arXiv subjects

S. Yaser Samadi

Publications and source records attributed to S. Yaser Samadi.

6 recordsLinked to original sources

arXiv2026

Predicting the 2026 FIFA World Cup with Sufficient Dimension Reduction of Elo Rating Histories

We study probabilistic forecasting of the 2026 FIFA World Cup, the first edition with 48 teams and an added Round of 32. The main idea is to describe team strength not only by the current Elo rating, but by a short history of recent Elo differences. We then reduce this history to a few informative directions using categorical sufficient dimension reduction (SDR). The reduced scores are used in a Poisson double-regression model for home and away goals, which gives full outcome probabilities. We compare eleven models, including logistic regression, standard Poisson regression, ARIMA, and neural-network forecasts of the Elo series, gradient boosting, an ensemble model, and four categorical SDR variants based on sliced inverse regression (SIR) and sliced average variance estimation (SAVE). The models are evaluated out of sample on the 2018 and 2022 World Cups using the ranked probability score (RPS). The results show that SDR-based poisson models improve the traditional approaches, suggesting that recent Elo history contains useful predictive information that is not captured by the current Elo difference alone.

stat.AP↗

arXiv2023

Fourier Methods for Sufficient Dimension Reduction in Time Series

Dimensionality reduction has always been one of the most significant and challenging problems in the analysis of high-dimensional data. In the context of time series analysis, our focus is on the estimation and inference of conditional mean and variance functions. By using central mean and variance dimension reduction subspaces that preserve sufficient information about the response, one can effectively estimate the unknown mean and variance functions of the time series. While the literature presents several approaches to estimate the time series central mean and variance subspaces (TS-CMS and TS-CVS), these methods tend to be computationally intensive and infeasible for practical applications. By employing the Fourier transform, we derive explicit estimators for TS-CMS and TS-CVS. These proposed estimators are demonstrated to be consistent, asymptotically normal, and efficient. Simulation studies have been conducted to evaluate the performance of the proposed method. The results show that our method is significantly more accurate and computationally efficient than existing methods. Furthermore, the method has been applied to the Canadian Lynx dataset.

stat.ME↗

arXiv2023

Reduced-rank Envelope Vector Autoregressive Models

The standard vector autoregressive (VAR) models suffer from overparameterization which is a serious issue for high-dimensional time series data as it restricts the number of variables and lags that can be incorporated into the model. Several statistical methods, such as the reduced-rank model for multivariate (multiple) time series (Velu et al., 1986; Reinsel and Velu, 1998; Reinsel et al., 2022) and the Envelope VAR model (Wang and Ding, 2018), provide solutions for achieving dimension reduction of the parameter space of the VAR model. However, these methods can be inefficient in extracting relevant information from complex data, as they fail to distinguish between relevant and irrelevant information, or they are inefficient in addressing the rank deficiency problem. We put together the idea of envelope models into the reduced-rank VAR model to simultaneously tackle these challenges, and propose a new parsimonious version of the classical VAR model called the reduced-rank envelope VAR (REVAR) model. Our proposed REVAR model incorporates the strengths of both reduced-rank VAR and envelope VAR models and leads to significant gains in efficiency and accuracy. The asymptotic properties of the proposed estimators are established under different error assumptions. Simulation studies and real data analysis are conducted to evaluate and illustrate the proposed method.

stat.ME↗

arXiv2023

itdr: An R package of Integral Transformation Methods to Estimate the SDR Subspaces in Regression

Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and user-friendly tool that introduces several functions based on integral transformation methods for estimating SDR subspaces. In particular, the itdr package incorporates two key methods, namely the Fourier method (FM) and the convolution method (CM). These methods allow for estimating the SDR subspaces, namely the central mean subspace (CMS) and the central subspace (CS), in cases where the response is univariate. Furthermore, the itdr package facilitates the recovery of the CMS through the iterative Hessian transformation (IHT) method for univariate responses. Additionally, it enables the recovery of the CS by employing various Fourier transformation strategies, such as the inverse dimension reduction method, the minimum discrepancy approach using Fourier transformation, and the Fourier transform sparse inverse regression approach, specifically designed for cases with multivariate responses. To demonstrate its capabilities, the itdr package is applied to five different datasets. Furthermore, this package is the pioneering implementation of integral transformation methods for estimating SDR subspaces, thus promising significant advancements in SDR research.

stat.ME↗

arXiv2023

MLE for the parameters of bivariate interval-valued models

With contemporary data sets becoming too large to analyze the data directly, various forms of aggregated data are becoming common. The original individual data are points, but after aggregation, the observations are interval-valued (e.g.). While some researchers simply analyze the set of averages of the observations by aggregated class, it is easily established that approach ignores much of the information in the original data set. The initial theoretical work for interval-valued data was that of Le-Rademacher and Billard (2011), but those results were limited to estimation of the mean and variance of a single variable only. This article seeks to redress the limitation of their work by deriving the maximum likelihood estimator for the all important covariance statistic, a basic requirement for numerous methodologies, such as regression, principal components, and canonical analyses. Asymptotic properties of the proposed estimators are established. The Le-Rademacher and Billard results emerge as special cases of our wider derivations.

stat.ME↗

arXiv2020

Modeling Count Data via Copulas

Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective tool to measure the degree of dependence between two random variables. In this paper, we derived the population version of Spearman's rho correlation via copulas when both random variables are discrete. The closed-form expressions of the Spearman correlation are obtained for some copulas of simple structure such as Archimedean copulas with different marginal distributions. We derive the upper bound and the lower bound of the Spearman's rho for Bernoulli random variables. Then, the proposed Spearman's rho correlations are compared with their corresponding Kendall's tau values. We characterize the functional relationship between these two measures of dependence in some special cases. An extensive simulation study is conducted to demonstrate the validity of our theoretical results. Finally, we propose a bivariate copula regression model to analyze the count data of a \emph{cervical cancer} dataset.

stat.ME↗