1
|
Lau JW, Cripps E. Thinned completely random measures with applications in competing risks models. BERNOULLI 2022. [DOI: 10.3150/21-bej1361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- John W. Lau
- Department of Mathematics and Statistics, University of Western Australia, Perth, Australia
| | - Edward Cripps
- Department of Mathematics and Statistics, University of Western Australia, Perth, Australia
| |
Collapse
|
2
|
Laverny O, Masiello E, Maume-Deschamps V, Rullière D. Estimation of multivariate generalized gamma convolutions through Laguerre expansions. Electron J Stat 2021. [DOI: 10.1214/21-ejs1918] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Oskar Laverny
- Institut Camille Jordan - ICJ, Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, F-69622 Villeurbanne, France SCOR SE
| | - Esterina Masiello
- Institut Camille Jordan - ICJ, Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, F-69622 Villeurbanne, France
| | - Véronique Maume-Deschamps
- Institut Camille Jordan - ICJ, Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, F-69622 Villeurbanne, France
| | - Didier Rullière
- Mines Saint-Étienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, Institut Henri Fayol, Saint-Etienne, France
| |
Collapse
|
3
|
Buchmann B, Lu KW, Madan DB. Self-decomposability of weak variance generalised gamma convolutions. Stoch Process Their Appl 2020. [DOI: 10.1016/j.spa.2019.02.012] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
4
|
Buchmann B, Lu KW, Madan DB. Weak subordination of multivariate Lévy processes and variance generalised gamma convolutions. BERNOULLI 2019. [DOI: 10.3150/17-bej1004] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
5
|
Subordinators which are infinitely divisible w.r.t. time: Construction, properties, and simulation of max-stable sequences and infinitely divisible laws. LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2019. [DOI: 10.30757/alea.v16-35] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
6
|
Leonenko NN, Taqqu MS, Terdik GH. Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem. Electron J Stat 2018. [DOI: 10.1214/18-ejs1473] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
7
|
James LF. Bayesian Poisson calculus for latent feature modeling via generalized Indian Buffet Process priors. Ann Stat 2017. [DOI: 10.1214/16-aos1517] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
8
|
|
9
|
Buchmann B, Kaehler B, Maller R, Szimayer A. Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing. Stoch Process Their Appl 2017. [DOI: 10.1016/j.spa.2016.10.008] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
10
|
Behme A, Bondesson L. A class of scale mixtures of $\operatorname{Gamma}(k)$-distributions that are generalized gamma convolutions. BERNOULLI 2017. [DOI: 10.3150/15-bej761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
11
|
|
12
|
Gasbarra D, Arjas E, Vehtari A, Slama R, Keiding N. The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective. LIFETIME DATA ANALYSIS 2015; 21:594-625. [PMID: 26067898 DOI: 10.1007/s10985-015-9333-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Accepted: 06/06/2015] [Indexed: 06/04/2023]
Abstract
This paper was inspired by the studies of Niels Keiding and co-authors on estimating the waiting time-to-pregnancy (TTP) distribution, and in particular on using the current duration design in that context. In this design, a cross-sectional sample of women is collected from those who are currently attempting to become pregnant, and then by recording from each the time she has been attempting. Our aim here is to study the identifiability and the estimation of the waiting time distribution on the basis of current duration data. The main difficulty in this stems from the fact that very short waiting times are only rarely selected into the sample of current durations, and this renders their estimation unstable. We introduce here a Bayesian method for this estimation problem, prove its asymptotic consistency, and compare the method to some variants of the non-parametric maximum likelihood estimators, which have been used previously in this context. The properties of the Bayesian estimation method are studied also empirically, using both simulated data and TTP data on current durations collected by Slama et al. (Hum Reprod 27(5):1489-1498, 2012).
Collapse
Affiliation(s)
- Dario Gasbarra
- Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.
| | - Elja Arjas
- Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.
| | - Aki Vehtari
- Department of Computer Science, Aalto University, Espoo, Finland.
| | - Rémy Slama
- French Institute of Health and Medical Research, Team of Environmental Epidemiology applied to Reproduction and Respiratory Health, Inserm-Univ. Grenoble Alpes, Grenoble, France.
| | - Niels Keiding
- Department of Public Health, University of Copenhagen, Copenhagen, Denmark.
| |
Collapse
|
13
|
Burridge J, Kuznetsov A, Kwaśnicki M, Kyprianou A. New families of subordinators with explicit transition probability semigroup. Stoch Process Their Appl 2014. [DOI: 10.1016/j.spa.2014.06.005] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
14
|
|
15
|
|
16
|
|
17
|
Bondesson L. A Class of Probability Distributions that is Closed with Respect to Addition as Well as Multiplication of Independent Random Variables. J THEOR PROBAB 2013. [DOI: 10.1007/s10959-013-0523-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
18
|
Behme A, Maejima M, Matsui M, Sakuma N. Distributions of exponential integrals of independent increment processes related to generalized gamma convolutions. BERNOULLI 2012. [DOI: 10.3150/11-bej382] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
19
|
|
20
|
Keller-Ressel M, Mijatović A. On the limit distributions of continuous-state branching processes with immigration. Stoch Process Their Appl 2012. [DOI: 10.1016/j.spa.2012.03.012] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
21
|
Madan D, Yor M. Moments of Wiener integrals for subordinators. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2012. [DOI: 10.1214/ecp.v17-2206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Marc Yor
- Université Pierre et Marie Curie
| |
Collapse
|
22
|
Vakeroudis S, Yor M. Some infinite divisibility properties of the reciprocal of planar Brownian motion exit time from a cone. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2012. [DOI: 10.1214/ecp.v17-2090] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Marc Yor
- Université Pierre et Marie Curie and
| |
Collapse
|
23
|
|
24
|
|
25
|
FAVARO STEFANO, PRÜNSTER IGOR, WALKER STEPHENG. On a Class of Random Probability Measures with General Predictive Structure. Scand Stat Theory Appl 2010. [DOI: 10.1111/j.1467-9469.2010.00702.x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
26
|
|
27
|
Aoyama T, Lindner A, Maejima M. A New Family of Mappings of Infinitely Divisible Distributions Related to the Goldie-Steutel-Bondesson Class. ELECTRON J PROBAB 2010. [DOI: 10.1214/ejp.v15-791] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
28
|
Lijoi A, Prünster I. Distributional properties of means of random probability measures. STATISTICS SURVEYS 2009. [DOI: 10.1214/09-ss041] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
29
|
Nikeghbali A, Yor M. The Barnes $G$ function and its relations with sums and products of generalized Gamma convolution variables. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2009. [DOI: 10.1214/ecp.v14-1488] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
30
|
Perez Abreu V, Sakuma N. Free Generalized Gamma Convolutions. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2008. [DOI: 10.1214/ecp.v13-1413] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
31
|
Kyprianou A, Rivero V. Special, conjugate and complete scale functions for spectrally negative Lévy processes. ELECTRON J PROBAB 2008. [DOI: 10.1214/ejp.v13-567] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|