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Gaussian white noise models have become increasingly popular as a canonical type of model in which to address certain statistical problems. We briefly review some statistical problems formulated in terms of Gaussian "white noise", and pursue a particular group of problems connected with the estimation of monotone functions. These new results are related to the recent development of likelihood ratio tests for monotone functions studied by [2]. We conclude with some open problems connected with multivariate interval censoring.

Gaussian white noise models: some results for monotone functions