Estimating the asymptotic variance of generalized L-statistics

Mary E. Putt; Vernon M. Chinchilli

doi:10.1081/STA-120003650

Estimating the asymptotic variance of generalized L-statistics

Mary E. Putt
, Vernon M. Chinchilli

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

Abstract

Strong convergence of the estimated asymptotic variance (σ²(T_a(H_N))) of generalized L-statistics is demonstrated for smooth and discrete weighting functions. For smooth weighting functions that are trimmed, such as the 25%-trimmed mean, and for discrete functions, such as the median, minimal conditions are required for strong convergence of σ²(T_a(H_N)). In a simulation study, σ²(T_a(H_N)) for the trimmed mean, but not the median, appeared to converge to the sample variance of the statistic for samples from three distributions (normal, contaminated normal and Cauchy). For the smallest sample in the study (n = 16), σ²(T_a(H_N)) tended to underestimate the sample variance of the GL-statistics.

Original language	English (US)
Pages (from-to)	733-751
Number of pages	19
Journal	Communications in Statistics - Theory and Methods
Volume	31
Issue number	5
DOIs	https://doi.org/10.1081/STA-120003650
State	Published - May 2002

All Science Journal Classification (ASJC) codes

Statistics and Probability

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10.1081/STA-120003650

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title = "Estimating the asymptotic variance of generalized L-statistics",

abstract = "Strong convergence of the estimated asymptotic variance (σ2(Ta(HN))) of generalized L-statistics is demonstrated for smooth and discrete weighting functions. For smooth weighting functions that are trimmed, such as the 25\%-trimmed mean, and for discrete functions, such as the median, minimal conditions are required for strong convergence of σ2(Ta(HN)). In a simulation study, σ2(Ta(HN)) for the trimmed mean, but not the median, appeared to converge to the sample variance of the statistic for samples from three distributions (normal, contaminated normal and Cauchy). For the smallest sample in the study (n = 16), σ2(Ta(HN)) tended to underestimate the sample variance of the GL-statistics.",

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AU - Putt, Mary E.

AU - Chinchilli, Vernon M.

PY - 2002/5

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N2 - Strong convergence of the estimated asymptotic variance (σ2(Ta(HN))) of generalized L-statistics is demonstrated for smooth and discrete weighting functions. For smooth weighting functions that are trimmed, such as the 25%-trimmed mean, and for discrete functions, such as the median, minimal conditions are required for strong convergence of σ2(Ta(HN)). In a simulation study, σ2(Ta(HN)) for the trimmed mean, but not the median, appeared to converge to the sample variance of the statistic for samples from three distributions (normal, contaminated normal and Cauchy). For the smallest sample in the study (n = 16), σ2(Ta(HN)) tended to underestimate the sample variance of the GL-statistics.

AB - Strong convergence of the estimated asymptotic variance (σ2(Ta(HN))) of generalized L-statistics is demonstrated for smooth and discrete weighting functions. For smooth weighting functions that are trimmed, such as the 25%-trimmed mean, and for discrete functions, such as the median, minimal conditions are required for strong convergence of σ2(Ta(HN)). In a simulation study, σ2(Ta(HN)) for the trimmed mean, but not the median, appeared to converge to the sample variance of the statistic for samples from three distributions (normal, contaminated normal and Cauchy). For the smallest sample in the study (n = 16), σ2(Ta(HN)) tended to underestimate the sample variance of the GL-statistics.

UR - https://www.scopus.com/pages/publications/34548155506

UR - https://www.scopus.com/pages/publications/34548155506#tab=citedBy

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DO - 10.1081/STA-120003650

M3 - Article

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SN - 0361-0926

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SP - 733

EP - 751

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 5

ER -

Estimating the asymptotic variance of generalized L-statistics

Abstract

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