Back to Search
Start Over
Nonparametric density estimation for stationary processes under multiplicative measurement errors
- Publication Year :
- 2024
-
Abstract
- 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
- Subjects :
- Mathematics - Statistics Theory
62G05, 62G07, 60G10, 62G20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.13410
- Document Type :
- Working Paper