arXiv subjects

Daniel Gervini

Publications and source records attributed to Daniel Gervini.

16 recordsLinked to original sources

arXiv2026

Trend and seasonality estimation for point-process time series

This article introduces estimators of trend and seasonality for time series of point processes. We assume the point processes follow a temporal or spatial doubly-stochastic Poisson model with log-Gaussian intensity functions. The proposed estimators are computationally simple M-estimators. Their asymptotic distribution is derived, and their finite-sample performance is studied by simulation. As an example of real-data application, we study the patterns of bike demand in the Divvy bike-sharing system of the city of Chicago.

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arXiv2025

Autocorrelation functions for point-process time series

This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is sliced into 365 daily replications. We assume the point processes follow a doubly-stochastic Poisson model with log-Gaussian intensity functions. The proposed autocorrelograms are computationally simple and based on binning. The asymptotic distribution of the autocorrelations is established. The ability of the method to detect the patterns of common autoregressive and moving-average time series models is shown by simulation. Two examples of application to temporal and spatial point-process time series are shown, pertaining bike demand in the Divvy bike-sharing system of Chicago and street theft in Chicago, respectively.

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arXiv2021

Spatial kriging for replicated temporal point processes

This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are available at the spatial sites, this method avoids assumptions like isotropy, which are not valid in many applications. As part of the derivations, new nonparametric estimators for the mean and covariance functions of temporal point processes are introduced, and their properties are studied theoretically and by simulation. The method is applied to the analysis of bike demand patterns in the Divvy bicycle sharing system of the city of Chicago.

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arXiv2019

Doubly stochastic models for replicated spatio-temporal point processes

This paper proposes a log-linear model for the latent intensity functions of a replicated spatio-temporal point process. By simultaneously fitting correlated spatial and temporal Karhunen-Loève expansions, the model produces spatial and temporal components that are usually easy to interpret and capture the most important modes of variation and spatio-temporal correlation of the process. The asymptotic distribution of the estimators is derived. The finite sample properties are studied by simulations. As an example of application, we analyze bike usage patterns on the Divvy bike sharing system of the city of Chicago.

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arXiv2018

Joint models for grid point and response processes in longitudinal and functional data

The distribution of the grid points at which a response function is observed in longitudinal or functional data applications is often informative and not independent of the response process. In this paper we introduce a covariation model to estimate and make inferences about this interrelation, by treating the data as replicated realizations of a marked point process. We derive maximum likelihood estimators, the asymptotic distribution of the estimators, and study the estimators' behavior by simulation. We apply the model to an online auction data set and show that there is a strong correlation between bidding patterns and price trajectories.

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arXiv2018

Exploring patterns of demand in bike sharing systems via replicated point process models

Understanding patterns of demand is fundamental for fleet management of bike sharing systems. In this paper we analyze data from the Divvy system of the city of Chicago. We show that the demand of bicycles can be modeled as a multivariate temporal point process, with each dimension corresponding to a bike station in the network. The availability of daily replications of the process allows nonparametric estimation of the intensity functions, even for stations with low daily counts, and straightforward estimation of pairwise correlations between stations. These correlations are then used for clustering, revealing different patterns of bike usage.

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arXiv2017

Multiplicative component models for replicated point processes

We propose a multiplicative semiparametric model for the intensity function of replicated point processes. Two examples of applications are given: a temporal one, about the dynamics of Internet auctions, and a spatial one, about the spatial distribution of street robberies in Chicago.

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arXiv2015

Independent component models for replicated point processes

We propose a semiparametric independent-component model for the intensity functions of a point process. When independent replications of the process are available, we show that the estimators are consistent and asymptotically normal. We study the finite-sample behavior of the estimators by simulation, and as an example of application we analyze the spatial distribution of street robberies in the city of Chicago.

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arXiv2014

Warped Functional Regression

A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we introduce a functional regression method that incorporates time warping as an intrinsic part of the model. The method achieves good predictive power in a parsimonious way and allows unified statistical inference about phase and amplitude components. The asymptotic distribution of the estimators is derived and the finite-sample properties are studied by simulation. An example of application involving ground-level ozone trajectories is presented.

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arXiv2013

Warped Functional Analysis of Variance

This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability. The focus is on single-random-factor models but the approach can be easily generalized to more complex ANOVA models. The behavior of the estimators is studied by simulation, and an application to the analysis of growth curves of flour beetles is presented. Although the model assumes a smooth latent process behind the observed trajectories, smoothness of the observed data is not required; the method can be applied to the sparsely observed data that is often encountered in longitudinal studies.

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arXiv2013

Dynamic Retrospective Regression for Functional Data

Samples of curves, or functional data, usually present phase variability in addition to amplitude variability. Existing functional regression methods do not handle phase variability in an efficient way. In this paper we propose a functional regression method that incorporates phase synchronization as an intrinsic part of the model, and then attains better predictive power than ordinary linear regression in a simple and parsimonious way. The finite-sample properties of the estimators are studied by simulation. As an example of application, we analyze neuromotor data arising from a study of human lip movement.

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arXiv2013

Analysis of AneuRisk65 data: warped logistic discrimination

We analyze the AneuRisk65 curvature functions using a likelihood-based warping method for sparsely sampled curves, and combine it with logistic regression in order to discriminate subjects with aneurysms at or after the terminal bifurcation of the internal carotid artery (the most life-threatening) from subjects with no aneurysms or aneurysms along the carotid artery (the less serious). Significantly lower misclassification rates are obtained when the warping functions are included in the logistic discrimination model, rather than being treated as mere nuisance parameters.

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arXiv2012

Functional robust regression for longitudinal data

We present a robust regression estimator for longitudinal data, which is especially suited for functional data that has been observed on sparse or irregular time grids. We show by simulation that the proposed estimators possess good outlier-resistance properties compared with the traditional functional least-squares estimator. As an example of application, we study the relationship between levels of oxides of nitrogen and ozone in the city of San Francisco.

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arXiv2012

The functional singular value decomposition for bivariate stochastic processes

In this article we present some statistical applications of the functional singular value decomposition (FSVD). This tool allows us to decompose the sample mean of a bivariate stochastic process into components that are functions of separate variables. These components are sometimes interpretable functions that summarize salient features of the data. The FSVD can be used to visually detect outliers, to estimate the mean of a stochastic process or to obtain individual smoothers of the sample surfaces. As estimators of the mean, we show by simulation that FSVD estimators are competitive with tensor-product splines in some situations.

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arXiv2012

Outlier detection and trimmed estimation for general functional data

This article introduces trimmed estimators for the mean and covariance function of general functional data. The estimators are based on a new measure of outlyingness or data depth that is well defined on any metric space, although this paper focuses on Euclidean spaces. We compute the breakdown point of the estimators and show that the optimal breakdown point is attainable for the appropriate choice of tuning parameters. The small-sample behavior of the estimators is studied by simulation, and we show that they have better outlier-resistance properties than alternative estimators. This is confirmed by two real-data applications, that also show that the outlyingness measure can be used as a graphical outlier-detection tool in functional spaces where visual screening of the data is difficult.

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arXiv2010

Detecting and handling outlying trajectories in irregularly sampled functional datasets

Outlying curves often occur in functional or longitudinal datasets, and can be very influential on parameter estimators and very hard to detect visually. In this article we introduce estimators of the mean and the principal components that are resistant to, and then can be used for detection of, outlying sample trajectories. The estimators are based on reduced-rank t-models and are specifically aimed at sparse and irregularly sampled functional data. The outlier-resistance properties of the estimators and their relative efficiency for noncontaminated data are studied theoretically and by simulation. Applications to the analysis of Internet traffic data and glycated hemoglobin levels in diabetic children are presented.

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