arXiv subjects

Rishideep Roy

Publications and source records attributed to Rishideep Roy.

9 recordsLinked to original sources

arXiv2026

Optimising football transfer strategy under budget constraints: A weighted multi-criteria approach

The football transfer market is a complex, dynamic environment in which clubs compete to acquire players who strengthen their squads. While several frameworks estimate a player's worth, a comprehensive approach that captures both squad optimisation and transfer market dynamics remains limited. In this paper, we propose a quantitative framework for optimising football transfer strategy under budget constraints, integrated with a competitive bidding paradigm. Using data from professional football leagues, we construct player performance and transfer price models using linear mixed-effects frameworks that incorporate player characteristics, recent performance, team context, and league effects. The predicted ratings and estimated transfer prices are then integrated into a weighted multi-criteria constrained optimisation framework that determines a club's transfer activities at the end of the season. Finally, these optimal transfer decisions are embedded within an independent private-value auction model with a random reserve price to analyse market behaviour when multiple teams compete for the same player. We illustrate our approach using the 2018-19 season of the English Premier League to demonstrate its ability to capture transfer-market dynamics.

stat.AP↗

arXiv2026

Nonparametric regression of spatio-temporal data using infinite-dimensional covariates

In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies alongside second-order stationary explanatory variables, which may be infinite-dimensional and accommodate spatio-temporal covariates. Because of the absence of a mixing-type dependence condition in this case, which is typically required by the existing studies, we consider a weaker polynomially decaying moment contraction (PMC) condition on the covariates. In this paper, we obtain nonparametric point estimates of the mean and covariate functions of such a regression model, which we then show to be statistically consistent. We also obtain a simultaneous confidence interval of the mean function using the central limit theorem for the proposed estimator. Such simultaneous inference tools can be used to test for certain specifications of the mean function. Some simulation studies and two real-data analyses have been illustrated to corroborate the findings.

stat.ME↗

arXiv2023

How fast do rumours spread?

We study a rumour propagation model along the lines of \cite{lebensztayn2008disk} as a long-range percolation model on $\Z$. We begin by showing a sharp phase transition-type behaviour in the sense of exponential decay of the survival time of the rumour cluster in the sub-critical phase. In the super-critical phase, \update{under the assumption that radius of influence r.v. has $2+\epsilon$ moment finite (for some $\epsilon>0$)}, we show that the rightmost vertex in the rumour cluster has a deterministic speed in the sense that after appropriate scaling, the location of the rightmost vertex converges a.s.\ to a deterministic positive constant. \update{Under the assumption that radius of influence r.v. has $4+\epsilon$ moment finite,} we obtain a central limit theorem for appropriately scaled and centred rightmost vertex. Later, we introduce a rumour propagation model with reactivation. For this section, we work with a family of exponentially decaying i.i.d. radius of influence r.v.'s, and we obtain the speed result for the scaled rightmost position of the rumour cluster. Each of these results is novel, in the sense that such properties have never been established before in the context of the rumour propagation model on $\Z$, to the best of our knowledge.

math.PR↗

arXiv2023

Real-time forecasting within soccer matches through a Bayesian lens

This paper employs a Bayesian methodology to predict the results of soccer matches in real-time. Using sequential data of various events throughout the match, we utilize a multinomial probit regression in a novel framework to estimate the time-varying impact of covariates and to forecast the outcome. English Premier League data from eight seasons are used to evaluate the efficacy of our method. Different evaluation metrics establish that the proposed model outperforms potential competitors inspired by existing statistical or machine learning algorithms. Additionally, we apply robustness checks to demonstrate the model's accuracy across various scenarios.

stat.AP↗

arXiv2022

Effect of influence in voter models and its application in detecting significant interference in political elections

In this article, we study the effect of vector-valued interventions in votes under a binary voter model, where each voter expresses their vote as a $0-1$ valued random variable to choose between two candidates. We assume that the outcome is determined by the majority function, which is true for a democratic system. The term intervention includes cases of counting errors, reporting irregularities, electoral malpractice etc. Our focus is to analyze the effect of the intervention on the final outcome. We construct statistical tests to detect significant irregularities in elections under two scenarios, one where exit poll data is available and more broadly under the assumption of a cost function associated with causing the interventions. Relevant theoretical results on the consistency of the test procedures are also derived. Through a detailed simulation study, we show that the test procedure has good power and is robust across various settings. We also implement our method on three real-life data sets. The applications provide results consistent with existing knowledge and establish that the method can be adopted for crucial problems related to political elections.

stat.AP↗

arXiv2021

Forecasting Elections from Partial Information Using a Bayesian Model for a Multinomial Sequence of Data

Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be observed in batches, each of which is based on a large number of such trials and can be modeled via multinomial distributions. We postulate that the multinomial probabilities of the categories vary randomly depending on batches. The challenge is to predict accurately on cumulative data based on data up to a few batches as early as possible. On the theoretical front, we first derive sufficient conditions of asymptotic normality of the estimates of the multinomial cell probabilities and present corresponding suitable transformations. Then, in a Bayesian framework, we consider hierarchical priors using multivariate normal and inverse Wishart distributions and establish the posterior convergence. The desired inference is arrived at using these results and ensuing Gibbs sampling. The methodology is demonstrated with election data from two different settings -- one from India and the other from the United States of America. Additional insights of the effectiveness of the proposed methodology are attained through a simulation study.

stat.AP↗

arXiv2020

Coexistence in discrete time Multi-type competing Frog Models

We study coexistence in discrete time multi-type frog models. We first show that for two types of particles on $\mathbb{Z}^d$, for $d\geq2$, for any jumping parameters $p_1, p_2 \in (0,1)$, coexistence occurs with positive probability for sufficiently rich deterministic initial configuration. We extend this to the case of random distribution of initial particles. We study the question of coexistence for multiple types and show positive probability coexistence of $2^d$ types on $\mathbb{Z}^d$ for rich enough initial configuration. We also show an instance of infinite coexistence on $\mathbb{Z}^d$ for $d \geq 3$ provided we have sufficiently rich initial configuration.

math.PR↗

arXiv2018

Branching random walk in the presence of a hard wall

We consider a branching random walk on a $d$-ary tree of height $n$ ($n \in \mathbb{N}$), under the presence of a hard wall which restricts each value to be positive, where $d$ is a natural number satisfying $d\geqslant2$. The question of behaviour of Gaussian processes with long range interactions, for example the discrete Gaussian free field, under the condition that it is positive on a large subset of {\color{blue}vertices}, and a relation with the expected maximum of the processes has been observed. We find the probability of the event that the branching random {\color{blue}walk} is positive at every vertex in the $n^{th}$ generation, and show that the conditional expectation of the Gaussian variable at a typical vertex, under positivity, is less than the expected maximum by order of $\log n$.

math.PR↗

arXiv2015

Convergence of the centered maximum of log-correlated Gaussian fields

We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a randomly shifted Gumbel distribution, and characterize the random shift as the limit in distribution of a sequence of random variables, reminiscent of the derivative martingale in the theory of Branching Random Walk and Gaussian Chaos. We also discuss applications of the main convergence theorem and discuss examples that show that for logarithmically correlated fields, some additional structural assumptions of the type we make are needed for convergence of the centered maximum.

math.PR↗