Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model

  title={Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model},
  author={S. Val{\`e}re Bitseki Penda and Angelina Roche},
  journal={Journal of Nonparametric Statistics},
  pages={535 - 562}
ABSTRACT We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on . Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidths are selected by a method inspired by the works of Goldenshluger and Lepski [(2011), ‘Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality’, The Annals of Statistics 3: 1608–1632… 

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