{"ID":6267204,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-13T01:02:08.706470581Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.08472","arxiv_id":"2607.08472","title":"A screening approach to nonparametric inference from the M/G/1 workload","abstract":"We address a long-standing open problem posed by Hansen and Pitts (2006) on nonparametric inference for the service-time distribution in an M/G/1 workload model. We consider an M/G/1 queue with unknown arrival rate $λ\u003e0$ and service-time distribution $B(\\cdot)$, without assuming stability or stationarity. A statistician observes the workload process at discrete times $t=0,1,\\ldots,n$ and aims to estimate $B(w)$ at a fixed point $w\u003e0$. We propose an estimator $B_n(w)$ based solely on the observed workload trajectory. The construction relies on a screening mechanism that extracts conditionally i.i.d. compound Poisson increments from the workload process, thereby reducing the dependent-data problem to a Laplace-transform inversion framework. Under mild regularity assumptions on $B(\\cdot)$, i.e., continuous differentiability on $[0,\\infty)$, twice differentiability at $w$, and a finite second moment, we establish the bound \\[ \\mathbb{E}\\bigl|B_n(w)-B(w)\\bigr| =\\mathcal{O}\\!\\left(\\frac{\\log n}{\\sqrt{n}}\\right), \\qquad n\\to\\infty. \\]This provides the first solution to the Hansen-Pitts problem achieving a parametric $L^1$-risk rate (up to a logarithmic factor), without requiring stationarity, stability, or knowledge of the arrival rate.","short_abstract":"We address a long-standing open problem posed by Hansen and Pitts (2006) on nonparametric inference for the service-time distribution in an M/G/1 workload model. We consider an M/G/1 queue with unknown arrival rate $λ\u003e0$ and service-time distribution $B(\\cdot)$, without assuming stability or stationarity. A statisticia...","url_abs":"https://arxiv.org/abs/2607.08472","url_pdf":"https://arxiv.org/pdf/2607.08472v1","authors":"[\"Royi Jacobovic\",\"Binyamin Kobzantsev\"]","published":"2026-07-09T13:30:03Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}