Summary: Submitted to the Annals of Statistics
SUPPLEMENT TO "KERNEL ESTIMATORS OF
ASYMPTOTIC VARIANCE FOR ADAPTIVE MARKOV
CHAIN MONTE CARLO"
By Yves F. Atchad´e
University of Michigan
This is a supplement to the paper "Kernel estimators of asymp-
totic variance for adaptive Markov Chain Monte Carlo" and contains
the proofs to Theorems 4.1-4.3. For improved readability, we recall
the theorems and their assumptions.
1. Statement of the theorems.
A1 For each , P is phi-irreducible, aperiodic with invariant dis-
tribution . There exists a measurable function V : X [1, ) with
V (x)¯µ(dx, d) < such that for any (0, 1], there exist (0, 1),
C (0, ) such that for any (x, ) X × ,
(x, ·) - (·) V Cn
(x), n 0.