Related papers: An Asympirical Smoothing Parameters Selection Appr…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the…
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…
We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…
The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to…
The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate…