SOME PROPERTIES OF AUTOREGRESSIVE ESTIMATES FOR PROCESSES WITH MIXED SPECTRA

Abstract. A formal justification for the use of the method of autoregressive spectral estimation for time series consisting of a sinusoidal signal in additive noise is given in this paper. The analytical properties of the autoregressive approximation to the generalized spectral density of the process are presented, and the operational characteristics of the statistical estimation procedure are discussed. In particular, strong convergence of the autoregressive parameters and the autoregressive transfer function approximation is shown.     

A cautionary tale about Weibull analysis [reliability estimation]

This paper makes three points about possible perils of unguarded fitting of Weibull distributions to data: (1) bias is introduced by incomplete data, which may have counter-intuitive effects; (2) bias is introduced into percentile estimates by using regression on log-transformed variables to fit the Weibull parameters, particularly if the percentile to be predicted lies outside the range of the data; and (3) the amount of variation associated with such estimates can be very substantial. A partial solution to the incomplete data problem using simulation is presented, and the maximum likelihood approach to parameter estimation and its advantages relative to regression estimation are explained. The problem arose in predicting life expectancy of long-lived components subject to natural aging which cannot be investigated using accelerated testing and for which the collection of data provides an incomplete life record