R/ddst.extr.test.R

In ddst: Data Driven Smooth Tests

`ddst.extr.test` <-
function(x, base = ddst.base.legendre, c = 100, B=1000, compute.p = F, Dmax = 5, ...) {
# method.name = as.character(substitute(base)) 
 # only Legendre is implemented yet
 base = ddst.base.legendre
 method.name = "ddst.base.legendre"

n   = length(x)
if(n<5) 
	stop("length(x) should be at least 5")
sx  = sort(x)
er2 = sum(sx*(1:n - n:1))/(n*(n-1)*log(2))
er1 = mean(x)+0.5772156649*er2
maxN = max(min(Dmax, length(x)-2, 20),1)

u = NULL
for (j in 1:maxN) 
u[j] = ddst.phi(1-pgumbel(-x,-er1,er2), j, base)
coord = NULL
gg1=mean(1-exp((x-er1)/er2))
gg2=mean((1-exp((x-er1)/er2))*(x-er1)/er2+1)
for (k in 1:Dmax) {
korekta = u[1:k] + t(MMextr12[[k]]) %*% sM22 %*% c(gg1,gg2)
    coord[k] = t(korekta) %*% MMextr[[k]] %*% korekta * n
}

l = ddst.IIC(coord, n, c)
attr(l, "names") = "n. coord"
t = coord[l]
attr(t, "names") = "WT*"
result = list(statistic = t, parameter = l, method = "Data Driven Smooth Test for Extreme Values")
result$data.name = paste(paste(as.character(substitute(x)), collapse=""), ",   base: ", method.name, ",   c: ", c, sep="")
class(result) = "htest"
if (compute.p) {
tmp = numeric(B)
for (i in 1:B) {
y = rnorm(n)
tmpC = ddst.extr.Nk(y, base, Dmax = Dmax, n=length(y))
l = ddst.IIC(tmpC, n, c)
tmp[i] = tmpC[l]
}
p.val = mean(tmp > t)
result$p.value = p.val  
}
result
}


`MMextr12` <-
list(structure(c(0.866025403784439, -0.234141092407759), .Dim = c(2L, 
1L)), structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
1.10810510880576), .Dim = c(2L, 2L)), structure(c(0.866025403784439, 
-0.234141092407759, 0.372677996249965, 1.10810510880576, 0.220479275922049, 
0.215016389907248), .Dim = 2:3), structure(c(0.866025403784439, 
-0.234141092407759, 0.372677996249965, 1.10810510880576, 0.220479275922049, 
0.215016389907248, 0.15, 0.489380181546808), .Dim = c(2L, 4L)), 
    structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152), .Dim = c(2L, 
    5L)), structure(c(0.866025403784439, -0.234141092407759, 
    0.372677996249965, 1.10810510880576, 0.220479275922049, 0.215016389907248, 
    0.15, 0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853), .Dim = c(2L, 6L)), 
    structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287), .Dim = c(2L, 7L)), structure(c(0.866025403784439, 
    -0.234141092407759, 0.372677996249965, 1.10810510880576, 
    0.220479275922049, 0.215016389907248, 0.15, 0.489380181546808, 
    0.110554159678513, 0.142331828329152, 0.0858464589396188, 
    0.294178041927853, 0.069160416896561, 0.100333337378287, 
    0.0572653559113564, 0.202528656207688), .Dim = c(2L, 8L)), 
    structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129), .Dim = c(2L, 9L)), 
    structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937), .Dim = c(2L, 10L)), structure(c(0.866025403784439, 
    -0.234141092407759, 0.372677996249965, 1.10810510880576, 
    0.220479275922049, 0.215016389907248, 0.15, 0.489380181546808, 
    0.110554159678513, 0.142331828329152, 0.0858464589396188, 
    0.294178041927853, 0.069160416896561, 0.100333337378287, 
    0.0572653559113564, 0.202528656207688, 0.0484322104837853, 
    0.0754369796383129, 0.0416597790450531, 0.150701656278937, 
    0.0363320569947933, 0.0594232320521485), .Dim = c(2L, 11L
    )), structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937, 0.0363320569947933, 0.0594232320521485, 
    0.0320512820512820, 0.117963013416300), .Dim = c(2L, 12L)), 
    structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937, 0.0363320569947933, 0.0594232320521485, 
    0.0320512820512820, 0.117963013416300, 0.0285502880368496, 
    0.0484291463698838), .Dim = c(2L, 13L)), structure(c(0.866025403784439, 
    -0.234141092407759, 0.372677996249965, 1.10810510880576, 
    0.220479275922049, 0.215016389907248, 0.15, 0.489380181546808, 
    0.110554159678513, 0.142331828329152, 0.0858464589396188, 
    0.294178041927853, 0.069160416896561, 0.100333337378287, 
    0.0572653559113564, 0.202528656207688, 0.0484322104837853, 
    0.0754369796383129, 0.0416597790450531, 0.150701656278937, 
    0.0363320569947933, 0.0594232320521485, 0.0320512820512820, 
    0.117963013416300, 0.0285502880368496, 0.0484291463698838, 
    0.0256436419387357, 0.0956922480067001), .Dim = c(2L, 14L
    )), structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937, 0.0363320569947933, 0.0594232320521485, 
    0.0320512820512820, 0.117963013416300, 0.0285502880368496, 
    0.0484291463698838, 0.0256436419387357, 0.0956922480067001, 
    0.0231990181784584, 0.0404954537147379), .Dim = c(2L, 15L
    )), structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937, 0.0363320569947933, 0.0594232320521485, 
    0.0320512820512820, 0.117963013416300, 0.0285502880368496, 
    0.0484291463698838, 0.0256436419387357, 0.0956922480067001, 
    0.0231990181784584, 0.0404954537147379, 0.0211197156122722, 
    0.0797299850375612), .Dim = c(2L, 16L)), structure(c(0.866025403784439, 
    -0.234141092407759, 0.372677996249965, 1.10810510880576, 
    0.220479275922049, 0.215016389907248, 0.15, 0.489380181546808, 
    0.110554159678513, 0.142331828329152, 0.0858464589396188, 
    0.294178041927853, 0.069160416896561, 0.100333337378287, 
    0.0572653559113564, 0.202528656207688, 0.0484322104837853, 
    0.0754369796383129, 0.0416597790450531, 0.150701656278937, 
    0.0363320569947933, 0.0594232320521485, 0.0320512820512820, 
    0.117963013416300, 0.0285502880368496, 0.0484291463698838, 
    0.0256436419387357, 0.0956922480067001, 0.0231990181784584, 
    0.0404954537147379, 0.0211197156122722, 0.0797299850375612, 
    0.0193335940624170, 0.0345719293822885), .Dim = c(2L, 17L
    )), structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937, 0.0363320569947933, 0.0594232320521485, 
    0.0320512820512820, 0.117963013416300, 0.0285502880368496, 
    0.0484291463698838, 0.0256436419387357, 0.0956922480067001, 
    0.0231990181784584, 0.0404954537147379, 0.0211197156122722, 
    0.0797299850375612, 0.0193335940624170, 0.0345719293822885, 
    0.0177858553517492, 0.0680306326567245), .Dim = c(2L, 18L
    )), structure(c(0.866025403784439, -0.234141092407759, 0.372677996249965, 
    1.10810510880576, 0.220479275922049, 0.215016389907248, 0.15, 
    0.489380181546808, 0.110554159678513, 0.142331828329152, 
    0.0858464589396188, 0.294178041927853, 0.069160416896561, 
    0.100333337378287, 0.0572653559113564, 0.202528656207688, 
    0.0484322104837853, 0.0754369796383129, 0.0416597790450531, 
    0.150701656278937, 0.0363320569947933, 0.0594232320521485, 
    0.0320512820512820, 0.117963013416300, 0.0285502880368496, 
    0.0484291463698838, 0.0256436419387357, 0.0956922480067001, 
    0.0231990181784584, 0.0404954537147379, 0.0211197156122722, 
    0.0797299850375612, 0.0193335940624170, 0.0345719293822885, 
    0.0177858553517492, 0.0680306326567245, 0.0164342052589432, 
    0.0305267178695429), .Dim = c(2L, 19L)), structure(c(0.866025403784439, 
    -0.234141092407759, 0.372677996249965, 1.10810510880576, 
    0.220479275922049, 0.215016389907248, 0.15, 0.489380181546808, 
    0.110554159678513, 0.142331828329152, 0.0858464589396188, 
    0.294178041927853, 0.069160416896561, 0.100333337378287, 
    0.0572653559113564, 0.202528656207688, 0.0484322104837853, 
    0.0754369796383129, 0.0416597790450531, 0.150701656278937, 
    0.0363320569947933, 0.0594232320521485, 0.0320512820512820, 
    0.117963013416300, 0.0285502880368496, 0.0484291463698838, 
    0.0256436419387357, 0.0956922480067001, 0.0231990181784584, 
    0.0404954537147379, 0.0211197156122722, 0.0797299850375612, 
    0.0193335940624170, 0.0345719293822885, 0.0177858553517492, 
    0.0680306326567245, 0.0164342052589432, 0.0305267178695429, 
    0.0152455338986496, 0.0615566914608176), .Dim = c(2L, 20L
    )))
`MMextr` <-
list(structure(32.3209404708014, .Dim = c(1L, 1L)), structure(c(34.3970537843995, 
-2.66186048577395, -2.66186048577395, 3.41286826654214), .Dim = c(2L, 
2L)), structure(c(122.44648288656, -0.177860727429421, 19.0055823736559, 
-0.177860727429428, 3.48294543640426, 0.536174538605836, 19.0055823736559, 
0.536174538605838, 4.10237936855581), .Dim = c(3L, 3L)), structure(c(130.209043428429, 
-4.51451571759888, 19.2377674248368, -3.97418625924684, -4.51451571759888, 
5.90567391656528, 0.406461352419979, 2.22023062880676, 19.2377674248368, 
0.406461352419978, 4.10932422878602, -0.118871425868910, -3.97418625924684, 
2.22023062880676, -0.118871425868908, 2.03465806649702), .Dim = c(4L, 
4L)), structure(c(281.015537230139, 3.08029658576524, 44.6135396937781, 
-2.97344456375853, 19.0177199641021, 3.08029658576527, 6.28815859921544, 
1.68441843886300, 2.27062928969849, 0.957757255169728, 44.6135396937781, 
1.684418438863, 8.37923198946806, 0.0495204830241909, 3.20005669993291, 
-2.97344456375852, 2.27062928969849, 0.0495204830241905, 2.04129892071915, 
0.126200303723139, 19.0177199641021, 0.957757255169724, 3.20005669993290, 
0.126200303723138, 2.39826325455559), .Dim = c(5L, 5L)), structure(c(296.630711253731, 
-3.76147597987010, 45.5081153807952, -6.21381817139198, 19.0790606375848, 
-5.08407622736899, -3.76147597987012, 9.28587426790755, 1.29246101436860, 
3.69039567959708, 0.930880901671609, 2.22758281153032, 45.5081153807952, 
1.29246101436860, 8.43048122041436, -0.136116861898231, 3.20357083785028, 
-0.291260986081566, -6.21381817139199, 3.69039567959708, -0.136116861898234, 
2.71372313457567, 0.113471230122805, 1.05501907320863, 19.0790606375848, 
0.930880901671611, 3.20357083785028, 0.113471230122806, 2.39850421749443, 
-0.0199716416450984, -5.08407622736899, 2.22758281153032, -0.291260986081566, 
1.05501907320863, -0.0199716416450986, 1.65530214691452), .Dim = c(6L, 
6L)), structure(c(512.313849849907, 9.8270826615388, 82.4198846430386, 
-3.58734355413421, 35.325426722725, -4.50507317114052, 20.1350606258432, 
9.8270826615388, 10.1419862808949, 3.61799162581456, 3.85586992384758, 
1.95444120265120, 2.26406140245924, 1.26855744887350, 82.4198846430386, 
3.61799162581456, 14.7475198120127, 0.31337504403547, 5.9839556198402, 
-0.192171055581001, 3.44589158308727, -3.58734355413420, 3.85586992384758, 
0.313375044035469, 2.74570694638404, 0.311310840687776, 1.06206986466315, 
0.245194065678628, 35.325426722725, 1.95444120265120, 5.9839556198402, 
0.311310840687776, 3.62226427908448, 0.0236418539537150, 1.51667658493421, 
-4.50507317114052, 2.26406140245924, -0.192171055581001, 1.06206986466315, 
0.0236418539537147, 1.65685648510389, 0.0540527262148954, 20.1350606258432, 
1.26855744887349, 3.44589158308726, 0.245194065678627, 1.51667658493421, 
0.0540527262148952, 1.87970496463079), .Dim = c(7L, 7L)), structure(c(537.174461265744, 
0.512782902530479, 84.20268600263, -8.05436983232551, 35.6479469866289, 
-7.29503636643204, 20.1498606421399, -6.06457494052765, 0.512782902530449, 
13.6316904780056, 2.95004561289220, 5.52949013738349, 1.83360546107918, 
3.30935160400959, 1.26301246102393, 2.27215927887482, 84.20268600263, 
2.9500456128922, 14.8753678618693, -0.00696384018943662, 6.00708415659915, 
-0.392244581311429, 3.44695292018524, -0.434902113567518, -8.05436983232552, 
5.52949013738349, -0.00696384018943565, 3.54835509675595, 0.253359470545891, 
1.56337848897983, 0.242534756114088, 1.08970029627342, 35.6479469866288, 
1.83360546107917, 6.00708415659915, 0.25335947054589, 3.62644838054873, 
-0.0125527372001168, 1.51686858766016, -0.0786765971912042, -7.29503636643205, 
3.30935160400959, -0.392244581311428, 1.56337848897983, -0.0125527372001164, 
1.96995798131718, 0.0523918056498745, 0.680592307088952, 20.1498606421399, 
1.26301246102393, 3.44695292018524, 0.242534756114088, 1.51686858766016, 
0.0523918056498743, 1.87971377537474, -0.0036103620484587, -6.06457494052766, 
2.27215927887482, -0.434902113567518, 1.08970029627342, -0.078676597191204, 
0.680592307088952, -0.00361036204845865, 1.47941129017510), .Dim = c(8L, 
8L)), structure(c(819.143661337148, 20.6552663424948, 132.998745280787, 
-3.57835751069945, 57.2260677899828, -5.91381020282217, 32.703279767742, 
-5.66993879870671, 21.4830243288986, 20.6552663424948, 15.0705697564038, 
6.43579446665671, 5.84923429398857, 3.37503956394234, 3.40801956178766, 
2.15976656320369, 2.30035013074599, 1.53464088161272, 132.998745280787, 
6.43579446665671, 23.3197490229125, 0.767630557072814, 9.74127662004923, 
-0.153217078523954, 5.61937949600029, -0.366608524889314, 3.71773558375014, 
-3.57835751069946, 5.84923429398857, 0.767630557072808, 3.61940784400026, 
0.595893103896238, 1.58530423592562, 0.441809211162737, 1.09596479691003, 
0.34102406070451, 57.2260677899828, 3.37503956394235, 9.74127662004923, 
0.59589310389624, 5.27774681061211, 0.093147690391196, 2.47753803070139, 
-0.0484764677464773, 1.64402102808739, -5.91381020282216, 3.40801956178767, 
-0.153217078523954, 1.58530423592562, 0.0931476903911958, 1.97672391786116, 
0.113884730886574, 0.682525432281534, 0.105234597498713, 32.703279767742, 
2.15976656320369, 5.61937949600029, 0.441809211162737, 2.47753803070139, 
0.113884730886574, 2.43859868799330, 0.0139590493948294, 0.956435697295593, 
-5.66993879870671, 2.30035013074599, -0.366608524889314, 1.09596479691003, 
-0.0484764677464775, 0.682525432281534, 0.0139590493948297, 1.47996361179176, 
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-0.0222234234031314, 0.593176524602996, -0.00125643973800679, 
1.48685820293191, 0.0096705922174014, 0.409564070550109, 0.0157617645031750, 
0.353200128764924, 0.0240510544071112, 0.333071473264385, 41.9195599395492, 
3.53183809904524, 7.37643643515306, 0.900979927461779, 3.28450649176802, 
0.346414605778272, 1.91918806447347, 0.155570405480644, 1.28188268101651, 
0.0727950280940698, 0.927620160077448, 0.0317696234457983, 0.708135068697896, 
0.0096705922174015, 1.56168364217665, -0.00306785317168121, 0.458209053508693, 
-0.0132218233289650, 0.375819083499442, -0.0502493531206952, 
-14.2704851855762, 3.66086457875606, -1.40632197142389, 1.82518181962280, 
-0.425291550346271, 1.15890537318457, -0.174482184564971, 0.824086682340952, 
-0.0802290538084651, 0.626794819232806, -0.0372123106339058, 
0.498604387379541, -0.0151864930488915, 0.409564070550109, -0.00306785317168127, 
1.34476476774828, 0.00412326359120034, 0.297529484410813, 0.0127437038269759, 
0.281327288434012, 33.9271731796379, 2.95192660452802, 5.99127846070652, 
0.770173446355448, 2.67159834601481, 0.304907517627791, 1.56247901766638, 
0.142765907489780, 1.04432403977817, 0.0714390131171311, 0.75611411453881, 
0.0355033110908791, 0.577463335369652, 0.0157617645031748, 0.458209053508693, 
0.00412326359120027, 1.37392412852179, -0.00506903343847453, 
0.306869252173055, -0.0355905589218347, -13.1021524738154, 3.09219235564068, 
-1.35228598526935, 1.55785012509391, -0.42878957499005, 0.993410809928549, 
-0.186680124341070, 0.708113828052954, -0.0933576181879012, 0.539443848634976, 
-0.0495719979667637, 0.429610299148511, -0.0264353280166914, 
0.353200128764924, -0.0132218233289650, 0.297529484410813, -0.00506903343847442, 
1.25696486063390, 0.00392005321816716, 0.24368231409708, 27.4454665555356, 
2.52108136337265, 4.87689908797388, 0.681387107572845, 2.18015985900117, 
0.281604646540819, 1.27707819844879, 0.139496998656737, 0.854556963330302, 
0.0756254436816024, 0.619285288340011, 0.0426641202626641, 0.47332304194091, 
0.0240510544071110, 0.375819083499442, 0.0127437038269757, 0.306869252173055, 
0.00392005321816693, 1.25209329842128, -0.0215589090241893, -15.1974404066730, 
2.68424920473151, -1.77355723741429, 1.41137203952830, -0.625928730647603, 
0.91533912330227, -0.305393853225509, 0.658604608691971, -0.174377943404751, 
0.504800798937453, -0.109193320138244, 0.403782198439627, -0.0725786971898077, 
0.333071473264385, -0.0502493531206951, 0.281327288434012, -0.0355905589218345, 
0.24368231409708, -0.0215589090241892, 1.23362129709203), .Dim = c(20L, 
20L)))
`sM22` <-
structure(c(1.10866489886031, -0.257022055546625, -0.257022055546625, 
0.607927101854027), .Dim = c(2L, 2L))