In this paper, we propose control theoretic smoothing splines with L optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the res...

In this paper, some of the relationships between optimal control and trajectory planning are examined. When planning trajectories for linear control systems, a demand that arises naturally in air tra$c control or noise contaminated data interpolation is that the curve passes close to given points, or through intervals, at given times. In this paper, we produce these curves by solving an optimal...

The paper considers functional linear regression, where scalar responses Y1, . . . , Yn are modeled in dependence of random functions X1, . . . ,Xn. We propose a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty. Theoretical analysis concentrates on the error in an out-ofsample prediction of the response for a new random function ...

Given a data set (ti, yi), i = 1, . . . , n with the ti ∈ [0, 1] non-parametric regression is concerned with the problem of specifying a suitable function fn : [0, 1] → R such that the data can be reasonably approximated by the points (ti, fn(ti)), i = 1, . . . , n. If a data set exhibits large variations in local behaviour, for example large peaks as in spectroscopy data, then the method must ...

We discuss a flexible method for modeling survival data using penalized smoothing splines when the values of covariates change for the duration of the study. The Cox proportional hazards model has been widely used for the analysis of treatment and prognostic effects with censored survival data. However, a number of theoretical problems with respect to the baseline survival function remain unsol...

We study trend filtering, a recently proposed tool of Kim et al. (2009) for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree splin...

In this paper, we develop a fast algorithm for a smoothing spline estimator in multivariate regression. To accomplish this, we employ general concepts associated with roughness penalty methods in conjunction with the theory of radial basis functions and reproducing kernel Hilbert spaces. It is shown that through the use of compactly supported radial basis functions it becomes possible to recove...

In this paper we present a unified discussion of different approaches to the identification of smoothing spline analysis of variance (ANOVA) models: (i) the “classical” approach (in the line of Wahba in Spline Models for Observational Data, 1990; Gu in Smoothing Spline ANOVA Models, 2002; Storlie et al. in Stat. Sin., 2011) and (ii) the State-Dependent Regression (SDR) approach of Young in Nonl...

In this article, we consider control theoretic splines with L optimization for rejecting outliers in data. Control theoretic splines are either interpolating or smoothing splines, depending on a cost function with a constraint defined by linear differential equations. Control theoretic splines are effective for Gaussian noise in data since the estimation is based on L optimization. However, in ...

Smoothing splines provide a powerful and flexible means for nonparametric estimation inference. With cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace derive low-rank approximation of estimates. We develop method approximate eigensystem when it unknown error bounds The proposed methods ar...