arXiv subjects

Subir Hait

Publications and source records attributed to Subir Hait.

3 recordsLinked to original sources

arXiv2026

Is the Linear Threshold Good Enough? A Scale-Free Parameter and Adequacy Test for Curvature-Induced Threshold Displacement

Applied work often locates a threshold by linearizing a smooth function about a reference point and solving for the crossing. When the function is curved, the linear crossing can be substantively displaced even when standard errors are valid. We introduce the curvature-overstatement parameter \(\Theta_{COT}=\log(|h_2^*|/|h_1^*|)\), the log ratio of second- to first-order threshold displacement. On the quadratic branch continuous with the linear solution, \(|h_2^*/h_1^*|=2/(1+\sqrt{1-u})\), where \(u=2qa/b^2\) is a dimensionless index formed from the local gap, slope, and curvature. Thus \(\Theta_{COT}\) is scale-free, depends on the local parameters through one scalar, and has regular-domain range \((-\infty,\log 2)\), with boundary limit \(\log 2\) at tangency. We derive regular asymptotic inference, characterize local-to-tangency and weak-slope failures, and give a remainder bound linking the second-order crossing to the true threshold. The main practical contribution is an adequacy test that can affirm that the linear threshold is accurate within a prespecified proportional tolerance, rather than treating failure to detect curvature as evidence of adequacy. Monte Carlo results confirm regular-case calibration, the predicted nonstandard behavior near tangency, and failure under weak slope, while bootstrap diagnostics identify regimes in which regular inference should not be used. COT therefore provides an effect-size scale, adequacy test, and diagnostics for deciding whether a first-order threshold is accurate enough to report.

stat.ME↗

arXiv2026

Orthogonal Validation-Augmented Cox Regression with Internally Validated Failure Indicators Cross-Fitted Estimation, Risk-Set Linearization, and Validation Design

Incomplete adjudication and endpoint misclassification arise when gold-standard event classification is available only for an internal validation sample. With accurate follow-up times and covariates but error-prone event indicators, naive Cox regression can be biased and inverseprobability weighting inefficient. We develop orthogonal validation-augmented Cox (OVAC) regression, a cross-fitted augmented Cox estimator for incomplete failure indicators. OVAC replaces the missing event indicator with a cross-fitted augmented pseudo-event and explicitly retains the first-order contribution from estimating the Cox risk-set mean. The same term emerges from projection of the full-data influence function through the validation mechanism, linking the score expansion to the observed-data efficient influence function. The score exhibits exact product-form nuisance drift, yielding double-robust identification, Neyman orthogonality, and root-n inference under product-rate conditions. In 1,000 R replications, full-variance SE/SD ratios were 0.997 and 0.992, with 95% coverage of 0.955 and 0.948. A 200-replication diagnostic showed that the risk-set term alone was 77.8% and 81.1% of the full-SE magnitude, although covariance cancellation made its net SE effect smaller than 0.3%. In a 250-replication method comparison, OVAC reduced empirical variance by 38.8% and 37.7% relative to IPW. OVAC provides machine-learning-compatible Cox estimation with explicit risk-set linearization, calibrated inference, and validation-design guidance.

stat.ME↗

arXiv2026

Evidence, Calibration, and Stability: A Triadic Framework for Hypothesis Testing Under Model Uncertainty

Statistical tests are often asked to do too much. A single reported result is expected to describe what the observed data say, reassure readers about repeated-sampling behavior, and remain convincing when the working model is perturbed. Those tasks are connected, but they are not equivalent. Fisherian inductive inference and Neyman-Pearson decision theory clarify the first two; robust testing, sensitivity analysis, fragility measures, multiverse analysis, and distributional-stability methods speak to the third. I propose Evidence-Calibration-Stability (ECS) as a framework for keeping these roles separate while reporting them together. Evidence is post-data. Calibration belongs to the design or procedure. Stability is the post-data distance from the benchmark analysis to a conclusion-reversing perturbation within a declared model neighborhood. Full ECS support is conjunctive: a strong coordinate cannot rescue a failed one. For finite-dimensional affine perturbations, I derive an exact ellipsoidal stability radius. For smooth nonlinear margins, a uniform quadratic-remainder condition yields a certified lower bound over a declared neighborhood, showing when the affine formula is only a surrogate. I also establish coordinate invariance and a matrix extension for multiple claims, and distinguish confirmatory calibration from descriptive calibration profiles when prespecification is unavailable. Simulations for the one-sample t test and Student's historical sleep data show that the three coordinates can lead to different interpretations. ECS is a formal synthesis, not a claim that evidence, power, or robustness is itself new.

stat.ME↗