When the value of the population mean μ0 is known, in order to construct approximate intervals for the population variance σ20 , we may use the normal approximation of the standard estimates of σ20 or that of the Zhang's estimator σ020. Otherwise, we may use the empirical likelihood method. In this case, if we don't employ a restriction about μ0, we obtain the empirical likelihood ratio statistic for σ20, lE (σ2 0). While, if we impose a constraint about the mean, we have the modified empirical likelihood ratio statistic, lmE (σ20). Both of them have an asymptotic X 21 distribution. We prove that the error in a X 21 approximation of the distribution of lm E (σ20) is of order O(n-1) like that of lE (σ 20). In addition, by a simulation study we analyze the effect of the population coefficients of skewness and kurtosis on the distributions of the analyzed pivots.

Confidence intervals for population variance with known mean / G. Diana, C. Tommasi. - In: METRON. - ISSN 0026-1424. - 1:2(1999), pp. 37-50.

### Confidence intervals for population variance with known mean

#### Abstract

When the value of the population mean μ0 is known, in order to construct approximate intervals for the population variance σ20 , we may use the normal approximation of the standard estimates of σ20 or that of the Zhang's estimator σ020. Otherwise, we may use the empirical likelihood method. In this case, if we don't employ a restriction about μ0, we obtain the empirical likelihood ratio statistic for σ20, lE (σ2 0). While, if we impose a constraint about the mean, we have the modified empirical likelihood ratio statistic, lmE (σ20). Both of them have an asymptotic X 21 distribution. We prove that the error in a X 21 approximation of the distribution of lm E (σ20) is of order O(n-1) like that of lE (σ 20). In addition, by a simulation study we analyze the effect of the population coefficients of skewness and kurtosis on the distributions of the analyzed pivots.
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Edgeworth expansion; Empirical likelihood
1999
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/21927`
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