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- W4384920009 abstract "This work presents a non-parametric estimator for the cumulative distribution function (CDF) of the jump-size distribution for a storage system with compound Poisson input. The workload process is observed according to an independent Poisson sampling process. The nonparametric estimator is constructed by first estimating the characteristic function (CF) and then applying an inversion formula. The convergence rate of the CF estimator at $s$ is shown to be of the order of $s^2/n$, where $n$ is the sample size. This convergence rate is leveraged to explore the bias-variance tradeoff of the inversion estimator. It is demonstrated that within a certain class of continuous distributions, the risk, in terms of MSE, is uniformly bounded by $C n^{-frac{eta}{1+eta}}$, where $C$ is a positive constant and the parameter $eta>0$ depends on the smoothness of the underlying class of distributions. A heuristic method is further developed to address the case of an unknown rate of the compound Poisson input process." @default.
- W4384920009 created "2023-07-21" @default.
- W4384920009 creator A5071554096 @default.
- W4384920009 date "2023-07-19" @default.
- W4384920009 modified "2023-09-24" @default.
- W4384920009 title "Nonparametric estimation of the jump-size distribution for a stochastic storage system with periodic observations" @default.
- W4384920009 doi "https://doi.org/10.48550/arxiv.2307.10116" @default.
- W4384920009 hasPublicationYear "2023" @default.
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