Related papers: Fast Partial Quantile Regression
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
Popular Hough Transform-based object detection approaches usually construct an appearance codebook by clustering local image features. However, how to choose appropriate values for the parameters used in the clustering step remains an open…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in…
In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional…
Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising…
I show that ordinary least squares (OLS) predictions can be rewritten as the output of a restricted attention module, akin to those forming the backbone of large language models. This connection offers an alternative perspective on…
This paper investigates a partially linear spatial autoregressive panel data model that incorporates fixed effects, constant and time-varying regression coefficients, and a time-varying spatial lag coefficient. A two-stage least squares…
Spline quantile regression (SQR) is a method introduced recently by Li and Megiddo (2026) for linear quantile regression where the regression coefficients are treated as smooth functions of the quantile level. With the coefficients…
This paper addresses computational challenges in estimating Quantile Regression with Selection (QRS). The estimation of the parameters that model self-selection requires the estimation of the entire quantile process several times. Moreover,…
We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…
The class of Lq-regularized least squares (LQLS) are considered for estimating a p-dimensional vector \b{eta} from its n noisy linear observations y = X\b{eta}+w. The performance of these schemes are studied under the high-dimensional…
We propose an extreme dimension reduction method extending the Extreme-PLS approach to the case where the covariate lies in a possibly infinite-dimensional Hilbert space. The ideas are partly borrowed from both Partial Least-Squares and…
In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the…
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…
Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…
In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, we allow predictors to have various degrees of persistence and exhibit different signal strengths. The number of…
The Partial Least Square Regression (PLSR) exhibits admirable competence for predicting continuous variables from inter-correlated brain recordings in the brain-computer interface. However, PLSR is in essence formulated based on the least…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
Quantitative portfolio allocation requires the accurate and tractable estimation of covariances between a large number of assets, whose histories can greatly vary in length. Such data are said to follow a monotone missingness pattern, under…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…