  In this paper, we present a semiparametric model for describing the effect of
temperature on Antarctic ice accumulation on a paleoclimatic time scale. The
model is motivated by sharp ups and downs in the rate of ice accumulation
apparent from ice core records, which are synchronous with movements of
temperature. We prove strong consistency of the estimators under reasonable
conditions. We conduct extensive simulations to assess the performance of the
estimators and bootstrap based standard errors and confidence limits for the
requisite range of sample sizes. Analysis of ice core data from two Antarctic
locations over several hundred thousand years show a reasonable fit. The
apparent accumulation rate exhibits a thinning pattern that should facilitate
the understanding of ice condensation, transformation and flow over the ages.
There is a very strong linear relationship between temperature and the apparent
accumulation rate adjusted for thinning.
