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The analysis of spatial point patterns that occur in the network domain have recently gained much attraction and various intensity functions and measures have been proposed. However, the linkage of spatial network statistics to regression…
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
The fractional Brownian motion (fBm) is parameterized by the Hurst exponent $H\in(0,1)$, which determines the dependence structure and regularity of sample paths. Empirical findings suggest that the Hurst exponent may be non-constant in…
Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…
We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) $B_t$ with Hurst parameter $H>1/2$, where the integrands are vector fields…
This paper proposes econometric methods for studying how economic variables respond to function-valued shocks. Our methods are developed based on linear projection estimation of predictive regression models with a function-valued predictor…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian…
This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown…
In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…
Fractal dimension is an effective scaling exponent of characterizing scale-free phenomena such as cities. Urban growth can be described with time series of fractal dimension of urban form. However, how to explain the factors behind fractal…
The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations,…
In this paper, we propose the Continuous Time Fractional Topic Model (cFTM), a new method for dynamic topic modeling. This approach incorporates fractional Brownian motion~(fBm) to effectively identify positive or negative correlations in…
Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data…