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

 nsgpr R Documentation

## Estimation of a nonseparable and/or nonstationary covariance structure (NSGPR model)

### 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

``````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[[1]] <- seq(0,1,length.out = n1)
input[[2]] <- 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]] <- 1:n1
inputSubsetIdx[[2]] <- 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

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

GPFDA documentation built on Sept. 11, 2023, 1:08 a.m.