Description Usage Arguments Details Value Variance Estimation References Examples

View source: R/createNparReg.R

This function takes the lattice from formLattice (which fills the region of interest) along with the list of responses and their locations, and creates a prediction surface. The approach is kernel non-parametric regression with the kernels created by a k-step diffusion on the lattice about each location where a response was collected.

1 | ```
createNparReg(formLatticeOutput, Z, PointPattern = NULL, M = 0.5, k)
``` |

`formLatticeOutput` |
An object returned by formLattice or editLattice. |

`Z` |
Vector of responses to be smoothed. |

`PointPattern` |
A 2 column matrix or data frame of locations. |

`M` |
The maximum probability that the random walk will move. |

`k` |
Number of steps. |

We denote by *K_{ik}(s)* the kernel obtained by assigning the node
nearest to the ith response and then running a k-step diffusion on
the lattice and evaluating the resulting density at location s.
Then the estimator *\hat{f}(s) = (∑_i K_{ik}(s)*Z_i)/∑_i K_{ik}(s)*
which is the traditional kernal regression estimator with diffusion
kernels. This approach leads to a non-parametric regression that
respects the boundaries of the polygonal region. The construction of the
kernels is detailed in Barry and McIntyre (2011). Using kernels to
perform nonparametric regression is described in many publications, including
Wasserman (2006).

A list of class NparRegOut with elements:

EW_locs Vector of EW locations.

NS_locs Vector of NS locations.

nodes Matrix of node locations in lattice.

boundaryPoly Matrix showing bounding polynomial.

hole_list List of polygons, holes in region.

PointPattern Matrix of the locations of the data.

which_nodes Matrix locations of nodes closest to data.

NparRegNum Vector of numerators of the regression estimates

NparRegDenom Vector of denominators of the regression estimates

sigma2 Numeric, estimate of the noise variance.

We use the variance estimator *∑ e_{i,-i}^2/n*, where *e_{i,-i}* is the ith deleted residual.

Larry Wasserman. All of Nonparametric Statistics. Springer Science + Business Media, Inc. N.Y. 2006.

#' @references Julie McIntyre, Ronald P. Barry (2018) A Lattice-Based Smoother for Regions with Irregular Boundaries and Holes. Journal of Computational and Graphical Statistics. <doi:10.1080/10618600.2017.1375935>

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
data(nparExample)
attach(nparExample)
plot.new()
# Simulate a response variable
index1 = (grid2[,2]<0.8)|(grid2[,1]>0.6)
Z = rep(NA,length(grid2[,1]))
n1 = sum(index1)
n2 = sum(!index1)
Z[index1] <- 3*grid2[index1,1] + 4 + rnorm(n1,0,sd=0.4)
Z[!index1] <- -2*grid2[!index1,1] + 4 + rnorm(n2,0,sd=0.4)
#
coords=rbind(polygon2,polygon2[1,])
plot(coords,type="l")
points(grid2,pch=19,cex=0.5,xlim=c(-0.1,1))
text(grid2,labels=round(Z,1),pos=4,cex=0.5)
#
nodeFillingOutput <- nodeFilling(poly=polygon2, node_spacing=0.025)
plot(nodeFillingOutput)
formLatticeOutput <- formLattice(nodeFillingOutput)
NparRegOut <- createNparReg(formLatticeOutput,Z,PointPattern=grid2,k=2)
plot(NparRegOut)
``` |

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