Related papers: Cheating with (Recursive) Models
Different agents need to make a prediction. They observe identical data, but have different models: they predict using different explanatory variables. We study which agent believes they have the best predictive ability -- as measured by…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
Uncoupled regression is the problem to learn a model from unlabeled data and the set of target values while the correspondence between them is unknown. Such a situation arises in predicting anonymized targets that involve sensitive…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…
In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structural equations. These linear models have a long tradition and…
The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with…
In this paper, we consider the problem of treating linear regression equation coefficients in the case of correlated predictors. It is shown that in general there are no natural ways of interpreting these coefficients similar to the case of…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
It is well known that individual parameters of strongly correlated predictor variables in a linear model cannot be accurately estimated by the least squares regression due to multicollinearity generated by such variables. Surprisingly, an…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
It is well known that parameters for strongly correlated predictor variables in a linear model cannot be accurately estimated. We look for linear combinations of these parameters that can be. Under a uniform model, we find such linear…
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Results in epidemiology and social science often require the removal of confounding effects from measurements of the pairwise correlation of variables in survey data. This is typically accomplished by some variant of linear regression…
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…
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…