arXiv subjects

Helder Rojas

Publications and source records attributed to Helder Rojas.

14 recordsLinked to original sources

arXiv2026

Mayoral Experience or Municipal Capacity? Negative-Outcome Evidence on Municipal Budget Execution in Peru

When experienced mayors govern better-performing municipalities, it is tempting to credit the leader. Yet municipalities with stronger administrative capacity may also be more likely to attract and elect experienced mayors, generating selection on pre-existing municipal capacity. We examine this identification problem using a balanced panel of 1,642 Peruvian district municipalities from 2015 to 2022. Within-municipality estimators and panel double machine learning recover a positive association between prior public-management experience and investment-budget execution, while formal education is substantially weaker. Negative-outcome controls reveal an important distinction. Across municipalities, mayoral human capital predicts GDP and HDI measured before the mayor took office, providing evidence of selection in cross-sectional comparisons. By contrast, the first-difference negative control aligned with the within-municipality design shows that changes in mayoral experience do not predict pre-determined district GDP, while they remain associated with budget execution. Sensitivity analysis and partial-identification bounds nevertheless do not support a clean causal interpretation of that within association. The results therefore separate two sources of variation often conflated in studies of political leadership and show how negative-outcome controls can sharpen the identification of leader effects.

stat.AP↗

arXiv2025

Beneath the kinetic interpretation of noise

Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the probability density of the stochastic process that solves a corresponding stochastic differential equation. The kinetic interpretation of noise refers to a prospective notion of stochastic integration that would connect a stochastic differential equation with a Fokker-Planck equation consistent with the Fick law of diffusion, without introducing correction terms in the drift. This work is devoted to identifying the precise conditions under which such a correspondence can occur. One of these conditions is a structural constraint on the diffusion tensor, which severely restricts its possible form and thereby renders the kinetic interpretation of noise a non-generic situation. This point is illustrated through a series of examples. Furthermore, the analysis raises additional questions, including the possibility of defining a stochastic integral inspired by numerical algorithms, the behavior of stochastic transport equations in heterogeneous media, and the development of alternative models for anomalous diffusion. All these topics are addressed using stochastic analytical tools similar to those employed to study the main problem: the existence of the kinetic interpretation of noise.

math.PR↗

arXiv2025

Stochastic Processes and Diffusion Equations

In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random fluctuations and is deeply connected to the heat equation. This connection forms the basis for understanding diffusion phenomena, where the probability distribution of Brownian motion evolves according to the heat equation over time. To extend this classical result to more general stochastic systems, we introduce the Itô calculus, a powerful framework that allows us to analyze processes driven by both deterministic drift and stochastic fluctuations. This mathematical tool is essential for understanding the dynamics of more complex diffusion processes, where randomness is no longer purely Brownian, but also depends on the underlying system's state. Building on these concepts, we turn to the study of diffusion processes, which generalize Brownian motion by incorporating the Fokker-Planck equation. This equation describes how the probability density of a diffusion process evolves over time and serves as an extension of the heat equation to more complex stochastic systems. By using Itô calculus, we can rigorously study how these processes behave and connect the microscopic randomness of individual particles to their macroscopic description via partial differential equations.

math.PR↗

arXiv2025

Stochastic cloaking: concealing a region from diffusive particles

We introduce "stochastic cloaking," where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different interpretations of the Langevin equation affect the cloaking performance of an annular single-layer invisibility cloak of smoothly varying diffusivity in two dimensions. Near-perfect cloaking is achieved under the Ito convention, indicated by the cloak preventing particles from accessing an inner core without disturbing the particle density outside the cloak. The cloak's performance can be further improved by regularising its singular behaviour. We believe our demonstration of stochastic cloaking is a significant milestone, comparable to earlier developments that extended cloaking from optics and acoustics to thermodynamics.

cond-mat.mtrl-sci↗

arXiv2024

Dynamic Interconnections between Corruption and Economic Growth

This study explores the dynamic relationship between corruption and economic growth through an approach based on a system of stochastic equations. In the context of globalization and economic interdependencies, corruption not only affects investment and distorts markets, but it can also, under certain conditions, temporarily boost economic activity. Using data from the Gross Domestic Product (GDP) and the Corruption Perception Index (CPI), we implement a time-series-based model to capture the interactions between these two variables. Through a coupled vector autoregressive equations system, our model identifies patterns of interdependence between economic fluctuations and perceptions of corruption at a global level. Employing graph theory and Granger causality, we build a network of interconnections that illustrates how corruption dynamics in one country can influence economic growth and corruption perception in others. The results provide a robust tool for analyzing international political-economic relationships and can serve as a basis for designing policies that promote transparency and sustainable development.

stat.AP↗

arXiv2024

Sparsity, Regularization and Causality in Agricultural Yield: The Case of Paddy Rice in Peru

This study introduces a novel approach that integrates agricultural census data with remotely sensed time series to develop precise predictive models for paddy rice yield across various regions of Peru. By utilizing sparse regression and Elastic-Net regularization techniques, the study identifies causal relationships between key remotely sensed variables-such as NDVI, precipitation, and temperature-and agricultural yield. To further enhance prediction accuracy, the first- and second-order dynamic transformations (velocity and acceleration) of these variables are applied, capturing non-linear patterns and delayed effects on yield. The findings highlight the improved predictive performance when combining regularization techniques with climatic and geospatial variables, enabling more precise forecasts of yield variability. The results confirm the existence of causal relationships in the Granger sense, emphasizing the value of this methodology for strategic agricultural management. This contributes to more efficient and sustainable production in paddy rice cultivation.

stat.ME↗

arXiv2024

A simple algorithm for output range analysis for deep neural networks

This paper presents a novel approach for the output range estimation problem in Deep Neural Networks (DNNs) by integrating a Simulated Annealing (SA) algorithm tailored to operate within constrained domains and ensure convergence towards global optima. The method effectively addresses the challenges posed by the lack of local geometric information and the high non-linearity inherent to DNNs, making it applicable to a wide variety of architectures, with a special focus on Residual Networks (ResNets) due to their practical importance. Unlike existing methods, our algorithm imposes minimal assumptions on the internal architecture of neural networks, thereby extending its usability to complex models. Theoretical analysis guarantees convergence, while extensive empirical evaluations-including optimization tests involving functions with multiple local minima-demonstrate the robustness of our algorithm in navigating non-convex response surfaces. The experimental results highlight the algorithm's efficiency in accurately estimating DNN output ranges, even in scenarios characterized by high non-linearity and complex constraints. For reproducibility, Python codes and datasets used in the experiments are publicly available through our GitHub repository.

cs.LG↗

arXiv2024

Central Limit Theorem on Symmetric Kullback-Leibler (KL) Divergence

In this paper we provide an asymptotic theory for the symmetric version of the Kullback--Leibler (KL) divergence. We define a estimator for this divergence and study its asymptotic properties. In particular, we prove Law of Large Numbers (LLN) and the convergence to the normal law in the Central Limit Theorem (CLT) using this estimator.

math.PR↗

arXiv2023

Anti-Itô noise-induced phase transitions in tumor growth with chemotherapy

The objective of this work is to apply the Hänggi-Klimontovich stochastic differential equations to model and study the effects of anti-tumor chemotherapy in the case of continuous infusion delivering. The fluctuations generated by variations in drug concentration are modeled by the Hänggi-Klimontovich stochastic integral. This integral, which in the physics literature is sometimes called anti-Itô integral, in the last decade it has been referenced quite as the more appropriate stochastic integral for model various biological and physical systems. Then, we make some comparisons with the model based on Itô stochastic differential equations and their phase transitions that they generate, showing that the Hänggi-Klimontovich stochastic differential equations lead to more biologically realistic results.

math.PR↗

arXiv2023

Statistical Hypothesis Testing for Information Value (IV)

Information Value (IV) is a widely used technique for feature selection prior to the modeling phase, particularly in credit scoring and related domains. However, conventional IV-based practices rely on fixed empirical thresholds, which lack statistical justification and may be sensitive to characteristics such as class imbalance. In this work, we develop a formal statistical framework for IV by establishing its connection with Jeffreys divergence and propose a novel nonparametric hypothesis test, referred to as the J-Divergence test. Our method provides rigorous asymptotic guarantees and enables interpretable decisions based on \(p\)-values. Numerical experiments, including synthetic and real-world data, demonstrate that the proposed test is more reliable than traditional IV thresholding, particularly under strong imbalance. The test is model-agnostic, computationally efficient, and well-suited for the pre-modeling phase in high-dimensional or imbalanced settings. An open-source Python library is provided for reproducibility and practical adoption.

math.ST↗

arXiv2023

It\^o versus H\"anggi-Klimontovich

Interpreting the noise in a stochastic differential equation, in particular the It\^o versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of noise, given by the so-called H\"anggi-Klimontovich integral, has been proposed as better adapted to describe certain physical systems, particularly in statistical mechanics. Herein, we introduce this integral in a precise mathematical manner and analyze its properties, signaling those that have made it appealing within the realm of physics. Subsequently, we employ this integral to model some statistical mechanical systems, such as the random dispersal of Langevin particles and the relativistic Brownian motion. We show that, for these classical examples, the H\"anggi-Klimontovich integral is worse adapted than the It\^o integral and even the Stratonovich one.

math-ph↗

arXiv2021

Order book dynamics with liquidity fluctuations: limit theorems and large deviations

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

q-fin.TR↗

arXiv2020

Stress Testing Network Reconstruction via Graphical Causal Model

An resilience optimal evaluation of financial portfolios implies having plausible hypotheses about the multiple interconnections between the macroeconomic variables and the risk parameters. In this paper, we propose a graphical model for the reconstruction of the causal structure that links the multiple macroeconomic variables and the assessed risk parameters, it is this structure that we call Stress Testing Network (STN). In this model, the relationships between the macroeconomic variables and the risk parameter define a "relational graph" among their time-series, where related time-series are connected by an edge. Our proposal is based on the temporal causal models, but unlike, we incorporate specific conditions in the structure which correspond to intrinsic characteristics this type of networks. Using the proposed model and given the high-dimensional nature of the problem, we used regularization methods to efficiently detect causality in the time-series and reconstruct the underlying causal structure. In addition, we illustrate the use of model in credit risk data of a portfolio. Finally, we discuss its uses and practical benefits in stress testing.

stat.AP↗

arXiv2019

Transmission of Macroeconomic Shocks to Risk Parameters: Their uses in Stress Testing

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.

stat.AP↗