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In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square…
Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…
Sparsity in a regression context makes the model itself an object of interest, pointing to a confidence set of models as the appropriate presentation of evidence. A difficulty in areas such as genomics, where the number of candidate…
The incorporation of unlabeled data in regression and classification analysis is an increasing focus of the applied statistics and machine learning literatures, with a number of recent examples demonstrating the potential for unlabeled data…
Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, there is no notion of design optimality…
Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is poorly…
The conditionality principle $C$ plays a key role in attempts to characterize the concept of statistical evidence. The standard version of $C$ considers a model and a derived conditional model, formed by conditioning on an ancillary…
Causal inference, as a major research area in statistics and data science, plays a central role across diverse fields such as medicine, economics, education, and the social sciences. Design-based causal inference begins with randomized…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data.…
Informative interim adaptations lead to random sample sizes. The random sample size becomes a component of the sufficient statistic and estimation based solely on observed samples or on the likelihood function does not use all available…
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,…
The increasing occurrence of ordinal data, mainly sociodemographic, led to a renewed research interest in ordinal regression, i.e. the prediction of ordered classes. Besides model accuracy, the interpretation of these models itself is of…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
R. A. Fisher founded modern statistical inference in 1922 and identified its fundamental problems to be: specification, estimation and distribution. Since then the problem of statistical model specification has received scant attention in…
Observational studies often benefit from an abundance of observational units. This can lead to studies that -- while challenged by issues of internal validity -- have inferences derived from sample sizes substantially larger than randomized…
Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…