Related papers: Assumption Lean Regression
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
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…
In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted…
The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…
Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. This article develops a continuous threshold expectile regression for modeling data in which…
We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…
We introduce a new regression method that relates the mean of an outcome variable to covariates, under the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse…
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…
Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we…
Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…
Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…
Response-biased sampling, in which samples are drawn from a popula- tion according to the values of the response variable, is common in biomedical, epidemiological, economic and social studies. In particular, the complete obser- vations in…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a…