In this paper we study penalized regression splines (P-splines), which are low–order basis function splines with a penalty to avoid undersmoothing. Such P–splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. While frequentist methods are available to address this issue, no Bayesian techniques have been developed. Our approach is to model t...

The penalized spline is a popular method for function estimation when the assumption of “smoothness” is valid. In this paper, methods for estimation and inference are proposed using penalized splines under the additional constraints of shape, such as monotonicity or convexity. The constrained penalized spline estimator is shown to have the same convergence rates as the corresponding unconstrain...

In this paper, the analysis of similarity metrics used for performance evaluation of image retrieval frameworks is provided. Image retrieval based on similarity metrics obtains remarkable results in comparison with robust discrimination methods. Thus, the similarity metrics are used in matching process between visual query from user and descriptors of images in preprocessed collection. In contr...

In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One these equations, dissipative wave equation, has found a plethora useful applications different fields. A special class solutions studied for equation including exact approximate solutions. The...

We used two standard methods (the common percentile and the log-power gaussian transformation) and two novel methods (weighted percentile and smoothed spline interpolation) to estimate the 2.5th and 97.5th percentiles of 1000 sets of data from eight diverse distributional forms, generated by Monte Carlo simulation. For each distributional form we derived an estimate of optimal performance. Alth...

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...

Landmark-based thin-plate spline image registration is one of the most commonly used methods for non-rigid medical image registration and anatomical shape analysis. It is well known that this method does not produce a unique correspondence between two images away from the landmark locations because interchanging the role of source and target landmarks does not produce forward and reverse transf...

An adaptive spline method for smoothing is proposed which combines features from both regression spline and smoothing spline approaches One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous curvature of true functions at di erent locations This method can be applied to many multivariate function estimation problems which is illustrated in this pap...

Methods of numerical integration of sampled data are compared in terms of their frequency responses and resolving power. Compared, theoretically and by numerical experiments, are trapezoidal, Simpson, Simpson-3/8 methods, method based on cubic spline data interpolation and Discrete Fourier Transform (DFT) based method. Boundary effects associated with DFT- based and spline-based methods are inv...

Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and op...