Paper: arXiv 2604.06116

Authors: Masahiro Kato, Kei Nakagawa

Abstract

Financial statement auditing is conducted under a risk-based evidence approach to obtain reasonable assurance. In practice, auditors often perform additional sampling or related procedures when an initial sample does not provide a sufficient basis for a conclusion. Across jurisdictions, current standards and practice manuals acknowledge such extensions, while the statistical design of sequential audit procedures has not been fully explored. This study formulates audit sampling with additional, sequentially collected items as a sequential testing problem for a finite population under sampling without replacement. We define null and alternative hypotheses in terms of a tolerable deviation rate, specify stopping and decision rules, and formulate exact sequential boundary conditions in terms of finite-population error probabilities. For practical implementation, we calibrate those boundaries by Monte Carlo simulation at least-favorable deviation rates. The exact design yields ex ante control of decision error probabilities, and the simulation-based implementation approximates that design while allowing the computation of expected stopping times. The framework is most naturally suited to attribute auditing and deviation-rate auditing, especially tests of controls, and it can be extended to one-sided, two-stage, and truncated designs.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a formal statistical framework for sequential audit sampling without replacement, controlling error probabilities via Monte Carlo boundary calibration. While mathematically sound and novel in its application to audit standards, it relies primarily on simulation and synthetic design rather than empirical testing on real-world financial audit datasets.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Design sequential audit sampling with exact error control"] --> B["Define Null & Alternative Hypotheses<br>(Tolerable Deviation Rate)"]
    B --> C["Formulate Sequential Testing Problem<br>(Finite Population, No Replacement)"]
    C --> D["Set Boundary Conditions & Decision Rules<br>(Ex Ante Control of Decision Errors)"]
    D --> E["Calibrate Boundaries via Monte Carlo Simulation<br>(Least-Favorable Rates)"]
    E --> F["Outcomes:<br>Exact Error Probability Control & Expected Stopping Times"]