boot_dd {snowboot}

Bootstrapping Empirical Degree Distribution

Description

This function delivers bootstrap estimates of network degree distribution based on an LSMI sample. The bootstrap scheme is non-weighted for seeds (resampling with replacement) and weighted for non-seeds (resampling with replacement, with weights proportional to inverse of the degrees), as described in Section 3.3 by Thompson et al. (2016) and in Algorithm 1 by Gel et al. (2017).

Usage

boot_dd(x, B = 100, cl = 1)

Arguments

x

a list that is the output of lsmi_dd, i.e., an estimate of the degree distribution together with all degrees of seeds and non-seeds from an LSMI.

B

a positive integer, the number of bootstrap replications to perform. Default is 100.

cl

parameter to specify computer cluster for bootstrapping, passed to the package parallel (default is 1, meaning no cluster is used). Possible values are:

• cluster object (list) produced by makeCluster. In this case, new cluster is not started nor stopped;

• NULL. In this case, the function will attempt to detect available cores (see detectCores) and, if there are multiple cores (>1), a cluster will be started with makeCluster. If started, the cluster will be stopped after computations are finished;

• positive integer defining the number of cores to start a cluster. If cl = 1, no attempt to create a cluster will be made. If cl > 1, cluster will be started (using makeCluster) and stopped afterwards (using stopCluster).

Value

A list object of class "snowboot" consisting of:

fkb

A matrix of dimensions length(x$fk)\timesB with B bootstrap estimates of the degree distribution. The bootstrap estimates are computed according to Equation 1 by Gel et al. (2017), also see Chen et al. (2018).

mub

A vector of length B with bootstrapped estimates of the network mean degree. The bootstrap estimates are computed according to Equation 2 by Gel et al. (2017).

fk

A vector with an estimate of the degree distribution, copied from the input x$fk.

mu

An estimate of the mean degree, copied from the input x$mu.

B

The number of bootstrap replications performed.

References

Chen Y, Gel YR, Lyubchich V, Nezafati K (2018). “Snowboot: bootstrap methods for network inference.” The R Journal, 10(2), 95–113. doi: 10.32614/RJ-2018-056.

Gel YR, Lyubchich V, Ramirez Ramirez LL (2017). “Bootstrap quantification of estimation uncertainties in network degree distributions.” Scientific Reports, 7, 5807. doi: 10.1038/s41598-017-05885-x.

Thompson ME, Ramirez Ramirez LL, Lyubchich V, Gel YR (2016). “Using the bootstrap for statistical inference on random graphs.” Canadian Journal of Statistics, 44(1), 3–24. doi: 10.1002/cjs.11271.

See Also

lsmi, lsmi_dd, boot_ci

Examples

net <- artificial_networks[[1]]
lsmiEstimate <- lsmi_dd(net = net, n.seed = 5, n.wave = 3)
bootEstimates <- boot_dd(lsmiEstimate, B = 10)