Description Usage Arguments Value Examples

View source: R/bootstrap_functions.R

`bootSVD_LD`

Calculates the bootstrap distribution of the principal components (PCs) of a low dimensional matrix. If the score matrix is inputted, the output of `bootSVD_LD`

can be used to to calculate bootstrap standard errors, confidence regions, or the full bootstrap distribution of the high dimensional components. Most users may want to instead consider using `bootSVD`

, which also calculates descriptions of the high dimensional components. Note that `bootSVD`

calls `bootSVD_LD`

.

1 2 3 | ```
bootSVD_LD(UD, DUt = t(UD), bInds = genBootIndeces(B = 1000, n =
dim(DUt)[2]), K, warning_type = "silent", verbose = getOption("verbose"),
centerSamples = TRUE)
``` |

`UD` |
(optional) a ( |

`DUt` |
the transpose of |

`bInds` |
a ( |

`K` |
the number of PCs to be estimated. |

`warning_type` |
passed to |

`verbose` |
if |

`centerSamples` |
whether each bootstrap sample should be centered before calculating the SVD. |

For each bootstrap matrix *(DU')^b*, let *svd(DU')=:A^b D^b U^b*, where *A^b* and *U^b* are (*n* by *n*) orthonormal matrices, and *D^b* is a (*n* by *n*) diagonal matrix *K*. Here we calculate only the first `K`

columns of *A^b*, but all `n`

columns of *U^b*. The results are stored as a list containing

`As` |
a |

`ds` |
a |

`Us` |
a |

`time` |
The computation time required for the procedure, taken using |

If the score matrix is inputted to `bootSVD_LD`

, the results can be transformed to get the PCs on the original space by multiplying each matrix *A^b* by the PCs of the original sample, *V* (see `As2Vs`

). The bootstrap scores of the original sample are equal to *U^b D^b*.

1 2 3 4 5 6 7 | ```
#use small n, small B, for a quick illustration
set.seed(0)
Y<-simEEG(n=100, centered=TRUE, wide=TRUE)
svdY<-fastSVD(Y)
DUt<- tcrossprod(diag(svdY$d),svdY$u)
bInds<-genBootIndeces(B=50,n=dim(DUt)[2])
bootSVD_LD_output<-bootSVD_LD(DUt=DUt,bInds=bInds,K=3,verbose=interactive())
``` |

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