A new kernel estimator of hazard ratio and its asymptotic mean squared error
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866909260158337024 |
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| author | Moriyama, Taku Maesono, Yoshihiko |
| author_facet | Moriyama, Taku Maesono, Yoshihiko |
| contents | The hazard function is a ratio of a density and survival function, and it is a basic tool of the survival analysis. In this paper we propose a kernel estimator of the hazard ratio function, which are based on a modification of Ćwik and Mielniczuk's method. We study nonparametric estimators of the hazard function and compare those estimators by means of asymptotic mean squared error ($AMSE$). We obtain asymptotic bias and variance of the new estimator, and compare them with a naive estimator. The asymptotic variance of the new estimator is always smaller than the naive estimator's, so we also discuss an improvement of $AMSE$ using Terrell and Scott's bias reduction method. The new modified estimator ensures the non-negativity, and we demonstrate the numerical improvement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_08049 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A new kernel estimator of hazard ratio and its asymptotic mean squared error Moriyama, Taku Maesono, Yoshihiko Statistics Theory The hazard function is a ratio of a density and survival function, and it is a basic tool of the survival analysis. In this paper we propose a kernel estimator of the hazard ratio function, which are based on a modification of Ćwik and Mielniczuk's method. We study nonparametric estimators of the hazard function and compare those estimators by means of asymptotic mean squared error ($AMSE$). We obtain asymptotic bias and variance of the new estimator, and compare them with a naive estimator. The asymptotic variance of the new estimator is always smaller than the naive estimator's, so we also discuss an improvement of $AMSE$ using Terrell and Scott's bias reduction method. The new modified estimator ensures the non-negativity, and we demonstrate the numerical improvement. |
| title | A new kernel estimator of hazard ratio and its asymptotic mean squared error |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/1611.08049 |