The behavior of the NPMLE of a decreasing density near the boundaries of the support

By V. Kulikov, Hendrik P. Lopuhaä. 2006

53 citations recorded by the source corpus.

We investigate the behavior of the nonparametric maximum likelihood estimator f n for a decreasing density f near the boundaries of the support of f. We establish the limiting distribution of f n (n -α ), where we need to distinguish between different values of 0 < a < 1. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of f at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4f3e52ecfc40cac0ded334beabe1345c44ba8244

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Nonparametric Shape-Restricted Regression (2017, background): “, [10, 83, 138] for detailed discussions on the properties of the LSE for a nonincreasing density near 0).”
Testing equality of functions under monotonicity constraints (2012, background): “ts. Hence, for each j= 0,1,...,J, we have that on the event Sc j both concave majorants diﬀer at t, which implies that they diﬀer on the interval [t−dn−1/3 j ,t+dn −1/3 j ]. According to Lemma 1.3 in [30], this happenswith probability bounded by 8exp(−Cjnd3), where the constant Cj >0 only depends”