Estimation of integrals with respect to infinite measures using regenerative sequences
2015 ◽
Vol 52
(04)
◽
pp. 1133-1145
◽
Keyword(s):
Letfbe an integrable function on an infinite measure space (S,, π). We show that if aregenerative sequence{Xn}n≥0with canonical measureπcould be generated then a consistent estimator of λ ≡ ∫Sfdπ can be produced. We further show that under appropriate second moment conditions, a confidence interval for λ can also be derived. This is illustrated with estimating countable sums and integrals with respect to absolutely continuous measures on ℝdusing a simple symmetric random walk on ℤ.
2015 ◽
Vol 52
(4)
◽
pp. 1133-1145
◽
1967 ◽
Vol 18
(5)
◽
pp. 818-818
◽
1980 ◽
Vol 87
(3)
◽
pp. 383-392
1982 ◽
Vol 2
(3-4)
◽
pp. 417-438
◽
1981 ◽
Vol 81
(1)
◽
pp. 27-30
◽
1983 ◽
Vol 87
(3)
◽
pp. 475-475
2009 ◽
Vol 19
(01)
◽
pp. 409-417
◽
2011 ◽
Vol 261
(10)
◽
pp. 2877-2889
◽
Keyword(s):
2006 ◽
Vol 06
(02)
◽
pp. 245-253
◽