6533b861fe1ef96bd12c44ed
RESEARCH PRODUCT
Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model
Angelina RocheS. Valère Bitseki Pendasubject
Statistics and ProbabilityKernel density estimationadaptive estimationNonparametric kernel estimation01 natural sciences010104 statistics & probability[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]0502 economics and businessbinary treesApplied mathematicsbifurcating autoregressive processes0101 mathematics[MATH]Mathematics [math]050205 econometrics MathematicsBinary treeStationary distributionMarkov chainStochastic processModel selection05 social sciencesEstimator[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Adaptive estimatorStatistics Probability and UncertaintyGoldenshluger-Lepski methodologydescription
International audience; We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain onRd. 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 Statistics3: 1608-1632). Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty. Finally, we investigate the performance of the method by simulation studies and application to real data.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-07-15 |