Robust and Adaptive Confidence Intervals with Finite-Sample Validity Article Swipe
SÉRGIO DE ANDRADE, PAULO
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17606263
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17606263
This paper introduces a novel framework for constructing confidence intervals that possess guaranteed finite-sample coverage probability without relying on asymptotic approximations or specific distributional assumptions. Traditional methods for interval estimation, such as those based on the central limit theorem or standard bootstrap techniques, often fail to achieve the nominal coverage level when sample sizes are small or when the underlying data distribution deviates from normality. Our proposed method, termed Robust Adaptive Conformal Intervals (RACI), synthesizes principles from robust statistics, adaptive inference, and conformal prediction to address these shortcomings. By employing a robustly studentized pivot statistic within a conformal inference framework, RACI ensures valid coverage for any finite sample size under the mild assumption of data exchangeability. The adaptive component allows the interval's width to adjust to the data's characteristics, such as skewness or heavy tails, thereby maintaining efficiency. We conduct extensive Monte Carlo simulations across a range of distributional scenarios, including normal, heavy-tailed, skewed, and contaminated distributions. The results demonstrate that RACI consistently achieves the nominal coverage rate, whereas classical and bootstrap intervals exhibit significant under-coverage in non-ideal settings. Furthermore, RACI maintains competitive average interval lengths, highlighting its practical utility for reliable uncertainty quantification in modern data analysis.
Related Topics
Concepts
Studentized range
Coverage probability
Mathematics
Prediction interval
Confidence interval
Skewness
Range (aeronautics)
Statistics
Monte Carlo method
Sample size determination
Statistic
Interval (graph theory)
Inference
Limit (mathematics)
Studentized residual
Statistical inference
Predictive inference
Probability distribution
Nominal level
Term (time)
Robust confidence intervals
Confidence region
Sample (material)
Robustness (evolution)
Algorithm
Conformal map
Spurious relationship
Computer science
Asymptotic distribution
Central limit theorem
Data mining
Mathematical optimization
Empirical distribution function
Econometrics
Component (thermodynamics)
Tolerance interval
Location parameter
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17606263
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7105736667
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7105736667Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17606263Digital Object Identifier
- Title
-
Robust and Adaptive Confidence Intervals with Finite-Sample ValidityWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-14Full publication date if available
- Authors
-
SÉRGIO DE ANDRADE, PAULOList of authors in order
- Landing page
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https://doi.org/10.5281/zenodo.17606263Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.5281/zenodo.17606263Direct OA link when available
- Concepts
-
Studentized range, Coverage probability, Mathematics, Prediction interval, Confidence interval, Skewness, Range (aeronautics), Statistics, Monte Carlo method, Sample size determination, Statistic, Interval (graph theory), Inference, Limit (mathematics), Studentized residual, Statistical inference, Predictive inference, Probability distribution, Nominal level, Term (time), Robust confidence intervals, Confidence region, Sample (material), Robustness (evolution), Algorithm, Conformal map, Spurious relationship, Computer science, Asymptotic distribution, Central limit theorem, Data mining, Mathematical optimization, Empirical distribution function, Econometrics, Component (thermodynamics), Tolerance interval, Location parameterTop concepts (fields/topics) attached by OpenAlex
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| abstract_inverted_index.based | 33 |
| abstract_inverted_index.heavy | 133 |
| abstract_inverted_index.level | 50 |
| abstract_inverted_index.limit | 37 |
| abstract_inverted_index.novel | 4 |
| abstract_inverted_index.often | 43 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.pivot | 93 |
| abstract_inverted_index.range | 146 |
| abstract_inverted_index.rate, | 167 |
| abstract_inverted_index.sizes | 53 |
| abstract_inverted_index.small | 55 |
| abstract_inverted_index.these | 86 |
| abstract_inverted_index.those | 32 |
| abstract_inverted_index.under | 109 |
| abstract_inverted_index.valid | 102 |
| abstract_inverted_index.width | 122 |
| abstract_inverted_index.Robust | 69 |
| abstract_inverted_index.across | 144 |
| abstract_inverted_index.adjust | 124 |
| abstract_inverted_index.allows | 119 |
| abstract_inverted_index.data's | 127 |
| abstract_inverted_index.finite | 106 |
| abstract_inverted_index.modern | 195 |
| abstract_inverted_index.robust | 77 |
| abstract_inverted_index.sample | 52, 107 |
| abstract_inverted_index.tails, | 134 |
| abstract_inverted_index.termed | 68 |
| abstract_inverted_index.within | 95 |
| abstract_inverted_index.(RACI), | 73 |
| abstract_inverted_index.achieve | 46 |
| abstract_inverted_index.address | 85 |
| abstract_inverted_index.average | 183 |
| abstract_inverted_index.central | 36 |
| abstract_inverted_index.conduct | 139 |
| abstract_inverted_index.ensures | 101 |
| abstract_inverted_index.exhibit | 173 |
| abstract_inverted_index.method, | 67 |
| abstract_inverted_index.methods | 26 |
| abstract_inverted_index.nominal | 48, 165 |
| abstract_inverted_index.normal, | 151 |
| abstract_inverted_index.possess | 11 |
| abstract_inverted_index.relying | 17 |
| abstract_inverted_index.results | 158 |
| abstract_inverted_index.skewed, | 153 |
| abstract_inverted_index.theorem | 38 |
| abstract_inverted_index.thereby | 135 |
| abstract_inverted_index.utility | 189 |
| abstract_inverted_index.whereas | 168 |
| abstract_inverted_index.without | 16 |
| abstract_inverted_index.Adaptive | 70 |
| abstract_inverted_index.achieves | 163 |
| abstract_inverted_index.adaptive | 79, 117 |
| abstract_inverted_index.coverage | 14, 49, 103, 166 |
| abstract_inverted_index.deviates | 62 |
| abstract_inverted_index.interval | 28, 184 |
| abstract_inverted_index.lengths, | 185 |
| abstract_inverted_index.proposed | 66 |
| abstract_inverted_index.reliable | 191 |
| abstract_inverted_index.robustly | 91 |
| abstract_inverted_index.skewness | 131 |
| abstract_inverted_index.specific | 22 |
| abstract_inverted_index.standard | 40 |
| abstract_inverted_index.Conformal | 71 |
| abstract_inverted_index.Intervals | 72 |
| abstract_inverted_index.analysis. | 197 |
| abstract_inverted_index.bootstrap | 41, 171 |
| abstract_inverted_index.classical | 169 |
| abstract_inverted_index.component | 118 |
| abstract_inverted_index.conformal | 82, 97 |
| abstract_inverted_index.employing | 89 |
| abstract_inverted_index.extensive | 140 |
| abstract_inverted_index.framework | 5 |
| abstract_inverted_index.including | 150 |
| abstract_inverted_index.inference | 98 |
| abstract_inverted_index.intervals | 9, 172 |
| abstract_inverted_index.maintains | 181 |
| abstract_inverted_index.non-ideal | 177 |
| abstract_inverted_index.practical | 188 |
| abstract_inverted_index.settings. | 178 |
| abstract_inverted_index.statistic | 94 |
| abstract_inverted_index.assumption | 112 |
| abstract_inverted_index.asymptotic | 19 |
| abstract_inverted_index.confidence | 8 |
| abstract_inverted_index.framework, | 99 |
| abstract_inverted_index.guaranteed | 12 |
| abstract_inverted_index.inference, | 80 |
| abstract_inverted_index.interval's | 121 |
| abstract_inverted_index.introduces | 2 |
| abstract_inverted_index.normality. | 64 |
| abstract_inverted_index.prediction | 83 |
| abstract_inverted_index.principles | 75 |
| abstract_inverted_index.scenarios, | 149 |
| abstract_inverted_index.underlying | 59 |
| abstract_inverted_index.Traditional | 25 |
| abstract_inverted_index.competitive | 182 |
| abstract_inverted_index.demonstrate | 159 |
| abstract_inverted_index.efficiency. | 137 |
| abstract_inverted_index.estimation, | 29 |
| abstract_inverted_index.maintaining | 136 |
| abstract_inverted_index.probability | 15 |
| abstract_inverted_index.significant | 174 |
| abstract_inverted_index.simulations | 143 |
| abstract_inverted_index.statistics, | 78 |
| abstract_inverted_index.studentized | 92 |
| abstract_inverted_index.synthesizes | 74 |
| abstract_inverted_index.techniques, | 42 |
| abstract_inverted_index.uncertainty | 192 |
| abstract_inverted_index.Furthermore, | 179 |
| abstract_inverted_index.assumptions. | 24 |
| abstract_inverted_index.consistently | 162 |
| abstract_inverted_index.constructing | 7 |
| abstract_inverted_index.contaminated | 155 |
| abstract_inverted_index.distribution | 61 |
| abstract_inverted_index.highlighting | 186 |
| abstract_inverted_index.finite-sample | 13 |
| abstract_inverted_index.heavy-tailed, | 152 |
| abstract_inverted_index.shortcomings. | 87 |
| abstract_inverted_index.approximations | 20 |
| abstract_inverted_index.distributional | 23, 148 |
| abstract_inverted_index.distributions. | 156 |
| abstract_inverted_index.quantification | 193 |
| abstract_inverted_index.under-coverage | 175 |
| abstract_inverted_index.characteristics, | 128 |
| abstract_inverted_index.exchangeability. | 115 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile.value | 0.9102974 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |