A justification of conditional confidence intervals
| Autor: | Eric Beutner, Stephan Smeekes, Alexander Heinemann |
|---|---|
| Přispěvatelé: | Econometrics and Data Science, QE Econometrics, RS: GSBE Theme Data-Driven Decision-Making, RS: FSE DACS Mathematics Centre Maastricht |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Class (set theory) SDG 16 - Peace BOOTSTRAP PREDICTION INTERVALS Econometrics (econ.EM) parameter uncertainty TIME-SERIES Mathematics - Statistics Theory Statistics Theory (math.ST) Type (model theory) FOS: Economics and business sample-splitting Econometrics FOS: Mathematics Point estimation Mathematics Economics - Econometrics Series (mathematics) Estimation theory merging VARIANCE SDG 16 - Peace Justice and Strong Institutions Variance (accounting) prediction Confidence interval Justice and Strong Institutions Statistics Probability and Uncertainty Conditional confidence intervals FORECASTS |
| Zdroj: | Electronic Journal of Statistics, 15(1), 2517-2565. Institute of Mathematical Statistics Beutner, E, Heinemann, A & Smeekes, S 2021, ' A justification of conditional confidence intervals ', Electronic Journal of Statistics, vol. 15, no. 1, pp. 2517-2565 . https://doi.org/10.1214/21-EJS1833 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/21-EJS1833 |
| Popis: | © 2021, Institute of Mathematical Statistics. All rights reserved.To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the unrealistic assumption of observing two independent processes, where one is used for parameter estimation, and the other for conditioning upon. Such unrealistic foundation raises the question whether these intervals are theoretically justified in a realistic setting. This paper presents an asymptotic justification for this type of intervals that does not require such an unrealistic assumption, but relies on a samplesplit approach instead. By showing that our sample-split intervals coincide asymptotically with the standard intervals, we provide a novel, and realistic, justification for confidence intervals of conditional objects. The analysis is carried out for a rich class of time series models. We also present the results of a simulation study to evaluate the performance of the sample-split approach. The results indicate that also in practice sample-split intervals might be more appropriate than the standard intervals. |
| Databáze: | OpenAIRE |
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