On improved estimation of the larger location parameter

Lakshmi Kanta Patra; Naresh Garg; Neeraj Misra

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On improved estimation of the larger location parameter

Naresh Garg, Lakshmi Kanta Patra, Neeraj Misra

Statistics Theory · Submitted 25 Sep 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that a natural estimator (analogue of the BLEE of unordered location parameters) is inadmissible, under certain conditions on underlying densities, and propose a dominating estimator.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.31 · human participants 0.06 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.68 · mentions code or data availability 0.03.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

This paper investigates the problem of estimating the larger location parameter of two general location families from a decision-theoretic perspective. In this estimation problem, we use the criteria of minimizing the risk function and the Pitman closeness under a general bowl-shaped loss function. Inadmissibility of a general location and equivariant estimators is provided. We prove that a natural estimator (analogue of the BLEE of unordered location parameters) is inadmissible, under certain conditions on underlying densities, and propose a dominating estimator. We also derive a class of improved estimators using the Kubokawa's IERD approach and observe that the boundary estimator of this class is the Brewster-Zidek type estimator. Additionally, under the generalized Pitman criterion, we show that the natural estimator is inadmissible and obtain improved estimators. The results are implemented for different loss functions, and explicit expressions for the dominating estimators are provided. We explore the applications of these results to for exponential and normal distribution under specified loss functions. A simulation is also conducted to compare the risk performance of the proposed estimators. Finally, we present a real-life data analysis to illustrate the practical applications of the paper's findings.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper investigates the problem of estimating the larger location parameter of two general location families from a decision-theoretic perspective.	contribution 0.56	0.86	0.05	asserted 0.93
s1	In this estimation problem, we use the criteria of minimizing the risk function and the Pitman closeness under a general bowl-shaped loss function.	method 0.94	0.70	0.04	asserted 0.97
s2	Inadmissibility of a general location and equivariant estimators is provided.	result 0.98	0.87	0.13	asserted 1.00
s3	We prove that a natural estimator (analogue of the BLEE of unordered location parameters) is inadmissible, under certain conditions on underlying densities, and propose a dominating estimator.	result 0.83	0.96	0.48	asserted 1.00
s4	We also derive a class of improved estimators using the Kubokawa's IERD approach and observe that the boundary estimator of this class is the Brewster-Zidek type estimator.	contribution 0.60	0.96	0.14	asserted 1.00
s5	Additionally, under the generalized Pitman criterion, we show that the natural estimator is inadmissible and obtain improved estimators.	result 0.92	0.96	0.18	asserted 1.00
s6	The results are implemented for different loss functions, and explicit expressions for the dominating estimators are provided.	contribution 0.59	0.94	0.11	asserted 1.00
s7	We explore the applications of these results to for exponential and normal distribution under specified loss functions.	contribution 0.79	0.92	0.05	asserted 0.93
s8	A simulation is also conducted to compare the risk performance of the proposed estimators.	method 0.89	0.96	0.04	asserted 0.99
s9	Finally, we present a real-life data analysis to illustrate the practical applications of the paper's findings.	contribution 0.58	0.95	0.06	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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C citations
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Original abstract

This paper investigates the problem of estimating the larger location parameter of two general location families from a decision-theoretic perspective. In this estimation problem, we use the criteria of minimizing the risk function and the Pitman closeness under a general bowl-shaped loss function. Inadmissibility of a general location and equivariant estimators is provided. We prove that a natural estimator (analogue of the BLEE of unordered location parameters) is inadmissible, under certain conditions on underlying densities, and propose a dominating estimator. We also derive a class of improved estimators using the Kubokawa's IERD approach and observe that the boundary estimator of this class is the Brewster-Zidek type estimator. Additionally, under the generalized Pitman criterion, we show that the natural estimator is inadmissible and obtain improved estimators. The results are implemented for different loss functions, and explicit expressions for the dominating estimators are provided. We explore the applications of these results to for exponential and normal distribution under specified loss functions. A simulation is also conducted to compare the risk performance of the proposed estimators. Finally, we present a real-life data analysis to illustrate the practical applications of the paper's findings.

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[ref] investigated the problem of estimating the larger location parameter within two general location families, employing criteria that involve minimizing the risk function and achieving Pitman closeness, all within the context of a general bowl-shaped loss function.

Estimating location parameters of two exponential distributions with ordered scale parameters · Introduction · 0.82

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