Related papers: Single Index Fr\'echet Regression
Regressing a function $F$ on $\mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its…
In this paper, we propose a simplex regression model in which both the mean and the dispersion parameters are related to covariates by nonlinear predictors. We provide closed-form expressions for the score function, for Fisher's information…
In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…
Panel data analysis is an important topic in statistics and econometrics. Traditionally, in panel data analysis, all individuals are assumed to share the same unknown parameters, e.g. the same coefficients of covariates when the linear…
Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the…
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…
We develop IV Fr\'echet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fr\'echet…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
The distributional single index model is a semiparametric regression model in which the conditional distribution functions $P(Y \leq y | X = x) = F_0(\theta_0(x), y)$ of a real-valued outcome variable $Y$ depend on $d$-dimensional…
Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…
Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many…
Advancements in data collection have led to increasingly common repeated observations with complex structures in biomedical studies. Treating these observations as random objects, rather than summarizing features as vectors, avoids feature…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for machine learning, where the response variable is modeled as a monotonic function of a linear combination of features. Estimation in this context requires learning…
Consider a random vector (X',Y)', where X is d-dimensional and Y is one-dimensional. We assume that Y is subject to random right censoring. The aim of this paper is twofold. First, we propose a new estimator of the joint distribution of…
We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…
In this article, we consider the problem of estimating the index parameter $\alpha_0$ in the single index model $E[Y |X] = f_0(\alpha_0^T X)$ with $f_0$ the unknown ridge function defined on $\mathbb{R}$, $X$ a d-dimensional covariate and…
We provide the first regression framework that simultaneously accommodates responses taking values in a general metric space and predictors lying on a general torus. We propose intrinsic local constant and local linear estimators that…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…