Estimation of the Risk Measure under a Nuisance Autoregression
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910209267466240 |
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| author | Jurečková, Jana Picek, Jan |
| author_facet | Jurečková, Jana Picek, Jan |
| contents | The goal of an experiment is to evaluate the profit, loss, or the amount of a physical entity over a period. The measurements $X_t$ can be influenced by the values measured in the past; hence we describe the situation with an autoregression model, whose autoregression coefficients are generally unknown. The variable of interest is the error term $Z_t$ of the model, which is the increment of $X_t$ with respect to the past, but itself unobservable. The problem is to estimate various quantile functions of $Z$, as the risk measure of the loss or the related economic indicators. We construct an estimate of quantile functions of $Z$ in the situation that the inference is possible only by means of observations $X$. The proposed estimates are based on the R-estimators of autoregression coefficients, combined with the autoregression quantiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Estimation of the Risk Measure under a Nuisance Autoregression Jurečková, Jana Picek, Jan Methodology 62M10, 62G08, 62J05 The goal of an experiment is to evaluate the profit, loss, or the amount of a physical entity over a period. The measurements $X_t$ can be influenced by the values measured in the past; hence we describe the situation with an autoregression model, whose autoregression coefficients are generally unknown. The variable of interest is the error term $Z_t$ of the model, which is the increment of $X_t$ with respect to the past, but itself unobservable. The problem is to estimate various quantile functions of $Z$, as the risk measure of the loss or the related economic indicators. We construct an estimate of quantile functions of $Z$ in the situation that the inference is possible only by means of observations $X$. The proposed estimates are based on the R-estimators of autoregression coefficients, combined with the autoregression quantiles. |
| title | Estimation of the Risk Measure under a Nuisance Autoregression |
| topic | Methodology 62M10, 62G08, 62J05 |
| url | https://arxiv.org/abs/2605.10553 |