Asymptotic behavior of the Grenander estimator at density flat regions

Canadian Journal of Statistics

Volumn 27, Issue 3, 1999, Pages 557-566

  Carolan, Chris ^a   Dykstra, Richard ^b  

^a EAST CAROLINA UNIVERSITY   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Brownian motion; Isotonic regression; Least concave majorant; Monotone density estimation; Unimodal density estimation

Indexed keywords

EID: 0033263797     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316111     Document Type: Article

References (8)

1. P. Billingsley (1968). Convergence of Probability Measures. Wiley, New York.
2. U. Grenander (1956). On the theory of mortality measurement, Part II. Skandinavisk Aktuarietidskrift, 39, 125-153.
3. P. Groeneboom (1983). The concave majorant of Brownian motion. The Annals of Probability, 11, 1016-1027.
4. P. Groeneboom (1986). In Some Current Developments in Density Estimation, CWI Monographs, Amsterdam, vol. 1, pp. 163-192.
5. J. Komlós, P. Major & G. Tusnády (1975). An approximation of partial sums of independent r.v.'s and the sample d.f. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 32, 111-131.
6. B. L. S. Prakasa Rao (1969). Estimation of a unimodal density. Sankhyā Series A, 31, 23-36.
7. T. Robertson, F. T. Wright & R. L. Dykstra (1988). Order Restricted Inference. Wiley, New York.
8. G. R. Shorrack & J. A. Wellner (1986). Empirical Processes with Applications to Statistics. Wiley, New York.