wbs: Change-point detection via Wild Binary Segmentation In wbs: Wild Binary Segmentation for Multiple Change-Point Detection

Description

The function applies the Wild Binary Segmentation algorithm to identify potential locations of the change-points in the mean of the input vector `x`. The object returned by this routine can be further passed to the `changepoints` function, which finds the final estimate of the change-points based on chosen stopping criteria.

Usage

 ```1 2 3 4 5``` ```wbs(x, ...) ## Default S3 method: wbs(x, M = 5000, rand.intervals = TRUE, integrated = TRUE, ...) ```

Arguments

 `x` a numeric vector `...` not in use `M` a number of intervals used in the WBS algorithm `rand.intervals` a logical variable; if `rand.intervals=TRUE` intervals used in the procedure are random, thus the output of the algorithm may slightly vary from run to run; for `rand.intervals=FALSE` the intervals used depend on `M` and the length of `x` only, hence the output is always the same for given input parameters `integrated` a logical variable indicating the version of Wild Binary Segmentation algorithm used; when `integrated=TRUE`, augmented version of WBS is launched, which combines WBS and BS into one

Value

an object of class "wbs", which contains the following fields

 `x` the input vector provided `n` the length of `x` `M` the number of intervals used `rand.intervals` a logical variable indicating type of intervals `integrated` a logical variable indicating type of WBS procedure `res` a 6-column matrix with results, where 's' and 'e' denote start- end points of the intervals in which change-points candidates 'cpt' have been found; column 'CUSUM' contains corresponding value of CUSUM statistic; 'min.th' is the smallest threshold value for which given change-point candidate would be not added to the set of estimated change-points; the last column is the scale at which the change-point has been found

Examples

 ```1 2 3 4 5 6 7 8``` ```x <- rnorm(300) + c(rep(1,50),rep(0,250)) w <- wbs(x) plot(w) w.cpt <- changepoints(w) w.cpt th <- c(w.cpt\$th,0.7*w.cpt\$th) w.cpt <- changepoints(w,th=th) w.cpt\$cpt.th ```

Example output

```\$sigma
[1] 1.01788

\$th
[1] 4.469267

\$no.cpt.th
[1] 1

\$cpt.th
\$cpt.th[[1]]
[1] 52

\$Kmax
[1] 50

\$ic.curve
\$ic.curve\$ssic.penalty
[1]  -8.4004911 -15.2257319 -14.5474336 -13.2517953  -7.5276527  -1.7910167
[7]  -1.2690605  -0.9185226   4.8356312  10.0650358  15.5006957  16.7054999
[13]  18.7654211  22.8923430  25.9691081  27.5101908  28.9441351  32.4901492
[19]  35.9447042  41.5445190  46.7148157  49.4234377  52.9425058  58.6748659
[25]  60.9734957  63.6484703  69.4204024  73.4995736  75.6769348  80.1221500
[31]  83.3730628  88.2458964  90.9398746  95.9285430 100.6890101 104.6606878
[37] 107.8540699 110.3617279 110.6376928 114.4159685 116.7171077 121.6614364
[43] 124.3826817 129.3271983 132.1026213 135.0676393 137.7878851 139.7791018
[49] 142.4731503 146.3850549 151.9006760

\$ic.curve\$bic.penalty
[1]  -8.400491 -15.325912 -14.747793 -13.552335  -7.928372  -2.291916
[7]  -1.870140  -1.619781   4.034192   9.163417  14.498897  15.603522
[13]  17.563263  21.590005  24.566590  26.007493  27.341258  30.787092
[19]  34.141467  39.641102  44.711219  47.319661  50.738549  56.370730
[25]  58.569180  61.143974  66.815727  70.794718  72.871899  77.216935
[31]  80.367668  85.140321  87.734120  92.622608  97.282896 101.154393
[37] 104.247596 106.655074 106.830859 110.508955 112.709914 117.554063
[43] 120.175128 125.019465 127.694708 130.559546 133.179612 135.070649
[49] 137.664518 141.476243 146.891684

\$ic.curve\$mbic.penalty
[1]  -8.400491 -13.445467 -11.983714  -9.571232  -2.731608   4.835455
[7]   5.213725   5.460694  12.458591  19.273454  26.070967  27.165282
[13]  30.159508  35.289229  39.003768  40.397016  43.181954  47.268255
[19]  50.511059  56.833596  63.106145  65.688941  69.907763  76.413597
[25]  79.117848  82.585038  89.118173  93.515289  95.515395 101.137380
[31] 104.659081 109.821815 112.964919 118.291142 123.906201 127.686538
[37] 131.651225 134.349663 134.381607 138.511931 141.059464 146.520985
[43] 149.050890 153.804066 156.453663 159.206929 161.683154 163.752528
[49] 166.306376 169.915368 176.381766

\$cpt.ic
\$cpt.ic\$ssic.penalty
[1] 52

\$cpt.ic\$bic.penalty
[1] 52

\$cpt.ic\$mbic.penalty
[1] 52

\$no.cpt.ic
ssic.penalty  bic.penalty mbic.penalty
1            1            1

[[1]]
[1] 52 58 70

[[2]]
[1] 52
```

wbs documentation built on May 30, 2017, 3:56 a.m.