**Preprint series:**
06-14, Preprints

**The paper is published:**
Siberian Mathematical Journal, Vol. 47, No. 6, pp. 1154-1166, 2006

**MSC:**- 62H10 Distribution of statistics
- 62E20 Asymptotic distribution theory

**Abstract:** We get computable error bound of order $O(n^{-1})$ for

chi-squared with 1 degree of freedom approximation of

transformed chi-squared random variable with $n$ degrees of

freedom. The result is applied for likelihood ratio statistics

in multivariate case.

**Keywords:** *Computable error bound, chi-squared approximation, likelihood ratio statistics, transformation of random variables*

**Upload:** 2006-04-27-04-27

**Update:** 2006

The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.