Nonparametric density estimation for stationary processes under multiplicative measurement errors
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909143492722688 |
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| author | Dang, Duc Trong Hoang, Van Ha Thai, Phuc Hung |
| author_facet | Dang, Duc Trong Hoang, Van Ha Thai, Phuc Hung |
| contents | This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process. We propose a novel approach to handle non-independent data, typical in real-world scenarios. For instance, data collected from various groups may exhibit interdependencies within each group, resembling data generated from $m$-dependent stationary processes, a subset of stationary processes. This study extends the applicability of the model $Y_t = X_t U_t$ to diverse scientific domains dealing with complex dependent data. The paper outlines our estimation techniques, discusses convergence rates, establishes a lower bound on the minimax risk, and demonstrates the asymptotic normality of the estimator for $f_X$ under smooth error distributions. Through examples and simulations, we showcase the efficacy of our estimator. The paper concludes by providing proofs for the presented theoretical results.v |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonparametric density estimation for stationary processes under multiplicative measurement errors Dang, Duc Trong Hoang, Van Ha Thai, Phuc Hung Statistics Theory 62G05, 62G07, 60G10, 62G20 This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process. We propose a novel approach to handle non-independent data, typical in real-world scenarios. For instance, data collected from various groups may exhibit interdependencies within each group, resembling data generated from $m$-dependent stationary processes, a subset of stationary processes. This study extends the applicability of the model $Y_t = X_t U_t$ to diverse scientific domains dealing with complex dependent data. The paper outlines our estimation techniques, discusses convergence rates, establishes a lower bound on the minimax risk, and demonstrates the asymptotic normality of the estimator for $f_X$ under smooth error distributions. Through examples and simulations, we showcase the efficacy of our estimator. The paper concludes by providing proofs for the presented theoretical results.v |
| title | Nonparametric density estimation for stationary processes under multiplicative measurement errors |
| topic | Statistics Theory 62G05, 62G07, 60G10, 62G20 |
| url | https://arxiv.org/abs/2403.13410 |