Asymptotic normality in Monte Carlo integration

Author:
Masashi Okamoto

Journal:
Math. Comp. **30** (1976), 831-837

MSC:
Primary 65C05

DOI:
https://doi.org/10.1090/S0025-5718-1976-0421029-8

MathSciNet review:
0421029

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators and based on 2*N* and 4*N* observations, respectively, of the function. He also considered estimators and of the variances of and , respectively. This paper shows that all these estimators are asymptotically normally distributed as *N* tends to infinity.

**[1]**S. HABER, "A modified Monte-Carlo quadrature,"*Math. Comp.*, v. 20, 1966, pp. 361-368. MR**35**# 1178. MR**0210285 (35:1178)****[2]**S. HABER, "A modified Monte-Carlo quadrature. II,"*Math. Comp.*, v. 21, 1967, pp. 388-397. MR**38**# 2922. MR**0234606 (38:2922)****[3]**J. M. HAMMERSLEY & K. W. MORTON, "A new Monte Carlo technique: Antithetic variates,"*Proc. Cambridge Philos. Soc.*, v. 52, 1956, pp. 449-475. MR**18**, 336. MR**0080984 (18:336e)****[4]**T. KITAGAWA, "Random integrations,"*Bull. Math. Statist.*, v. 4, 1950, pp. 15-21. MR**14**, 457. MR**0051289 (14:457a)****[5]**M. LOÈVE,*Probability Theory*, 3rd ed., Van Nostrand, Princeton, N.J., 1963. MR**34**# 3596. MR**0203748 (34:3596)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65C05

Retrieve articles in all journals with MSC: 65C05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0421029-8

Keywords:
Monte Carlo integration,
Haber's estimators,
asymptotic normality,
Lyapunov condition

Article copyright:
© Copyright 1976
American Mathematical Society