Nonparametric Estimation of the CDF and the Plug-In Principle

Konstantin M. Zuev ()
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Konstantin M. Zuev: California Institute of Technology, Department of Computing and Mathematical Sciences

Chapter 4 in Fundamentals of Statistical Inference, 2026, pp 81-98 from Springer

Abstract: Abstract The basic goal of nonparametric inference is to use data X1, . . . ,Xn to infer an unknown quantity of interest θ, while making as few assumptions about as possible. Mathematically, “few assumptions” means that the stochastic model $${\mathcal{F}}$$ F used to model the data is large—so large that it cannot be parameterized by a finite number of parameters. Let’s consider the most general nonparametric model $${\mathcal{F}}$$ F = {all CDFs}, that assumes only that the data is an IID sample from some probability distribution defined by its CDF F. In this chapter, we will focus on one of the central problems in nonparametric statistical inference: estimation of a parameter θ of the distribution F.

Keywords: statistical functionals; plug-in estimates; plug-in principle (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-03848-7_4

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