Related papers: Goodness of fit tests for high-dimensional linear …
The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article,…
Given two candidate models, and a set of target observations, we address the problem of measuring the relative goodness of fit of the two models. We propose two new statistical tests which are nonparametric, computationally efficient…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case…
This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model…
Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to…
We discuss a goodness-of-fit method which tests the compatibility between statistically independent data sets. The method gives sensible results even in cases where the chi^2-minima of the individual data sets are very low or when several…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
Many scientific and engineering applications require fitting regression models that are nonlinear in the parameters. Advances in computer hardware and software in recent decades have made it easier to fit such models. Relative to fitting…
This paper presents a novel method to make statistical inferences for both the model support and regression coefficients in a high-dimensional logistic regression model. Our method is based on the repro samples framework, in which we…
Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also…
Linear regression models are checked by a lack-of-fit (LOF) test to be sure that the model is at least approximatively true. In many practical cases data are sampled sequentially. Such a situation appears in industrial production when goods…
Policy evaluation with linear function approximation is an important problem in reinforcement learning. When facing high-dimensional feature spaces, such a problem becomes extremely hard considering the computation efficiency and quality of…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…