An extension of Generalized Structured Component Analysis (GSCA), called Functional GSCA, is proposed to analyze functional data that are considered to arise from an underlying smooth curve varying over time or other continua. GSCA has been geared for the analysis of multivariate data. Accordingly, it cannot deal with functional data that often involve different measurement occasions across participants and a large number of measurement occasions that exceed the number of participants. Functional GSCA addresses these issues by integrating GSCA with spline basis function expansions that represent infinite-dimensional curves onto a finite-dimensional space. For parameter estimation, functional GSCA minimizes a penalized least squares criterion by using an alternating penalized least squares estimation algorithm. The usefulness of functional GSCA is illustrated with gait data.

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

Dual scaling (DS) is a multivariate exploratory method equivalent to correspondence analysis when analysing contingency tables. However, for the analysis of rating data, different proposals appear in the DS and correspondence analysis literature. It is shown here that a peculiarity of the DS method can be exploited to detect differences in response styles. Response styles occur when respondents use rating scales differently for reasons not related to the questions, often biasing results. A spline-based constrained version of DS is devised which can detect the presence of four prominent types of response styles, and is extended to allow for multiple response styles. An alternating nonnegative least squares algorithm is devised for estimating the parameters. The new method is appraised both by simulation studies and an empirical application.

This work presents a $\textsf{Python}$ EMD package named AdvEMDpy that is both more flexible and generalises existing empirical mode decomposition (EMD) packages in $\textsf{Python}$, $\textsf{R}$, and $\textsf{MATLAB}$. It is aimed specifically for use by the insurance and financial risk communities, for applications such as return modelling, claims modelling, and life insurance applications with a particular focus on mortality modelling. AdvEMDpy both expands upon the EMD options and methods available, and improves their statistical robustness and efficiency, providing a robust, usable, and reliable toolbox. Unlike many EMD packages, AdvEMDpy allows customisation by the user, to ensure that a broader class of linear, non-linear, and non-stationary time series analyses can be performed. The intrinsic mode functions (IMFs) extracted using EMD contain complex multi-frequency structures which warrant maximum algorithmic customisation for effective analysis. A major contribution of this package is the intensive treatment of the EMD edge effect which is the most ubiquitous problem in EMD and time series analysis. Various EMD techniques, of varying intricacy from numerous works, have been developed, refined, and, for the first time, compiled in AdvEMDpy. In addition to the EMD edge effect, numerous pre-processing, post-processing, detrended fluctuation analysis (localised trend estimation) techniques, stopping criteria, spline methods, discrete-time Hilbert transforms (DTHT), knot point optimisations, and other algorithmic variations have been incorporated and presented to the users of AdvEMDpy. This paper and the supplementary materials provide several real-world actuarial applications of this package for the user’s benefit.

Professional athletes such as soccer players are expected to be in better health than the average member of their age cohort, if only because of the very demands imposed on them by their profession. Moreover, during their active career, their health is monitored on a regular basis. However, whenever a (former) well-known athlete dies, such an event is publicised widely. Perceived mortality among athletes may be distorted. In this article, we examine medium-term mortality of professional soccer players in The Netherlands. More specifically, we answer two questions. First, we examine if the mortality of soccer players is significantly different from mortality in the general population. Second, we assess whether mortality varies by team. We find that mortality among soccer players is significantly lower than in the general population, with no significant between teams variation. The methodology used in this article is easily extended to examine atypical mortality among other groups of athletes.

In human–robot comanipulation, virtual guides are an important tool used to assist the human worker as they constrain the movement of the robot to improve the task accuracy and to avoid undesirable effects, such as collisions with the environment. Consequently, the physical effort and cognitive overload are reduced during accomplishment of comanipulative tasks. However, the construction of virtual guides often requires expert knowledge and modeling of the task, which restricts the usefulness of virtual guides to scenarios with fixed constraints. Moreover, few approaches have addressed the implementation of virtual guides enforcing orientation constraints and, when done, these approaches have treated translation and orientation separately, and consequently there is no synchronization of the translational and rotational motions. To overcome these challenges and enhance the programming flexibility of virtual guides, we present a new framework that allows the user to create 6D virtual guides through XSplines which we define as a combination of Akima splines for the translation component and spherical cubic interpolation of quaternions for the orientation component. For complex tasks, the user is able to initially define a 3D virtual guide and then use this assistance in translational motion to concentrate only on defining the orientations along the path. It is also possible for the user to modify a particular point or portion of a guide while being assisted by it. We demonstrate in an industrial scenario that these innovations provide an intuitive solution to extend the use of virtual guides to 6 degrees of freedom and increase the human worker’s comfort during the programming phase of these guides in an assisted human–robot comanipulation context.

Spot measurements of methane emission rate (n = 18 700) by 24 Angus steers fed mixed rations from GrowSafe feeders were made over 3- to 6-min periods by a GreenFeed emission monitoring (GEM) unit. The data were analysed to estimate daily methane production (DMP; g/day) and derived methane yield (MY; g/kg dry matter intake (DMI)). A one-compartment dose model of spot emission rate v. time since the preceding meal was compared with the models of Wood (1967) and Dijkstra et al. (1997) and the average of spot measures. Fitted values for DMP were calculated from the area under the curves. Two methods of relating methane and feed intakes were then studied: the classical calculation of MY as DMP/DMI (kg/day); and a novel method of estimating DMP from time and size of preceding meals using either the data for only the two meals preceding a spot measurement, or all meals for 3 days prior. Two approaches were also used to estimate DMP from spot measurements: fitting of splines on a ‘per-animal per-day’ basis and an alternate approach of modelling DMP after each feed event by least squares (using Solver), summing (for each animal) the contributions from each feed event by best-fitting a one-compartment model. Time since the preceding meal was of limited value in estimating DMP. Even when the meal sizes and time intervals between a spot measurement and all feeding events in the previous 72 h were assessed, only 16.9% of the variance in spot emission rate measured by GEM was explained by this feeding information. While using the preceding meal alone gave a biased (underestimate) of DMP, allowing for a longer feed history removed this bias. A power analysis taking into account the sources of variation in DMP indicated that to obtain an estimate of DMP with a 95% confidence interval within 5% of the observed 64 days mean of spot measures would require 40 animals measured over 45 days (two spot measurements per day) or 30 animals measured over 55 days. These numbers suggest that spot measurements could be made in association with feed efficiency tests made over 70 days. Spot measurements of enteric emissions can be used to define DMP but the number of animals and samples are larger than are needed when day-long measures are made.

In this article, we begin by recalling the inversion formula for the convolution with the box spline. The equivariant cohomology and the equivariant $K$-theory with respect to a compact torus $G$ of various spaces associated to a linear action of $G$ in a vector space $M$ can both be described using some vector spaces of distributions, on the dual of the group $G$ or on the dual of its Lie algebra $\mathfrak{g}$. The morphism from $K$-theory to cohomology is analyzed, and multiplication by the Todd class is shown to correspond to the operator (deconvolution) inverting the semi-discrete convolution with a box spline. Finally, the multiplicities of the index of a $G$-transversally elliptic operator on $M$ are determined using the infinitesimal index of the symbol.

In this paper, a new splines–based control method for robot manipulators is presented and discussed. The above method can be effectively used for path planning and control of rigid and flexible robots. The computational simplicity of the proposed algorithm, together with its flexibility and its high–level intelligence built in, can be considered as promising tools for achieving the goals of modem robot manipulator design.

For many years the modified Mercalli (MM) scale has been used to describe earthquake damage and effects observed at scattered locations. In the next stage of an analysis involving MM data, isoseismal lines based on the observations have been added to maps by hand, i.e. subjectively. However a few objective methods have been proposed (by e.g. De Rubeis et al., Brillinger, Wald et al. and Pettenati et al.). The work presented here develops objective methods further. In particular the ordinal character of the MM scale is specifically taken into account. Numerical smoothing is basic to the approach and methods involving splines, local polynomial regression and wavelets are illustrated. The approach also allows the inclusion of explanatory variables, for example site effects. The procedure is implemented for data from the 17 October 1989 Loma Prieta earthquake.

Positive, copositive, onesided and intertwining (co-onesided) polynomial and spline approximations of functions are considered. Both uniform and pointwise estimates, which are exact in some sense, are obtained.

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator Whenever T is well-defined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L2(ℝd), and for sets X of the form with Φ either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT* and T* T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators.

It is proved that a regular piecewise n-convex function differs from an n-convex function only by a polynomial spline of degree n - 1. The argument is given in terms of Peano and de la Vallée Poussin derivatives.