Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it completely, we use density as a threshold to determine where over a data range reliable multivariate smoothing is possible, whilst accepting that in large...

A simultaneous flexible variable selection procedure is proposed by applying a basis pursuit method to the likelihood function. The basis functions are chosen to be compatible with variable selection in the context of smoothing spline ANOVA models. Since it is a generalized LASSO-type method, it enjoys the favorable property of shrinking coefficients and gives interpretable results. We derive a...

N.P. Lourie, D.T. Chuss, R.M. Henry, E.J. Wollack Abstract The design, fabrication, and performance of truncated circular and square waveguide cross-sections are presented. An emphasis is placed upon numerical and experimental validation of simple analytical formulae that describe the propagation properties of these structures. A test component, a 90-degree phase shifter, was fabricated and tes...

Projection pursuit regression (PPR) can be used to estimate a smooth function of several variables from noisy and scattered data. The estimate is a sum of smoothed one-dimensional projections of the variables. This paper discusses an extension of PPR to exponential family distributions, called generalized projection pursuit regression (GPPR). The proposed model allows multiple responses and non...

This paper concerns the asymptotic properties of a class of criteria for model selection in linear regression models, which covers the most well known criteria as e.g. MALLOWS' Cp, CV (cross-validation), GCV ( generalized cross-validation), AKAIKE's AIC and FPE as well as SCHWARZ' BIC. These criteria are shown to be consistent in the sense of selecting the true or larger models, assuming i.i.d....

Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This paper tries to fill this gap by focusing on the problem of shrinkage parameter selection when estimating sparse precision matrices using the penalized likelih...

Discrete truncate power is very useful for studying the number of nonnegative integer solutions of linear Diophantine equations. In this paper, some detail information about discrete truncated power is presented. To study the number of integer solutions of linear Diophantine inequations, the generalized truncated power and generalized discrete truncated power are defined and discussed respectiv...

The asymptotic properties of smoothing parameter estimates for smoothing splines are developed. We consider a variety of estimates including Generalized Cross Validation, Generalized Maximum Likelihood, and more generally Type II ML estimates and the properties of the marginal posterior mode. Under the usual Sobolov space frequentist assumptions on the function to be estimated , consistency and...

Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive approaches based on Geisser's predictive sample reuse (PSR) methodology and the related Stone's cross-...