Related papers: Confidence Sets Based on Penalized Maximum Likelih…
A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study…
In the context of multiple regression model, suppose that the vector parameter of interest \beta is subjected to lie in the subspace hypothesis H\beta = h, where this restriction is based on either additional information or prior knowledge.…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…
We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
Understanding efficiency in high dimensional linear models is a longstanding problem of interest. Classical work with smaller dimensional problems dating back to Huber and Bickel has illustrated the benefits of efficient loss functions.…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
The accurate labeling of datasets is often both costly and time-consuming. Given an unlabeled dataset, programmatic weak supervision obtains probabilistic predictions for the labels by leveraging multiple weak labeling functions (LFs) that…
Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
We study tools for inference conditioned on model selection events that are defined by the generalized lasso regularization path. The generalized lasso estimate is given by the solution of a penalized least squares regression problem, where…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…
Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…