• Corpus ID: 235266105

Kernel based Dirichlet sequences

@inproceedings{Berti2021KernelBD,
  title={Kernel based Dirichlet sequences},
  author={Patrizia Berti and Emanuela Dreassi and Fabrizio Leisen and Luca Pratelli and Pietro Rigo},
  year={2021}
}

• Patrizia Berti, E. Dreassi, +2 authors Pietro Rigo
• Published 31 May 2021
• Mathematics

. Let X = ( X 1 ,X 2 ,... ) be a sequence of random variables with values in a standard space ( S, B ). Suppose X 1 ∼ ν and P (cid:0) X n +1 ∈ · | X 1 ,...,X n (cid:1) = θν ( · ) + P ni =1 K ( X i )( · ) n + θ a.s. where θ > 0 is a constant, ν a probability measure on B , and K a random probability measure on B . Then, X is exchangeable whenever K is a regular conditional distribution for ν given any sub- σ -field of B . Under this assumption, X enjoys all the main properties of classical Dirichlet sequences, including Sethuraman’s representation, conjugacy property, and convergence in total variation of predictive distributions. If µ is the weak limit of the empirical measures, conditions for µ to be a.s. discrete, or a.s. non-atomic, or µ ≪ ν a.s., are provided. Two CLT’s are proved as well. The first deals with stable convergence while the second concerns total variation distance.