Measuring Period of Human Biological Clock: Infill Asymptotic Analysis of Harmonic Regression Parameter Estimates

Abstract

Publisher Summary This chapter examines the infill asymptotic behavior of the maximum likelihood estimates of a harmonic regression plus continuous first-order autoregressive noise model in order to determine the precision with which the intrinsic period of the human biological clock can be estimated. It is found that the intrinsic period of the human biological clock is closer to 24 h instead of 25 h and that it can be estimated with a standard error of 1.4 to 2.1 min. It is shown that for the forced de-synchrony (FD) protocol, the intrinsic period of the clock can be estimated in a computationally efficient manner with near-maximal precision from a sampled series containing less than 2% of the original temperature data. The relation of the results to the classic formulas for the asymptotic covariance matrix of the harmonic regression parameter estimates is elaborated. The implications of these results for determining the precision with which the period of the human biological clock may be estimated are studied in an analysis of core temperature data from five male subjects monitored under FD.