On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Menendez, Patricia; Ghosh, Sucharita; Kuensch, Hans R.; Tinner, Willy (2013). On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series. Journal of Nonparametric Statistics, 25(4), pp. 765-785. Taylor & Francis 10.1080/10485252.2013.826357

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Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

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