Dimitris Politis · University of California, San Diego · PhdFit
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Dimitris Politis is a professor in the Department of Mathematics at the University of California, San Diego. He holds a Ph.D. in Statistics from Stanford University, obtained in 1990. His research areas include statistics, nonparametrics, bootstrap methods, and time series analysis. He has been recognized with honors such as a Guggenheim Fellowship and is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. His work focuses on advanced statistical methodologies and their applications, contributing significantly to the fields of statistical theory and practice.
ABSTRACT The notion of the inverse autocovariance function (iacf) for stationary time series was introduced by W. Cleveland in the 1970s who proposed two ways to estimate it: one way is to fit an autoregressive (AR) model to the data and use the fitted model's inverse autocovariance as the iacf estimator, and the other method is via a kernel‐smoothed spectral density estimator. Consistency of the iacf estimator at a fixed lag was subsequently proved by R.J. Bhansali in the 1980s based on a linear time series condition. In this article, we relax the linearity assumption and provide sufficient conditions for the consistency of the iacf estimator. We further consider the problem of estimating the vector consisting of the iacf at lags up to , based on a sample of size . We propose several competing estimators of the iacf vector and study their convergence. In addition, we discuss the difficult problem of choosing the order of a fitted AR model, and provide some alternative ways to approach it. Finally, we consider the inverse autocovariance matrix, i.e., the by Toeplitz matrix with element given by the iacf at lag ; we propose an estimator and investigate its consistency properties. Numerical simulations illustrate the finite sample performance of all iacf estimators, including the estimators of the order .
Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under the normality and linearity assumptions, the Prediction Interval (PI) for the response variable can be determined routinely based on the $t$ distribution. Unfortunately, these two assumptions are rarely met in practice. To fully avoid these two conditions, we develop a so-called calibration PI (cPI) which leverages estimations by Deep Neural Networks (DNN) or kernel methods. Moreover, the cPI can be easily adjusted to capture the estimation variability within the prediction procedure, which is a crucial error source often ignored in practice. Under regular assumptions, we verify that our cPI has an asymptotically valid coverage rate. We also demonstrate that cPI based on the kernel method ensures a coverage rate with a high probability when the sample size is large. Besides, with several conditions, the cPI based on DNN works even with finite samples. A comprehensive simulation study supports the usefulness of cPI, and the convincing performance of cPI with a short sample is confirmed with two empirical datasets.
Harvard Data Science Review · 2025-04-21 · 3 citations
articleOpen access
Statistics as a scientific discipline is currently facing the great challenge of finding its place in data science once more. While at the beginning of the last century, the development of the discipline of statistics was initiated by data-related research questions, nowadays, it is often viewed to have not kept up with the current developments in data science, which are largely focused on algorithmic, exploratory and computational aspects and often driven by other disciplines, such as computer science. However, statistics can—and should—contribute to the advances of data science. Of most interest are the strengths of statistics, such as the mathematical focus that leads to theoretical guarantees. This includes methods for formal modeling, hypothesis tests, uncertainty quantification and statistical inference. Of particular interest are also established statistical frameworks to handle causality or data deficiencies such as dependence, missingness, biases or confounding. This paper summarizes the findings of a discussion workshop on the topic that was held in June 2023 in Hannover, Germany. The discussion centered around the following questions: How must statistics be set up so that it can contribute (more) to modern data science? In which direction should it develop further? Which strengths can already be used now? What conditions must be created so that this can succeed? What can be done to arrive at a common language? What is the added value of formal modeling, inference, and the mathematical perspective taken in statistics?
This special issue honors Emeritus Professor Hira Lal Koul of the Department of Statistics and Probability at Michigan State University. Professor Koul's journey in statistics began with his MA in Statistics with distinction and the first position in the Faculty of Arts from the University of Poona in the year 1964. He then moved to the University of California, Berkeley, earning his Ph.D. in December 1967, under the guidance of Peter J. Bickel—a training that set the stage for a career devoted to precision in asymptotics and a deep feel for nonparametric inference. Professor Koul joined Michigan State University (MSU) shortly thereafter, where he spent most of his professional career, and became Professor Emeritus after 50 years, on January 1, 2018. During his tenure at MSU, he helped define the department's intellectual character—with periods of administrative leadership as Acting Chair (1981–82) and later as Chair beginning in 2009. He is a Fellow of the ASA and IMS, an elected member of the International Statistical Institute, recipient of the Alexander von Humboldt Research Award for Senior Scientists, and a recipient of MSU's Distinguished Faculty Award (2005). He also served the profession as President of the International Indian Statistical Association (2005–06) and of the Indian Statistical Association (2009–12). Professor Koul's research bears a distinctive signature: technically elegant and practically motivated. His areas of research include nonparametric inference, inference on short and long memory processes, time series analysis and survival analysis. One of his celebrated contributions is the Koul-Susarla-Van Ryzin estimator of the regression parameter vector in the randomly right-censored multiple linear regression model. One of his pioneering technical results is the weak convergence of weighted empirical processes of independent non-identically distributed random variables published in 1970. His work on weighted empirical processes provides a unifying method for deriving limit distributions of minimum distance, M- and R-estimators in regression and autoregressive models where classical smoothness assumptions may not hold and where errors may be independent or dependent forming short or long memory processes. His monograph on Weighted Empiricals and Linear Models (IMS Monographs, 1992) synthesized this vision, and its expanded version Weighted Empirical Processes in Dynamic Nonlinear Models (Springer, 2002) carries those ideas into the realm of nonlinear and dynamic models—anticipating applications in econometrics and finance. With L. Giraitis and D. Surgailis, he later coauthored the monograph on Large Sample Inference for Long Memory Processes (Imperial College Press, 2012), consolidating theory for dependent data that is perhaps the most authoritative account of the general approach to long memory processes based on Apell polynomials and that continues to inform work on diagnostics and inference in the presence of long-range dependence. Across reliability, censored data, semiparametric regression, and time series, Hira Koul's papers exemplify a philosophy: start from the structure of the stochastic process, choose the right distance or score, and let the asymptotics do the heavy lifting. That approach yielded robust tests and estimators that travel well across models—particularly where non-smooth scores and dependence challenge standard tools. His later grants and publications pressed these ideas into model diagnostics under long memory and spatial statistics, creating bridges from theory to applications that remain highly relevant. Equally consequential is his editorial and community leadership. Professor Koul served as Coordinating Editor of the Journal of Statistical Planning and Inference (1995–2006), Associate Editor of Statistics and Probability Letters from its inception in 1982 through 2007, and then as its Co-Editor-in-Chief (2007–2013). He edited and co-edited special issues and proceedings that celebrated milestones in our field and amplified emerging directions—helping to shape the research agenda as much as to reflect it. Last but not least, Hira Koul has supported the vision of the International Society for NonParametric Statistics (ISNPS) since its founding in 2012 by serving on the ISNPS Council for several years, and on the Scientific Committee of ISNPS conferences. Professor Koul's influence is also measured in people. He has supervised 35 doctoral students—who now populate universities, industry, and government laboratories worldwide—and his academic descendants, numbering in the dozens, continue to extend his ideas in robustness, empirical processes, and dependent data. Many of us were first drawn to these topics by his lucid lectures, his insistence on clean arguments, and his steady encouragement to “let the probability speak.” The international scope of his career is remarkable. From Australia to Austria, Belgium to New Zealand, India to China, Hong Kong and Korea, Professor Koul has been a frequent visiting scholar and plenary speaker, carrying the MSU banner while building global collaborations. Those visits—and the many workshops and symposia he organized or enlivened—seeded new work on change-point analysis, regression with dependence, robust time series, and model diagnostics. We dedicate this special issue with gratitude for Professor Koul's scholarship, mentorship, and service. He has shown that mathematical depth and methodological relevance can go hand in hand, that clarity and rigor invite rather than exclude, and that our community is at its best when we build tools that are robust to the world as it is. On behalf of the contributors, editors, and the broader statistical community, we thank Professor Koul for a lifetime of ideas—and for the example of how to pursue them. We are honored to serve as guest editors for this special issue of the Journal of Time Series Analysis as a tribute to Professor Koul's scientific contributions. This issue assembles 15 invited papers, spanning theoretical and applied statistics, with a strong emphasis on time series analysis, stochastic processes, econometrics, statistical learning, and applications in high-dimensional data, extremes, and forecasting. All papers were refereed as per the standards of the Journal. Gu, Li, Wang, and Wang develop generalized and hierarchical spatiotemporal semi-varying coefficient models with automatic structure identification to more accurately capture, separate, and interpret constant versus spatiotemporally varying effects, demonstrating improved inference, prediction, and practical insights through simulations and an application to particulate matter data. Verma, Stoev, and Chen propose a general framework for optimal prediction of extreme events in time series, deriving closed-form predictors and asymptotic properties for autoregressive and moving average models with light or heavy tails, and demonstrating both the potential and limitations of the approach through an application to solar flare forecasting. Kim, Düker, Fisher, and Pipiras introduce estimation and forecasting methods for high-dimensional count time series using latent Gaussian dynamic factor models, with theoretical guarantees, new model selection strategies, and validation via simulations and applications. Schick proposes empirical likelihood methods for martingale difference and approximate martingale difference sequences, establishing Wilks-type theorems and illustrating applications to confidence region construction for time series and blockwise empirical likelihood for Markov chains. Das, Kuffner, Lahiri, and Nordman establish the theoretical accuracy of Convolved Subsampling for time series statistics, showing it can achieve second-order correctness like the block bootstrap while providing practical guidance on tuning parameters, and demonstrating its effectiveness through numerical comparisons with other block resampling methods. Kreiss, Leucht, and Paparoditis construct simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for lag-window spectral density estimators evaluated at the set of all positive Fourier frequencies. McElroy extends the maximum entropy framework to a generalized class of extreme values with an application to the analysis of effects of crises, such as the Covid-19 epidemic. Cao, Gao, Shao, Sriram, Wang, Wen, and Zhang focus on tail index estimation for tail adversarial stable time series with an application to high-dimensional tail clustering. Bertail, Dudek, and Lenart show the mean square consistency for a generalized subsampling estimator based on the aggregation of the mean, median, and trimmed mean for general non-stationary time series. Bagchi, Bolanos, Lee, and Subba Rao study the dual frequency spectral density function of locally periodic stationary processes with application to testing for correlation between different frequency bands. Müller, Schick, and Wefelmeyer develop a blockwise empirical likelihood methodology for efficient estimation of the stationary distribution of an ergodic Markov chain under linear constraints. Dalla, Giraitis, and Phillips develop some practical and easily implemented statistical procedures to test the mean and variance stability of uncorrelated but serially dependent time series with application to analysis of volatility properties of stock market returns. Barigozzi and Hallin study some of the fundamental issues related to factor models in high-dimensional time series and point to the advantages of the dynamic factor model approach over its static counterpart. Davis and Fernandes consider independent component analysis (ICA) with heavy tail errors and derive consistency when using the distance covariance. Wang and Politis develop estimators of the inverse-autocovariance matrix and establish its consistency in the unbounded case where the dimension of the matrix is the same as the sample size. We are sincerely grateful to all the contributors for sharing their innovative research in areas where Professor Koul has made influential contributions. We would also like to express our heartfelt appreciation to Rob Taylor, Editor-in-Chief of the Journal of Time Series Analysis, for enthusiastically supporting this special issue and helping bring it to fruition. Our deepest thanks go to Priscilla Goldby for her exceptional assistance throughout the peer review process, and to the anonymous reviewers for their careful and insightful evaluations, which greatly enhanced the quality of this issue. The authors declare no conflicts of interest.
ACM / IMS Journal of Data Science · 2025-01-07 · 1 citations
articleSenior author
Deep neural networks (DNN) have received increasing attention in machine learning applications in the past several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN estimator with ReLU activation functions for estimating regression models. The article at hand gives a small improvement on the current error bound based on the latest results on the approximation ability of (forward) DNN. More importantly, however, a non-random subsampling technique—scalable subsampling—is applied to construct a “subbagged” DNN estimator. Under regularity conditions, it is shown that the subbagged DNN estimator is computationally efficient without sacrificing accuracy for either estimation or prediction tasks. Beyond point estimation/prediction, we propose different approaches to build confidence and prediction intervals based on the subbagged DNN estimator. In addition to being asymptotically valid, the proposed confidence/prediction intervals appear to work well in finite samples. All in all, the scalable subsampling DNN estimator offers the complete package in terms of statistical inference, i.e., (a) computational efficiency; (b) point estimation/prediction accuracy; and (c) allowing for the construction of practically useful confidence and prediction intervals.
The Annals of Statistics · 2024-10-01 · 2 citations
articleSenior author
Strict stationarity is an assumption commonly used in time-series analysis in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimators obtained by fitting a (linear) autoregressive model to a general weakly stationary time series is revisited and a Gaussian approximation theorem for the maximum of the estimators of the autoregressive coefficients is derived. To perform statistical inference for the aforementioned second-order parameters of interest, a bootstrap algorithm, the so-called second-order wild bootstrap is applied. Consistency of the bootstrap procedure is proven without imposing strict stationary conditions or structural process assumptions, like linearity. The good finite sample performance of the second-order wild bootstrap is demonstrated by means of simulations.
We investigate the application of prepivoting in conjunction with lag length selection to correct the size and power performance of the Augmented Dickey-Fuller test for a unit root. The bootstrap methodology used to perform the prepivoting is a residual based AR bootstrap that ensures that bootstrap replicate time series are created under the null irrespective of whether the originally observed series obeys the null hypothesis or not. Simulation studies wherein we examine the performance of our proposed method are given; we evaluate our method’s performance on ARMA(1,1) models with varying configurations for size and power performance. We also propose a novel data dependent lag selection technique that uses bootstrap data under the null to select an optimal lag length; the performance of our method is compared to existing lag length selection criteria.
In this paper, we provide a novel Model-free approach based on Deep Neural Network (DNN) to accomplish point prediction and prediction interval under a general regression setting. Usually, people rely on parametric or non-parametric models to bridge dependent and independent variables (Y and X). However, this classical method relies heavily on the correct model specification. Even for the non-parametric approach, some additive form is often assumed. A newly proposed Model-free prediction principle sheds light on a prediction procedure without any model assumption. Previous work regarding this principle has shown better performance than other standard alternatives. Recently, DNN, one of the machine learning methods, has received increasing attention due to its great performance in practice. Guided by the Model-free prediction idea, we attempt to apply a fully connected forward DNN to map X and some appropriate reference random variable Z to Y. The targeted DNN is trained by minimizing a specially designed loss function so that the randomness of Y conditional on X is outsourced to Z through the trained DNN. Our method is more stable and accurate compared to other DNN-based counterparts, especially for optimal point predictions. With a specific prediction procedure, our prediction interval can capture the estimation variability so that it can render a better coverage rate for finite sample cases. The superior performance of our method is verified by simulation and empirical studies.
