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Estimating Error in Natural Distribution Estimation
Balasundaram, Haricharan; Thangaraj, Andrew
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https://hdl.handle.net/2142/130303
Description
- Title
- Estimating Error in Natural Distribution Estimation
- Author(s)
- Balasundaram, Haricharan
- Thangaraj, Andrew
- Issue Date
- 2025-09-17
- Keyword(s)
- Distribution estimation
- Missing mass
- Good-Turing estimator
- Concentration
- Estimation
- Abstract
- Given i.i.d. samples from an unknown discrete distribution, the goal of distribution estimation is to construct an accurate estimate of the underlying distribution. Natural distribution estimators assign one probability estimate to all letters occurring with the same frequency, and this is well-justified for i.i.d. models. However, natural estimators can be significantly erroneous for low frequency or missing (frequency 0) letters in large alphabet scenarios. In this work, we introduce a statistic that captures the unavoidable error at a particular frequency of any natural distribution estimator. For this proposed error statistic, which depends on the distribution and the samples, we provide an estimator that is non-linear in the prevalences (frequencies of frequencies). We show that the proposed estimator has low bias and is consistent, and can be used to ascertain if the distribution restricted to letters of the same frequency is close to uniform. Our approach is validated through simulations on synthetic and natural language data.
- Publisher
- Allerton Conference on Communication, Control, and Computing
- Series/Report Name or Number
- 2025 61st Allerton Conference on Communication, Control, and Computing Proceedings
- ISSN
- 2836-4503
- Type of Resource
- Text
- Genre of Resource
- Conference Paper/Presentation
- Language
- eng
- Handle URL
- https://hdl.handle.net/2142/130303&&
- Copyright and License Information
- Copyright 2025 is held by Haricharan Balasundaram and Andrew Thangaraj.
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61st Allerton Conference - 2025 PRIMARY
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