hist2dsm: Smooth a 2D histogram

In JOPS: Practical Smoothing with P-Splines

Smooth a 2D histogram

Description

Fit a 2D smooth P-spline surface to a matrix of counts, assuming Poisson distributed observations.

Usage

hist2dsm(
  Y,
  nsegx = 10,
  nsegy = nsegx,
  bdeg = 3,
  lambdax = 10,
  lambday = lambdax,
  dx = 3,
  dy = dx,
  Mu = Y + 0.01,
  kappa = 1e-04,
  tol = 1e-05
)

Arguments

Y	a matrix of counts.
nsegx	the number of knots along x (default=10).
nsegy	the number of evenly spaced knots along y for Tensor product B-spline basis (default=10).
bdeg	the degree of the basis, default is 3.
lambdax	the positive number for the tuning parameter along x.
lambday	the positive number for the tuning parameter along y.
dx	the order of the difference penalty along x, default is 3.
dy	the order of the difference penalty along y, default is 3.
Mu	the initialization of the mean (default Y + 0.01).
kappa	a (small, positive) number for ridge tuning parameter to stabilize estimation (default 1e-4).
tol	the convergence criterion (default 1e-5).

Value

A list with elements:

ed	the effective dimension of the smooth 2D surface.
Mu	a matrix with the smooth estimates, with dimensions of dim(Y)
pen	the numerical value of the penalty.

Author(s)

Paul Eilers

References

Eilers, P.H.C., Marx, B.D., and Durban, M. (2015). Twenty years of P-splines, SORT, 39(2): 149-186.

Eilers, P.H.C. and Marx, B.D. (2021). Practical Smoothing, The Joys of P-splines. Cambridge University Press.

Examples

x = faithful$eruptions
y = faithful$waiting
h = hist2d(x, y, c(100, 100))
sm = hist2dsm(h$H, nsegx = 25, nsegy = 25, bdeg = 3, lambdax = 10, lambday = 10)
image(h$xgrid, h$ygrid, sm$Mu, xlab = 'Eruption length (min)',
      ylab = 'Waiting time (min)', main = 'Old Faithful')

JOPS documentation built on Sept. 8, 2023, 5:42 p.m.