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arxiv: 2605.23210 · v1 · pith:R6NR42ECnew · submitted 2026-05-22 · 📡 eess.SP · math.ST· stat.ME· stat.TH

Fundamental Bounds and Efficient Estimation for Dead-Time-Constrained Event Detection, with Application to Single-Photon Lidar

Frederic J. N. Jorgensen , Steven G. Johnson This is my paper

Pith reviewed 2026-05-25 04:05 UTC · model grok-4.3

classification 📡 eess.SP math.STstat.MEstat.TH
keywords dead-time event detectionsingle-photon lidarmaximum likelihood estimatorFisher information ratelocal asymptotic normalitysufficient statisticone-step estimator
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The pith

Dead-time event detection processes have fundamental estimation lower bounds attained by the maximum likelihood estimator.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an asymptotic theory for estimating parameters from dead-time event detection processes, which are periodic binary processes where each detection inactivates the detector for a recovery interval. It identifies a sufficient statistic that includes activation counts, which conventional methods often discard. Proving local asymptotic normality yields a Fisher-information rate that sets lower bounds on estimation error. The maximum likelihood estimator attains these bounds, and one-step estimators achieve the same performance without full iterative optimization. This framework applies directly to single-photon lidar and similar detection systems.

Core claim

We develop an asymptotic statistical theory for parameter estimation from dead-time event detection processes. We identify a sufficient statistic, prove local asymptotic normality, derive the Fisher-information rate to obtain fundamental lower bounds, and prove that the maximum likelihood estimator attains these bounds. We also propose Le Cam one-step estimators that attain the same asymptotic bounds with a single local correction.

What carries the argument

The Fisher-information rate obtained from local asymptotic normality of dead-time event detection processes, which supplies the Cramér-Rao-type lower bounds.

If this is right

  • Activation counts carry statistically useful information and should be retained rather than discarded by histogramming hardware.
  • The maximum likelihood estimator is asymptotically efficient for dead-time event detection processes.
  • One-step estimators achieve the same asymptotic efficiency as full maximum likelihood with a single correction step.
  • The theory supplies concrete lower bounds that quantify how dead time and gating degrade estimation precision in lidar and similar applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Hardware designs for detectors could prioritize recording activation counts to improve overall information extraction.
  • The same local asymptotic normality approach may extend to other recovery-time constrained processes outside photon detection.
  • Practical tests of one-step estimators on varied real datasets would confirm whether the asymptotic efficiency holds at moderate sample sizes.

Load-bearing premise

The dead-time event detection processes satisfy local asymptotic normality.

What would settle it

A large-sample simulation or experiment in which the variance of the maximum likelihood estimator exceeds the derived Fisher-information lower bound.

Figures

Figures reproduced from arXiv: 2605.23210 by Frederic J. N. Jorgensen, Steven G. Johnson.

Figure 1
Figure 1. Figure 1: Schematic of a dead-time event detection (DED) process. The periodic incidence probability [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mean-square error (MSE) for pulse parameters [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Relative MSE for pulse parameters [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Real single-photon lidar experiment [77] comparing estimation under a misspecified wrapped-Gaussian pulse model (left) and an experimentally [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Relative mean-square error for the delay parameter [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

We develop an asymptotic statistical theory for parameter estimation from a class of non-i.i.d. periodic binary event-detection processes subject to nonparalyzable dead time and gating, which we call "dead-time event detection" (DED) processes. Such processes arise in single-photon lidar, fluorescence lifetime imaging, X-ray astronomy, and particle or radiation flux measurements in nuclear physics, where each detection renders the radiation/particle detector inactive for a recovery interval. Our theory quantifies how dead time and gating affect the fundamental lower bounds of estimation and identifies practical estimators that attain these bounds. First, we identify a sufficient statistic, showing in particular that activation counts can carry statistically useful information discarded by conventional histogramming hardware. We then prove local asymptotic normality and derive the corresponding Fisher-information rate, thereby obtaining fundamental lower bounds for estimation from DED processes. We prove that the maximum likelihood estimator (MLE), widely used in DED applications, attains these lower bounds. Since computing the MLE typically requires solving a nonconvex optimization problem, we also propose Le Cam one-step estimators, which attain the same asymptotic bounds with only a single local correction rather than iterative optimization. We illustrate the validity of our asymptotic theory and the practical usefulness of one-step estimators through the example of single-photon lidar in both simulations and real-data experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper develops an asymptotic statistical theory for parameter estimation from a class of non-i.i.d. periodic binary event-detection processes subject to nonparalyzable dead time and gating (DED processes). It identifies a sufficient statistic (noting that activation counts carry information discarded by conventional histogramming), proves local asymptotic normality (LAN) and derives the corresponding Fisher-information rate to obtain fundamental lower bounds, proves that the maximum likelihood estimator (MLE) attains these bounds, proposes Le Cam one-step estimators that achieve the same asymptotic efficiency with a single local correction, and validates the theory via single-photon lidar simulations and real-data experiments.

Significance. If the central claims hold, the work supplies rigorous lower bounds and practical efficient estimators for DED processes that arise in single-photon lidar, fluorescence lifetime imaging, X-ray astronomy, and nuclear physics measurements. Explicit credit is due for the proofs of LAN for the non-i.i.d. DED model class, the resulting Fisher-information rates, and the demonstration that the widely used MLE attains the bounds; the one-step estimators address the nonconvex optimization issue in a computationally attractive way.

minor comments (3)
  1. [Abstract] Abstract: the statement that activation counts 'can carry statistically useful information' is a key modeling insight; the precise form of the sufficient statistic and the reduction step should be stated explicitly in the first section that introduces the DED process model.
  2. The LAN proof is load-bearing for all subsequent bounds and efficiency claims; the manuscript should include a short remark on the specific regularity conditions (e.g., on the gating function and dead-time length) that are verified for the periodic non-i.i.d. case.
  3. Figure captions and table headings in the lidar example section should explicitly label which estimator (MLE vs. one-step) is shown in each panel to avoid ambiguity when comparing empirical variances to the derived Fisher rate.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the significance of the LAN proofs and Fisher-information rates for DED processes, and the recommendation of minor revision. No major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is model-driven and self-contained

full rationale

The paper identifies a sufficient statistic for DED processes, then proves local asymptotic normality (LAN) to obtain Fisher-information rates and efficiency of the MLE. These steps follow directly from the defined non-i.i.d. process model with dead time and gating; the abstract states the proofs are contained in the manuscript. No equations reduce by construction to fitted inputs, no self-citation chains are invoked for load-bearing uniqueness or ansatzes, and no renaming of known results occurs. The derivation remains independent of the target bounds.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The theory rests on the domain definition of DED processes and standard asymptotic statistics assumptions; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Event-detection processes are non-i.i.d. periodic binary subject to nonparalyzable dead time and gating
    This defines the class of processes for which the sufficient statistic, LAN, and bounds are derived.

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