteria. The distance measures discussed are the rms log spectral deviation, its normalized cepstral distance approximation, the normalized autoregressive transfer function error, the equivalent Itakura distance, and the average squared ...