What question did this study set out to answer?

To derive the minimum variance unbiased estimator of population variance when observations have undergone a Gaussian-inducing transformation.

August 1, 1968The Annals of Mathematical StatisticsOpen Access

The Estimation of Variances After Using a Gaussianating Transformation

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Authors

MHM. H. HoyleUniversity of Exeter

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Implication

Methodological study derives minimum variance unbiased estimators of variance under normalizing transformations, improving statistical inference for skewed phenomena such as cloud seeding.

Key Points

To derive the minimum variance unbiased estimator of population variance when observations have undergone a Gaussian-inducing transformation.
Applied a Taylor series expansion of the transformation function around the mean rather than the origin.
Utilized the Neyman and Scott framework assuming the transformed variable follows a normal distribution with entire function characteristics of second order or less.
Verified theoretical estimators against established logarithmic transformation solutions developed by Finney, Sichel, and Meulenberg.
Obtained closed-form expressions for the minimum variance unbiased estimator of the variance on the original scale.
Derived the minimum variance unbiased estimator for the variance of the estimated mean across specific transformation families.
Demonstrated that expanding around the mean provides consistent variance estimators that align with classical solutions for log-normal variables.

Cite This Study

M. H. Hoyle (1968) studied this question.

synapsesocial.com/papers/6aa70c6a4bfde8663e6df739 https://doi.org/10.1214/aoms/1177698237

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Implication

Methodological study derives minimum variance unbiased estimators of variance under normalizing transformations, improving statistical inference for skewed phenomena such as cloud seeding.

The Estimation of Variances After Using a Gaussianating Transformation

Discussion

Member takes

Implication

Key Points

Cite This Study

The Estimation of Variances After Using a Gaussianating Transformation

Discussion

Member takes

Implication

Key Points

Cite This Study

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