Estimating a Polya frequency function$_2$
By Jayanta Kumar Pal, Michael Woodroofe, Mary C. Meyer. 2007
59 citations recorded by the source corpus.
We consider the non-parametric maximum likelihood estimation in the class of Polya Frequency functions, viz. the densities with a concave logarithm. This is a subclass of unimodal densities and fairly rich in general. The NPMLE is shown to be the solution to a convex programming problem in the Euclidean space and an algorithm is devised similar to the Iterative Convex Minorant algorithm by Jongbleod (1999). The estimator achieves Hellinger consistency when the true density is a PFF itself.
Subfields: Artificial Intelligence, Finance, Signal Processing
View Paper: https://www.semanticscholar.org/paper/473d900fd6c4cbf1301b5d13234d30c77d45a9c0
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In Artificial Intelligence
- Richard J. Samworth
- Arlene K. H. Kim
- M. Stewart
- Madeleine Cule
- Roger W. Koenker
- Lauren Hannah
- David B. Dunson
- Yining Chen
In Finance
In Signal Processing
Citations in the corpus
- QUASI-CONCAVE DENSITY ESTIMATION (2010, background): “Recently, Rufibach and D¨umbgen (2006) and Pal, Woodroofe, and Meyer (2006) , investigated an earlier proposal of Eggermont and LaRiccia (2001) to estimate logconcave probability densities via maximum likelihood.”
- Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, background): “Walther (2002), D¨umbgen and Rufibach (2007) and Pal et al. (2007) have proved the existence and uniqueness of the log-concave maximum likelihood estimator in one dimension and D¨umbgen and Rufibac h (2007), Pal et al. (2007) and Balabdaoui et al. (2008) have studied its theoretical properties.”
- Global rates of convergence in log-concave density estimation (2014, background): “; Cule, Gramacy and Samworth, 2009); see also Koenker and Mizera (2010) for an alternative approximation approach based on interior point methods. On the theoretical side, through a series of papers (Pal, Woodroofe, and Meyer, 2007; D¨umbgen and Rufibach, 2009; Seregin and Wellner, 2010; Schuhmacher ”