Approximating Data with weighted smoothing Splines

Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i, f_n(t_i)), 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 be able to adapt to the local changes in smoothness. Whilst many methods are able to accomplish this they are less successful at adapting derivatives. In this paper we show how the goal of local adaptivity of the function and its first and second derivatives can be attained in a simple manner using weighted smoothing splines. A residual based concept of approximation is used which forces local adaptivity of the regression function together with a global regularization which makes the function as smooth as possible subject to the approximation constraints

Nonparametric Regression, Confidence Regions and Regularization

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in that region where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler

Approximating data with weighted smoothing splines

Given a data set (t_i, y_i), i = 1,... ,n with the t_i ∈ [0, 1] non-parametric regression is concerned with the problem of specifying a suitable function f_n : [0, 1] → R such that the data can be reasonably approximated by the points (t_i, f_n(t_i)), i = 1,... ,n. A common desideratum is that the function fn be smooth but the path towards this goal is often the indirect one of assuming a “true” data generating function f and then measuring performance by the expected mean square. The approach taken in this paper is a different one. We specify precisely what we mean by a function fn being an adequate approximation to the data and then, using weighted splines, we try to maximize the smoothness given the approximation constraints

Confidence regions, non-parametric regression

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region An which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in An where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler. Although the procedure makes no attempt to minimize any loss function such as MISE the resulting estimates have optimal rates of convergence in the supremum norm both for shape and smoothness regularization. We show that rates of convergence can be misleading even for samples of size n = 10^6 and propose a different form of asymptotics which allows model complexity to increase with sample size

Pengaruh Partisipasi Anggaran, Ketepatan Anggaran terhadap Senjangan Anggaran dengan Komitmen Organisasi sebagai Variabel Moderasi (Studi pada Pemerintah Kabupaten Jayapura)

The purpose of this research is to understand the influence of the participation and the budget acuracy against budget gap with a current commitment of organization as moderation variables. This kind of research is quantitative research by the use of the primary data. The research population is civil servants of SKPD in Jayapura regency. The amount of sample was 105. Method used in the study was moderated regression analysis. The results of this study found that the budgeting participation has a positive and significant impact on budget gap, while the budget accuracy can not have positive and significant impact on budget gap. Organization commitment as moderate variable cannot moderating budgeting participation and the budget accuracy to budget gap in Jayapura regency. Keywords: Budget participation, budget accuracy, budget gap, organization commitment

Residual based localisation and quantification of peaks in X-ray diffractograms

We consider data consisting of photon counts of diffracted X-rays as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself must be identified. Most methods of de-noising data of this kind do not explicitly take into account the modality of the final estimate. The procedure we propose is based on the so called taut string method which minimizes the number of peaks subject to a tube constraint on the integrated data. The baseline is identified by combining the result of the taut string with an estimate of the first derivative of the baseline obtained using a weighted smoothing spline. Finally each individual peak is expressed as the finite sum of kernels chosen from a parametric family

Pengaruh Kepemimpinan Transformasional, Keadilan Distributif Dan Prosedural Kompensasi Terhadap Kepuasan Kerja Perawat Di RSU PKU Muhammadiyah Bantul

Background: RSU PKU Muhammadiyah Bantul is a privately-owned public hospital that has been burgeoning. Leadership held at PKU Muhammadiyah Hospital in Bantul today is a transformational leadership. While, for motivating employee, the management of the hospital strives to provide adequate and fair compensation based on employee status, class rank and tenure. Hence, the compensation system will encourage every employee to give excellent service for each patient.Methodology: The research is a quantitative analysis using cross-sectional survey method. Data is obtained by disseminating questionnaire to the population, the whole permanent employee up to 104 respondents.Result: The statistical result indicates that management\u27s policy transformational leadership and distributive justice and procedural compensation rate affect to the satisfaction of work of the nurses at RSU PKU Muhammadiyah Bantul.Summary: Regarding to the result of the research, management\u27s policy to appreciate its employee through a good and fair compensation can significantly improve the satisfaction of work of the nurses at RSU PKU Muhammadiyah Bantul. Moreover, the management should maintain a workable situation and pay a lot of attention to the nurses

Residual-based localization and quantification of peaks in x-ray diffractograms

We consider data consisting of photon counts of diffracted x-ray radiation as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself must be identified. Most methods of de-noising data of this kind do not explicitly take into account the modality of the final estimate. The residual-based procedure we propose uses the so-called taut string method, which minimizes the number of peaks subject to a tube constraint on the integrated data. The baseline is identified by combining the result of the taut string with an estimate of the first derivative of the baseline obtained using a weighted smoothing spline. Finally, each individual peak is expressed as the finite sum of kernels chosen from a parametric family.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS181 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org