Conduct an AMOC hypothesis test — amoc

Conduct an at-most one changepoint hypothesis test for changes in the covariance operator of functional data based on the FKWC (functional Kruskal–Wallis covariance changepoint) procedures outlined by Ramsay and Chenouri (2025).

Usage

amoc_test(data, ranks = NULL, depth = c("RPD", "FM", "LTR", "FMd", "RPDd"))

Arguments

data: Data in matrix or data.frame form, where each row is an observation and each column is a dimension.
ranks: Optional if data is already ranked.
depth: Depth function of choice.

Value

A list consisting of:

$changepoint : Index of the estimated changepoint.
$pvalue : The p-value based on the null distribution.
$ranks : A vector of depth-based ranks for each observation.
$method : A string "AMOC test (KWCChangepoint)"

Note

The options for the depth argument are as follows:

RPD: Random projection depth
FM: Frainman-Muniz depth
LTR: $L^2$-root depth, most suitable for detecting changes in the norm
FMd: Frainman-Muniz depth of the data and its first order derivative
RPDd: Random projection depth of the data and its first order derivative

The depth arguments that incorporate the first order derivative (which is approximated using fda.usc::fdata.deriv) result in a more robust detection of changes in the covariance structure (Ramsay and Chenouri, 2025).

References

Ramsay, K., & Chenouri, S. (2025). Robust changepoint detection in the variability of multivariate functional data. Journal of Nonparametric Statistics. https://doi.org/10.1080/10485252.2025.2503891

Examples

set.seed(11)
test_data <- rbind(replicate(3,rnorm(200,1,1)), #before changepoint
                   replicate(3,rnorm(200,1,5))) #after changepoint

amoc_test(test_data)
#> $changepoint
#> [1] 200
#> 
#> $pvalue
#> [1] 0
#> 
#> $ranks
#>   [1] 261 259 232 186 308 349 350 318 237 202 294 337 220 324 249 364 360 299
#>  [19] 339 357 272 372 387 380 356 321 395 325 289 334 309 330 238 258 231 394
#>  [37] 280 263 329 348 270 317 239 298 254 286 248 312 234 375 274 260 296 226
#>  [55] 326 389 365 366 221 253 307 195 400 228 320 290 215 303 384 292 371 247
#>  [73] 191 362 345 379 310 262 283 391 397 276 315 359 236 227 206 268 354 205
#>  [91] 331 347 374 244 243 266 314 291 222 201 265 279 370 218 198 346 355 332
#> [109] 264 242 287 328 376 233 323 378 295 383 340 393 194 327 187 277 368 240
#> [127] 358 197 319 363 361 316 219 342 382 386 257 208 217 229 216 336 304 388
#> [145] 353 390 306 302 293 275 301 385 300 190 284 373 267 196 224 333 311 281
#> [163] 273 367 245 399 271 255 396 250 377 297 278 209 210 351 200 241 252 230
#> [181] 344 343 235 341 282 352 269 313 392 305 223 213 381 214 369 251 288 225
#> [199] 398 338 199  53 145  63  61 147  44  69 175 166 180 161 207  25   4 116
#> [217] 162  23  55  38  36  96  58 137  79 104 109 179  81  21 131 193 164 119
#> [235]  50   7 103  78  16 121 155 335 154 125  20  48  89  97  60  54  35   8
#> [253]  26 105  86  92 152 120  34 163  11 138  72 141  87 113  77   1 112  68
#> [271]  18 177 181 159   2  90 178 107 140  99  93  94  39  73  31 174 142  85
#> [289]  46  13 150 184  51 108 158 160 183  84  70 149 167 171 246 144 101  80
#> [307]  28  88 139  91 127  42 156 129  66 165  43  59 111  74  40  75  12 151
#> [325] 168  95  83 146   3  64  14 134 153 172 122  57 212 143 188 157 133 169
#> [343]  45 211  15 204 170  47  30 118  19  71 136 106 135  17   9   5 110 123
#> [361]  82 203  32 256  29  24 114 115 322  33 185  37 126  27 117 176 102  62
#> [379]  65 189 148  98 124   6  67  76  10 132 128  56 285  49  22  52 100 182
#> [397] 192 173  41 130
#> 
#> $method
#> [1] "AMOC test (KWCChangepoint)"
#>