arXiv subjects

Aditya Ghosh

Publications and source records attributed to Aditya Ghosh.

7 recordsLinked to original sources

arXiv2025

Non-parametric Causal Inference in Dynamic Thresholding Designs

We consider causal inference in dynamic settings where treatment is assigned by thresholding a state variable that can change over time. There is a large literature on regression-discontinuity methods building on the fact that, in the static setting, treatment assignment via threshold crossing induces a quasi-experimental design that enables pragmatic causal inference. But dynamic settings involve challenges not present in the static setting, e.g., past treatments may affect current state and thus future treatments, and so existing regression-discontinuity methods do not apply. Here, we show that dynamic thresholding designs identify a marginal policy effect that nests the classical regression-discontinuity parameter in the static setting; and propose a tailored local linear regression estimator that is consistent for this marginal policy effect. We demonstrate our approach using an experiment that emulates real-world optimization of thresholds for continuous glucose monitoring using data generated from an FDA-approved simulator.

stat.ME↗

arXiv2025

Which Covariates to Adjust for? Specification-robust Causal Inference in Observational Studies

In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment effect, and standard remedies (adjusting for their union or intersection, or reporting the union or convex hull of confidence intervals) can fail or produce intervals whose width does not vanish with sample size. We propose a specification-robust procedure that returns a single point estimate and a confidence interval that is valid as long as at least one candidate adjustment set is valid and has width shrinking at the parametric $n^{-1/2}$ rate. Our approach mirrors how trimming and overlap weighting handle overlap violations:~We shift the target to a reweighted population, closest in KL-divergence to the original population, for which credible, specification-robust inference is feasible. We also provide diagnostic plots to assess the population shift and an extension to protect any function of the covariates used for reweighting, similar to calipers in matching. Synthetic and real-data examples demonstrate that our procedure provides substantially tighter confidence intervals than the convex hull while maintaining nominal coverage.

stat.ME↗

arXiv2025

PLRD: Partially Linear Regression Discontinuity Inference

Regression discontinuity designs have become one of the most popular research designs in empirical economics. We argue, however, that the widely used approaches to building confidence intervals in regression discontinuity designs often exhibit suboptimal behavior in practice. We propose a new estimator, the partially linear regression discontinuity (PLRD) estimator that, in set of a simulation studies carefully calibrated to twelve high-profile applications of regression discontinuity designs, has substantially lower estimation error than available comparison methods. Throughout our experiments, the confidence intervals built using PLRD are both valid and short. We also provide large-sample guarantees for PLRD. Our simulation study serves as a general template for how new econometric methods can be credibly evaluated relative to the existing alternatives by constructing simulation designs that generate synthetic data indistinguishable from the original data using the Wasserstein generative adversarial network methodology.

econ.EM↗

arXiv2022

Report: Statistics of approximations to zeroes of $\zeta$-function via truncated symmetrized Euler products

We look at approximations $ \zeta_X $ of the $\zeta$-function introduced in Gonek's paper (arXiv:0704.3448). We look at how close the approximate zeroes are to the actual zeroes when (i) X is fixed (Section 1)(ii) X varies like $ t/2\pi $ (Section 3.1). We establish a heuristic for estimating these differences, involving values of $ F_X^\star(t) $ and its near-constant slopes near zeta-zero ordinates $ \gamma $. In Section 3.2 we see the slope around the zeroes behaves logarithmically and we calculate a numerical formula for it. In Section 3.3 and 3.4 we scale the differences with the slopes and compare them with models involving 1 or 2 pairs of neighbouring zeta-zeroes. In Section 3.5, we also look at how often these models capture these scaled differences accurately. In Section 4, we look at our methods from a theoretical standpoint. In Section 5, we look at how close the approximate zeroes are to the actual zeroes when (i) X is fixed (ii) X varies like $ t/2\pi $. The errors seem to behave like powers of log which should be investigated further from a theoretical standpoint.

math.NT↗

arXiv2022

Zero-free half-planes of the \zeta -function via spaces of analytic functions

In this article, we introduce a general approach for deriving zero-free half-planes for the Riemann zeta function $\zeta$ by identifying topological vector spaces of analytic functions with specific properties. This approach is applied to weighted $\ell^2$ spaces and classical Hardy spaces $ H^p $ ($ 0<p\leq2 $). As a consequence precise conditions are obtained for the existence of zero-free half planes for the $\zeta$-function.

math.NT↗

arXiv2021

Robustness and Efficiency of Rosenbaum's Rank-based Estimator in Randomized Trials: A Design-based Perspective

Mean-based estimators of causal effects in randomized experiments may behave poorly if the potential outcomes have a heavy tail or contain outliers. An alternative estimator proposed by Rosenbaum (1993) estimates a constant additive treatment effect by inverting a randomization test using ranks. We develop a design-based asymptotic theory for this rank-based estimator and study its robustness and efficiency properties. We show that Rosenbaum's estimator is robust against outliers with a breakdown point that uniformly dominates that of any weighted quantile estimator. When pretreatment covariates are available, a regression-adjusted version of Rosenbaum's estimator uses an agnostic linear regression on the covariates and bases inference on the ranks of residuals. Under mild integrability conditions, we show that this estimator is at most 13.6% less efficient, in the worst case, than the commonly used mean-based regression adjustment method proposed by Lin (2013); often outperforming it when the residuals have heavy tails. Moreover, under suitable assumptions, Rosenbaum's regression-adjusted estimator is at least as efficient as the unadjusted one. Finally, we initiate the study of Rosenbaum's estimator when the constant treatment effect assumption may be violated. To analyze the regression-adjusted estimator, we develop local asymptotics of rank statistics under the design-based framework, which may be of independent interest.

stat.ME↗

arXiv2019

An Asymptotic Formula for the Chebyshev Theta Function

Let $\{p_n\}_{n\ge 1}$ be the sequence of primes and $\vartheta(x) = \sum_{p \leq x} \log p$, where $p$ runs over the primes not exceeding $x$, be the Chebyshev $\vartheta$-function. In this note we derive lower and upper bounds for $\vartheta(p_n)/n$ by comparing it with $\log p_{n+1}$ and deduce that $\vartheta(p_n)/n=\log p_{n+1}\left(1-\frac{1}{\log n}+\frac{\log\log n}{\log^2 n}\left(1+o(1)\right)\right).$

math.NT↗