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We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…
A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate t prior distribution for the…
In structured additive distributional regression, the conditional distribution of the response variables given the covariate information and the vector of model parameters is modelled using a P-parametric probability density function where…
Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$. The observations $y_i \in \mathbb{R}$ are thereby supposed to follow a noisy single-index…
The estimation law of unknown parameters vector ${\theta}$ is proposed for one class of nonlinearly parametrized regression equations $y\left( t \right) = \Omega \left( t \right)\Theta \left( \theta \right)$. We restrict our attention to…
Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T: \delta = 1_{Y \leq T}.…
We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case…
Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…
The purpose of this paper is to explain the interest and importance of (approximate) models and model selection in Statistics. Starting from the very elementary example of histograms we present a general notion of finite dimensional model…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection…
We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our…
We discuss semiparametric regression when only the ranks of responses are observed. The model is $Y_i = F (\mathbf{x}_i'{\boldsymbol\beta}_0 + \varepsilon_i)$, where $Y_i$ is the unobserved response, $F$ is a monotone increasing function,…