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

A semi-parametric model for ice accumulation rate and temperature based on Antarctic ice core data