Suchergebnisse

Penalized splines are used in various types of regression analyses, including non‐parametric quantile, robust and the usual mean regression. In this paper, we focus on the penalized spline estimator with general convex loss functions. By specifying the loss function, we can obtain the mean estimator, quantile estimator and robust estimator. We will first study the asymptotic properties of penalized splines. Specifically, we will show the asymptotic bias and variance as well as the asymptotic normality of the estimator. Next, we will discuss smoothing parameter selection for the minimization of the mean integrated squares error. The new smoothing parameter can be expressed uniquely using the asymptotic bias and variance of the penalized spline estimator. To validate the new smoothing parameter selection method, we will provide a simulation. The simulation results show that the consistency of the estimator with the proposed smoothing parameter selection method can be confirmed and that the proposed estimator has better behavior than the estimator with generalized approximate cross‐validation. A real data example is also addressed.

AbstractExponential smoothing has been one of the most popular forecasting methods used to support various decisions in organizations, in activities such as inventory management, scheduling, revenue management, and other areas. Although its relative simplicity and transparency have made it very attractive for research and practice, identifying the underlying trend remains challenging with significant impact on the resulting accuracy. This has resulted in the development of various modifications of trend models, introducing a model selection problem. With the aim of addressing this problem, we propose the complex exponential smoothing (CES), based on the theory of functions of complex variables. The basic CES approach involves only two parameters and does not require a model selection procedure. Despite these simplifications, CES proves to be competitive with, or even superior to existing methods. We show that CES has several advantages over conventional exponential smoothing models: it can model and forecast both stationary and non‐stationary processes, and CES can capture both level and trend cases, as defined in the conventional exponential smoothing classification. CES is evaluated on several forecasting competition datasets, demonstrating better performance than established benchmarks. We conclude that CES has desirable features for time series modeling and opens new promising avenues for research.

AbstractThe Healthcare sector is increasing in importance and relative size in BRICS countries (Brazil, Russia, India, China, South Africa). Despite BRICS relevance, the financial performance of their healthcare companies has been scarcely studied. This research fills this literature gap not only by focusing on the impacts of such diverse business environments on the financial performance of healthcare providers but also by proposing a novel approach to estimate an overall financial performance index based on weighted additive utility functions given a set of financial performance criteria. Precisely, bootstrapped Singular Value Decomposition is the cornerstone for identifying an orthogonal base of rotated financial performance criteria, upon which partial utility functions (PUFs) are estimated using locally estimated scatterplot smoothing (LOESS) polynomial regression. A compromise weighting scheme between singular values and quadratic programming results for minimal covariance and joint entropy matrices of residuals was used for summing up the PUFs. Results indicate that the values of financial performance range between 0.7 and 0.85. We further find that current assets, level of debt and liability, the company's Tobin Q are related to the financial performance. Besides, business freedom, government integrity, tax burden, monetary freedom and government spending are also the determinants of financial performance.

Ad hoc methods in the choice of smoothing parameter in kernel density estimation, al­though often used in practice due to their simplicity and hence the calculated efficiency, are char­acterized by quite big error. The value of the smoothing parameter chosen by Silverman method is close to optimal value only when the density function in population is the normal one. Therefore, this method is mainly used at the initial stage of determining a kernel estimator and can be used only as a starting point for further exploration of the smoothing parameter value. This paper pre­sents ad hoc methods for determining the smoothing parameter. Moreover, the interval of smooth­ing parameter values is proposed in the estimation of kernel density function. Basing on the results of simulation studies, the properties of smoothing parameter selection methods are discussed.

Abstract. Spatial mapping is one of the most useful methods to display information about the seismic parameters of a certain area. As in b-value time series, there is a certain arbitrariness regarding the function selected as smoothing kernel (which plays the same role as the window size in time series). We propose a new method for the calculation of the smoothing kernel as well as its parameters. Instead of using the spatial cell-event distance we study the distance between events (event-event distance) in order to calculate the smoothing function, as this distance distribution gives information about the event distribution and the seismic sources. We examine three different scenarios: two shallow seismicity settings and one deep seismicity catalog. The first one, Italy, allows calibration and showcasing of the method. The other two catalogs: the Lorca region (Spain) and Vrancea County (Romania) are examples of different function fits and data treatment. For these two scenarios, the prior to earthquake and after earthquake b-value maps depict tectonic stress changes related to the seismic settings (stress relief in Lorca and stress build-up zone shifting in Vrancea). This technique could enable operational earthquake forecasting (OEF) and tectonic source profiling given enough data in the time span considered.

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approachis nonparametric and does not assume a particular functional form for thediscount function although we do show how to impose various restrictions inthe estimation. Our method is based on kernel smoothing and is defined asthe minimum of some localized population moment condition. The solution tothe sample problem is not explicit and our estimation procedure isiterative, rather like the backfitting method of estimating additivenonparametric models. We establish the asymptotic normality of our methodsusing the asymptotic representation of our estimator as an infinite serieswith declining coefficients. The rate of convergence is standard for onedimensional nonparametric regression.

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is non-parametric and does not assume particular functional form for the discount function although we do show how to impose various restrictions in the estimation. Our method is based on Kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not explicit and our estimation procedure is iterative, rather like the backfitting method of estimating non-parametric models. We establish the asymptotic normality of our methods using the asymptotic representation of our estimator as an infinite series with declining coefficients. The rate of convergence is standard for one-dimensional nonparametric conversion.

The extended Hodrick-Prescott (HP) method was developed by Polasek (2011) for a class of data smoother based on second order smoothness. This paper develops a new extended HP smoothing model that can be applied for spatial smoothing problems. In Bayesian smoothing we need a linear regression model with a strong prior based on differencing matrices for the smoothness parameter and a weak prior for the regression part. We define a Bayesian spatial smoothing model with neighbors for each observation and we define a smoothness prior similar to the HP filter in time series. This opens a new approach to model-based smoothers for time series and spatial models based on MCMC. We apply it to the NUTS-2 regions of the European Union for regional GDP and GDP per capita, where the fixed effects are removed by an extended HP smoothing model.

The phenomenon of smoothing dichotomy in random‐design nonparametric regression is exposed in nontechnical terms from two recent papers published jointly with Jan Mielniczuk. This concerns the asymptotic distribution of kernel estimators when the errors exhibit long‐range dependence, being instantaneous functions either of Gaussian sequences or of infinite‐order moving averages, depending on the amount of smoothing.

Presents security and other reasons for the North Atlantic Treaty Organization's continued vitality. Other reasons include its role in smoothing relations among members and its institutional adaptability.