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Efficient estimation under bias sampling, censoring or truncation is a difficult question which has been partially answered and the usual estimators are not always consistent. Several biased designs are considered for models with variables…

An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…

Whereas confidence intervals are used to assess uncertainty due to unmeasured individuals, confounding intervals can be used to assess uncertainty due to unmeasured attributes. Previously, we have introduced a methodology for computing…

Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…

We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…

Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…

A criterion is proposed for testing hypothesis about the nature of the error variance in the dependent variable in linear model, which separates correctly and incorrectly specified models. In the former only measurement errors determine the…

We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty.…

Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

Researchers often use linear regression to analyse randomized experiments to improve treatment effect estimation by adjusting for imbalances of covariates in the treatment and control groups. Our work offers a randomization-based inference…

In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential…

Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…

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…

Regression adjustments are often made to experimental data. Since randomization does not justify the models, bias is likely; nor are the usual variance calculations to be trusted. Here, we evaluate regression adjustments using Neyman's…

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

We present methods for estimating loss-based measures of the performance of a prediction model in a target population that differs from the source population in which the model was developed, in settings where outcome and covariate data are…