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Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a…
The limitation of permutation tests is that they assume exchangeability. It is shown that in generalized linear models one can construct permutation tests from score statistics in particular cases. When under the null hypothesis the…
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…
In small area estimation different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
We use p-values to identify the threshold level at which a regression function takes off from its baseline value, a problem motivated by applications in toxicological and pharmacological dose-response studies and environmental statistics.…
Determining the lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model. This paper proposes a non-inferiority test for the coefficient…
In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualization in a low-dimension framework. However, some popular dimension reduction methodologies fail to achieve this aim when…
It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches although for different reasons. In the first…
We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors $k$ may depend on and diverge with sample size $n$. In addition to the…
In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…
Testing for series correlation among error terms is a basic problem in linear regression model diagnostics. The famous Durbin-Watson test and Durbin's h-test rely on certain model assumptions about the response and regressor variables. The…
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…
We propose a method for constructing p-values for general hypotheses in a high-dimensional linear model. The hypotheses can be local for testing a single regression parameter or they may be more global involving several up to all…
Suppose that a data analyst wishes to report the results of a least squares linear regression only if the overall null hypothesis, $H_0^{1:p}: \beta_1= \beta_2 = \ldots = \beta_p=0$, is rejected. This practice, which we refer to as…
A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…
The effectiveness of model-based versus model-free methods is a long-standing question in reinforcement learning (RL). Motivated by recent empirical success of RL on continuous control tasks, we study the sample complexity of popular…
Regression for spatially dependent outcomes poses many challenges, for inference and for computation. Non-spatial models and traditional spatial mixed-effects models each have their advantages and disadvantages, making it difficult for…
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
We consider the problem of solving linear least squares problems in a framework where only evaluations of the linear map are possible. We derive randomized methods that do not need any other matrix operations than forward evaluations,…