In this paper we develop a general theory of local asymptotics for least squares estimates over polynomial spline spaces in a regression problem. The polynomial spline spaces we consider include univariate splines, tensor product splines, and bivariate or multivariate splines on triangulations. We establish asymptotic normality of the estimate and study the magnitude of the bias due to spline a...

Estimation of small area means in the presence of area level auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. The assumptions on the area level regression are considerably weaker than standard small area models. Both the small area mean functions and the between area variance function are modeled as smooth functions of area level covar...

Let (Xj , Yj) n j=1 be a realization of a bivariate jointly strictly stationary process. We consider a robust estimator of the regression function m(x) = E(Y |X = x) by using local polynomial regression techniques. The estimator is a local M-estimator weighted by a kernel function. Under mixing conditions satisfied by many time series models, together with other appropriate conditions, consiste...

Factorization Machines (FM) are a new model class that combines the advantages of polynomial regression models with factorization models. Like polynomial regression models, FMs are a general model class working with any real valued feature vector as input for the prediction of real-valued, ordinal or categorical dependent variables as output. However, in contrast to polynomial regression models...

Abstract: We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. Th...

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combinations of study variables, in which the weights are calibrated to known control totals, but the assumptions on the superpopulation model are consid...

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have...

This paper deals with an absorption spectroscopic method for trace gas measurements called DOAS (Diierential Optical Absorption Spectroscopy) from a statistical point of view. The DOAS technique is an absorption spectrosco-pic technique to measure trace gas concentrations. It is capable of detecting and measuring a number of important trace gases at tropospheric concentration levels by observin...

We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical optimization. Ideal regression is useful whenever the solution to a learning problem can be described by a ...

Both equation discovery and regression methods aim at inducing models of numerical data. While the equation discovery methods are usually evaluated in terms of comprehensibility of the induced model, the emphasis of the regression methods evaluation is on their predictive accuracy. In this paper, we present Ciper, an efficient method for discovery of polynomial equations and empirically evaluat...