# est.nbdsmooth: Estimate edge probabilities by neighborhood smoothing In graphon: A Collection of Graphon Estimation Methods

## Description

`est.nbdsmooth` takes the expectation of the adjacency matrix in that it directly aims at estimating network edge probabilities without imposing structural assumptions as of usual graphon estimation requires, such as piecewise lipschitz condition. Note that this method is for symmetric adjacency matrix only, i.e., undirected networks.

## Usage

 `1` ```est.nbdsmooth(A) ```

## Arguments

 `A` either Case 1.an `(n-by-n)` binary adjacency matrix, or Case 2.a vector containing multiple of `(n-by-n)` binary adjacency matrices.

## Value

a named list containing

h

a quantile threshold value.

P

a matrix of estimated edge probabilities.

## References

Zhang, Y., Levina, E., and Zhu, J. (2015) Estimating neighborhood edge probabilities by neighborhood smoothing. Arxiv:1509.08588

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## generate a graphon of type No.4 with 3 clusters W = gmodel.preset(3,id=4) ## create a probability matrix for 100 nodes graphW = gmodel.block(W,n=100) P = graphW\$P ## draw 5 observations from a given probability matrix A = gmodel.P(P,rep=5,symmetric.out=TRUE) ## run nbdsmooth algorithm res2 = est.nbdsmooth(A) ## compare true probability matrix and estimated ones par(mfrow=c(1,2)) image(P); title("original P") image(res2\$P); title("nbdsmooth estimated P") ```

graphon documentation built on Nov. 17, 2017, 5:28 a.m.