# nsgpr: Estimation of a nonseparable and/or nonstationary covariance... In GPFDA: Gaussian Process for Functional Data Analysis

## Description

Estimate the covariance structure of a zero-mean Gaussian Process with Q-dimensional input coordinates (covariates).

Multiple realisations for the response variable can be used, provided they are observed on the same grid of dimension n_1 x n_2 x ... x n_Q.

Let n = n_1 x n_2 x ... x n_Q and let nSamples be the number of realisations.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```nsgpr( response, input, corrModel = "pow.ex", gamma = 2, nu = 1.5, whichTau = NULL, nBasis = 5, cyclic = NULL, unitSignalVariance = F, zeroNoiseVariance = F, sepCov = F, nInitCandidates = 300, absBounds = 6, inputSubsetIdx = NULL ) ```

## Arguments

 `response` Response variable. This should be a (n x nSamples) matrix where each column is a realisation `input` List of Q input variables (see Details). `corrModel` Correlation function specification used for g(.). It can be either "pow.ex" or "matern". `gamma` Power parameter used in powered exponential kernel function. It must be 0

## Details

The input argument for Q=2 can be constructed as follows:

n1 <- 10

n2 <- 1000

input <- list()

input[] <- seq(0,1,length.out = n1)

input[] <- seq(0,1,length.out = n2)

If we want to use every third lattice point in the second input variable (using Subset of Data), then we can set

inputSubsetIdx <- list()

inputSubsetIdx[] <- 1:n1

inputSubsetIdx[] <- seq(1,n2, by=3)

## Value

A list containing:

MLEsts

Maximum likelihood estimates of B-spline coefficients and noise variance.

response

Matrix of response.

inputMat

Input coordinates in a matrix form

corrModel

Correlation function specification used for g(.)

## References

Konzen, E., Shi, J. Q. and Wang, Z. (2020) "Modeling Function-Valued Processes with Nonseparable and/or Nonstationary Covariance Structure" <arXiv:1903.09981>.

## Examples

 ```1 2``` ```## See examples in vignette: # vignette("nsgpr", package = "GPFDA") ```

GPFDA documentation built on Jan. 29, 2021, 5:14 p.m.