 
Summary: Submitted to the Annals of Statistics
arXiv: math.PR/0911.1164
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 4.14.3. For improved readability, we recall
the theorems and their assumptions.
1. Statement of the theorems.
A1 For each , P is phiirreducible, 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 × ,
(1.1) Pn
(x, ·)  (·) V Cn
V
(x), n 0.
