Metodiev Martin

2025-10-21

Modelling the data

In this example, the correlation matrix of the data is a linear combination of the following covariates:

  1. The intercept

plot of chunk intercept 2. X1

plot of chunk X1 2. X2

plot of chunk X2

  1. The interaction between X1 and X2

plot of chunk interaction Let’s combine all these covariates into a list.

  1. There is also a spatial effect, which has the following adjacency matrix:

plot of chunk spatial

Preparing the data

We simulate data from the standard normal distribution:

The correlation matrix of this distribution is a weighted sum of the covariates:

![plot of chunk show sigma](figure/show sigma-1.png)

Computing the WSCE, SCE and IVE

The SCE estimates the linear coefficients of the covariates to estimate the correlation matrix. Notice how the squares representing different covariates have different sizes and colors.

![plot of chunk compute sce](figure/compute sce-1.png)

Suppose that one suspects that the data does not follow a normal distribution. In that case, one should use our semiparamteric estimator, the IVE.

Let’s initialize the data from a different distribution,

and compute the IVE:

![plot of chunk compute ive](figure/compute ive-1.png) One might also be worried about the model not being specified correctly. For example, one of the covariates could be unknown. In this case, one should use the WSCE.

Let us, e.g., suppose that we do not know that interactions are present. Let us simulate the data from the same normal distribution,

but compute the WSCE without X2 (NOTE: a lot faster if parallelize=TRUE and ncores>1):

![plot of chunk compute wsce](figure/compute wsce-1.png) Notice that the parameter lambda is far away from 1, indicating that the model is misspecified.

## [1] "lambda: 0.0726239379078317"