Obtaining accurate estimates or prediction from available data is one of the important goals in statistical research. In this thesis, we propose two new statistical methods, with examples of application and simulation studies, to achieve this goal. The parametric penalized spline smoothing procedure is a flexible algorithm that requires no restricted parametric assumption and is proved to obtai...

In this paper, a Catmull±Rom spline-based lane model which describes the perspective e€ect of parallel lines has been proposed for generic lane boundary. Since Catmull±Rom spline can form arbitrary shapes by di€erent sets of control points, it can describe a wider range of lane structures compared with other lane models, i.e. straight and parabolic models. Moreover, the lane detection problem h...

Recently, a novel laser data based SLAM algorithm using B-Spline as features has been developed in [Pedraza et al., 2007]. EKF is used in the proposed BS-SLAM algorithm and the state vector contains the current robot pose together with the control points of the splines. The obervation model used for the EKF update is the intersections of the laser beams with the splines contained in the map. In...

In [1] we proposed a spatially-variant method for removing noise from tomographic projection data using weighted spline smoothing. The projection model in [1] was based on detectors with the same width as their spacing. A better approximation for the detector response of many tomographs is a rectangular function or Gaussian function whose width is twice the detector spacing. (Such systems are a...

Smoothing is an important statistical tool in applied analysis of political data. Smoothers can be use to incorporate nonlinearity, deal with duration dependence, and diagnose residual plots. But smoothers invariably require the analyst to make choices about the amount of smoothing to apply and the criteria for this choice amounts to visual examination. Such visual methods can lead to seemingly...

We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smooth function. The smooth function is represented i...

Abstract: For the past two decades, single-index model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the high dimensional problem in nonparametric regression. In this paper, based on weakly dependent sample, we investigate the single-index prediction (SIP) model which is robust against deviation from the single-index model. The singleindex is...

The purpose of this study was to establish a new statistical method for the analysis of noisy mandibular helical axis parameters, especially the position vector of the finite helical axis (FHA). The subjects were children with anterior cross-bite who had received orthodontic treatment. Maximum mouth-opening was measured by means of an opto-electronic motion analysis system. These movements were...

The non-polynomial spline method is proposed to solve a singular boundary value problems. Some model problems are solved and the numerical results are compared with B-spline approximation and the exact solution. Results obtained by the method indicate the method is simple and effective. Key–Words: Singular point; Singular two-point boundary value problems; Cubic spline