Bootstrap inference on the Behrens–Fisher-type problem for the skew-normal population under dependent samples

Ye, Rendao; Fang, Bingni; Wang, Zhongchi; Luo, Kun; Ge, Wenting

doi:10.1080/03610926.2021.1980045

Cited by 1 publication

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References 34 publications

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“…Classical theorems of information theory considered the obtained additional properties of unbiased location parameter estimators. However, these theorems could be applied to other estimators, such as Bayesian [22] (as long as the prior pdf density is known), shrinkage [23], or bootstrap-based [24] ones. The assumption of the sample that came from a multivariate skew-normal distribution is too strong and not always applicable in the real world, so the properties revised here could be extended to more complex densities, for example, those that assess bimodality and heavy tails in data [7,11,13,19].…”

Section: Discussionmentioning

confidence: 99%

Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings

Contreras-Reyes

2022

Entropy

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In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean’s estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter (μ) estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for μ are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds.

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Section: Discussionmentioning

confidence: 99%

Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings

Contreras-Reyes

2022

Entropy

View full text Add to dashboard Cite

show abstract

Bootstrap inference on the Behrens–Fisher-type problem for the skew-normal population under dependent samples

Cited by 1 publication

References 34 publications

Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings

Information–Theoretic Aspects of Location Parameter Estimation under Skew–Normal Settings

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