SUMMARY Multivariate data analysis permits the study of observations which are finite sets numbers, but modern collection situations can involve data, or processes giving rise to them, functions. Functional involves infinite dimensional and/or data. The paper shows how theory L-splines support generalizations linear modelling and principal components samples drawn from random Spline smoothing rests on a partition function space into two orthogonal subspaces, one contains obvious structural...

Piecewise polynomials or splines extend the advantages of to include greater flexibility, local effects parameter changes and possibility imposing useful constraints on estimated functions. Among these is monotonicity, which can be an important property in many curve estimation problems. This paper shows virtues monotone through a number statistical applications, including response variable transformation nonlinear regression, variables multiple principal components canonical correlation,...

Summary We propose a new method for estimating parameters in models that are defined by system of non-linear differential equations. Such equations represent changes outputs linking the behaviour derivatives process to itself. Current methods from noisy data computationally intensive and often poorly suited realization statistical objectives such as inference interval estimation. The paper describes uses measurements on subset variables estimate defining approach is based modification...

Scale discriminability is the ability of a measure to discriminate among individuals ordered along some continuum, such as depressive severity. We used nonparametric item-response model examine scale in Beck Depression Inventory (BDI) and Center for Epidemiologic Studies (CES-D) both college depressed outpatient samples. In sample, CES-D was more discriminating than BDI, but standard cutoff score 16 overestimated likely prevalence depression (45%). The may be effective BDI detecting...

Summary Many situations call for a smooth strictly monotone function f of arbitrary flexibility. The family functions defined by the differential equation D 2 =w Df, where w is an unconstrained coefficient comprises twice differentiable functions. solution to this = C 0 + 1 −1{exp(D −1 w)}, and are constants partial integration operator. A basis expanding suggested that permits explicit in expression f. In fitting data, it also useful regularize penalizing integral since measure relative...

Summary Functional data analysis involves the extension of familiar statistical procedures such as principal components analysis, linear modelling, and canonical correlation to where raw observation xi is a function. An essential preliminary functional often registration or alignment salient curve features by suitable monotone transformations hi argument t, so that actual analyses are carried out on values xi{hi(t)}. This referred dynamic time warping in engineering literature. In effect,...

Summary We describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes. Adopting an approach that is typical functional analysis, we propose spline regression computationally efficient, allows spatially covariate information can impose various conditions boundaries domain. Accurate surface estimation achieved by use piecewise linear quadratic finite elements.

The abundance of functional observations in scientific endeavors has led to a significant development tools for data analysis (FDA). This kind comes with several challenges: infinite-dimensionality function spaces, observation noise, and so on. However, there is another interesting phenomena that creates problems FDA. often lateral displacements/deformations curves, phenomenon which different from the height or amplitude variability termed phase variation. presence artificially inflates...

Abstract The authors develop a functional linear model in which the values at time t of sample curves yi (t) are explained feed‐forward sense by covariate xi(s) observed times s ±.t. They give special attention to case ± [t — δ, t], where lag parameter δ is estimated from data. use finite element method estimate bivariate regression function β(s, t), defined on triangular domain t. apply their problem predicting acceleration lower lip during speech basis electromyographical recordings muscle...