Sampling experiments and the quandt statistic

Abstract

The distribution of the Quandt likelihood ratio λ_t. for a two-phase regression, has yet to be determined. In particular it is known that-2 log λ_t. is not distributed as chi-square (Quandt; 1960), for unknown switch point.

In this paper we describe sampling experiments which suggest that-log λ_t, has a Pearson Type III distribution, The parameters of the distribution appear to depend not only on the values of the x-vector (Feder; 1968) but also its dimension k.

Keywords:

• regression
• segmented
• likelihood ratio