Related papers: Multiscale quantile segmentation
Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…
Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
Motivated by a broad range of potential applications, we address the quantile prediction problem of real-valued time series. We present a sequential quantile forecasting model based on the combination of a set of elementary nearest…
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
I introduce a generic method for inference on entire quantile and regression quantile processes in the presence of a finite number of large and arbitrarily heterogeneous clusters. The method asymptotically controls size by generating…
In regression modelling approach, the main step is to fit the regression line as close as possible to the target variable. In this process most algorithms try to fit all of the data in a single line and hence fitting all parts of target…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
Quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for…
Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values…
Binary segmentation, which is sequential in nature is thus far the most widely used method for identifying multiple change points in statistical models. Here we propose a top down methodology called arbitrary segmentation that proceeds in a…