Edgeworth expansions for sampling without replacement from finite populations

G. Jogesh Babu; Kesar Singh

doi:10.1016/0047-259X(85)90084-3

Edgeworth expansions for sampling without replacement from finite populations

G. Jogesh Babu, Kesar Singh

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be expressed in a certain linear plus quadratic form. An application of the results to the theory of bootstrap is mentioned. A one-term expansion is also proved in the univariate lattice case.

Original language	English (US)
Pages (from-to)	261-278
Number of pages	18
Journal	Journal of Multivariate Analysis
Volume	17
Issue number	3
DOIs	https://doi.org/10.1016/0047-259X(85)90084-3
State	Published - Dec 1985

All Science Journal Classification (ASJC) codes

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/0047-259X(85)90084-3

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@article{3aec15343de143b19d1a84988c4b4002,

title = "Edgeworth expansions for sampling without replacement from finite populations",

abstract = "The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be expressed in a certain linear plus quadratic form. An application of the results to the theory of bootstrap is mentioned. A one-term expansion is also proved in the univariate lattice case.",

author = "Babu, {G. Jogesh} and Kesar Singh",

note = "Funding Information: Received November 8, 1982; revised March 30, 1984. AMS 1970 subject classifications: 62E20, 62DOS. Key words and phrases: edgeworth expansions, sampling without replacement, weak convergence, characteristic functions, ratio estimators, lattice distributions, rank tests. * On leave from the Indian Statistical Institute. + Research supported by NSF Grants MCS-81-02341 and MCS-8301082.",

year = "1985",

month = dec,

doi = "10.1016/0047-259X(85)90084-3",

language = "English (US)",

volume = "17",

pages = "261--278",

journal = "Journal of Multivariate Analysis",

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T1 - Edgeworth expansions for sampling without replacement from finite populations

AU - Babu, G. Jogesh

AU - Singh, Kesar

N1 - Funding Information: Received November 8, 1982; revised March 30, 1984. AMS 1970 subject classifications: 62E20, 62DOS. Key words and phrases: edgeworth expansions, sampling without replacement, weak convergence, characteristic functions, ratio estimators, lattice distributions, rank tests. * On leave from the Indian Statistical Institute. + Research supported by NSF Grants MCS-81-02341 and MCS-8301082.

PY - 1985/12

Y1 - 1985/12

N2 - The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be expressed in a certain linear plus quadratic form. An application of the results to the theory of bootstrap is mentioned. A one-term expansion is also proved in the univariate lattice case.

AB - The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be expressed in a certain linear plus quadratic form. An application of the results to the theory of bootstrap is mentioned. A one-term expansion is also proved in the univariate lattice case.

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JF - Journal of Multivariate Analysis

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ER -

Edgeworth expansions for sampling without replacement from finite populations

Abstract

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