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Conditionally identically distributed species sampling sequences
- Source :
- Bassetti, Federico ; Crimaldi, Irene ; Leisen, Fabrizio (2009) Conditionally identically distributed species sampling sequences. [Preprint], Bassetti, Federico ; Crimaldi, Irene ; Leisen, Fabrizio (2008) Conditionally identically distributed species sampling sequences. [Preprint]
- Publication Year :
- 2009
-
Abstract
- Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species Sampling Sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, a class of generalized species sampling sequences that are conditionally identically distributed is introduced and studied: the Generalized Ottawa sequences (GOS). This class contains a '`randomly reinforced'' version of the P\'olya urn and of the Blackwell-MacQueen urn scheme. For the empirical means and the predictive means of a GOS, we prove two convergence results toward suitable mixtures of Gaussian distributions. The first one is in the sense of stable convergence and the second one in the sense of almost sure conditional convergence. In the last part of the paper we study the length of the partition induced by a GOS at time $n$, i.e. the random number of distinct values of a GOS until time $n$. Under suitable conditions, we prove a strong law of large numbers and a central limit theorem in the sense of stable convergence. All the given results in the paper are accompanied by some examples.
- Subjects :
- Statistics and Probability
Discrete mathematics
Independent and identically distributed random variables
Class (set theory)
Sequence
Applied Mathematics
Probability (math.PR)
010102 general mathematics
Sampling (statistics)
species sampling sequence
conditional identity in distribution
stable convergence
almost sure conditional convergence
generalized Polya urn
Type (model theory)
01 natural sciences
Identity (music)
Combinatorics
010104 statistics & probability
Distribution (mathematics)
MAT/06 Probabilità e statistica matematica
FOS: Mathematics
0101 mathematics
Random variable
Mathematics - Probability
Mathematics
Subjects
Details
- Language :
- Italian
- Database :
- OpenAIRE
- Journal :
- Bassetti, Federico ; Crimaldi, Irene ; Leisen, Fabrizio (2009) Conditionally identically distributed species sampling sequences. [Preprint], Bassetti, Federico ; Crimaldi, Irene ; Leisen, Fabrizio (2008) Conditionally identically distributed species sampling sequences. [Preprint]
- Accession number :
- edsair.doi.dedup.....0a0aa23098afd83c37a656b0981799fa