fda (version 1.2.3)

pda.fd: Principal Differential Analysis

Description

Principal differential analysis (PDA) estimates a system of linear differential equations that define functions that fit the data and their derivatives.

Usage

pda.fd(xfdlist, bwtlist=NULL,
       awtlist=NULL, ufdlist=NULL, nfine=501)

Arguments

xfdlist

a list whose members are functional data objects. Each of these objects contain one or more functions that are variables to be represented by a differential equation. The length of the list is the size of the system of differential equations. The number

bwtlist

a list array with the first two dimensions are equal to the number of variables in the system (the length of list xfdlist) and the last dimension equal to the order of each equation. The order of the equations is assumed to be the same for e

awtlist

a list containing weight functions for forcing functions.

In addition to terms in each of the equations involving terms corresponding to each derivative of each variable in the system, each equation can also have a contribution from one or more exogenou

ufdlist

a list containing forcing functions. This is a list array of the same size as awtlist and each member is a functional data object corresponding to a forcing function. The number of replicates must be equal to that of the variables themselves,

nfine

a number of values for a fine mesh. The estimation of the differential equation involves discrete numerical quadrature estimates of integrals, and these require that functions be evaluated at a fine mesh of values of the argument. This argument defines t

Value

• a named list of length 3 with components:
• bwtlist
  a list array of the same dimensions as the corresponding argument, containing the estimated or fixed weight functions defining the system of linear differential equations.
• resfdlist
  a list of length equal to the number of variables or equations. Each members is a functional data object giving the residual functions or forcing functions defined as the left side of the equation (the derivative of order m of a variable) minus the linear fit on the right side. The number of replicates for each residual functional data object is the same as that for the variables.
• awtlist
  a list of the same dimensions as the corresponding argument. Each member is an estimated or fixed weighting function for a forcing function.

See Also

pca.fd, cca.fd

Examples

#See analyses of daily weather data for examples.