R/ddst.exp.test.R
In pbiecek/ddst: Data Driven Smooth Tests
Defines functions
`ddst.exp.Nk`
`ddst.exp.test`
#' Data Driven Smooth Test for Exponentiality
#'
#' Performs data driven smooth test for composite hypothesis of exponentiality.
#' Null density is given by \eqn{f(z;gamma) = exp(-z/gamma)} for z >= 0 and 0 otherwise.
#' Modelling alternatives similarly as in Kallenberg and Ledwina (1997 a,b).
#'
#' @param x a (non-empty) numeric vector of data values
#' @param base a function which returns an orthonormal system, possible choice: \code{ddst.base.legendre} for the Legendre polynomials and \code{ddst.base.cos} for the cosine system
#' @param d.n an integer specifying the maximum dimension considered, only for advanced users
#' @param c a calibrating parameter in the penalty in the model selection rule
#' @param nr an integer specifying the number of runs for a p-value and a critical value computation if any
#' @param compute.p a logical value indicating whether to compute a p-value or not
#' @param alpha a significance level
#' @param compute.cv a logical value indicating whether to compute a critical value corresponding to the significance level alpha or not
#' @param ... further arguments
#'
#' @return An object of class \code{htest}
#' \item{statistic }{the value of the test statistic.}
#' \item{parameter }{the number of choosen coordinates (k).}
#' \item{method }{a character string indicating the parameters of performed test. }
#' \item{data.name }{a character string giving the name(s) of the data. }
#' \item{p.value }{the p-value for the test, computed only if \code{compute.p=T}.}
#'
#' @export
#'
#' @references
#' Kallenberg, W.C.M., Ledwina, T. (1997 a). Data driven smooth tests for composite hypotheses: Comparison of powers. \eqn{ J. Statist. Comput. Simul.} \bold{ 59}, 101--121.
#'
#' Kallenberg, W.C.M., Ledwina, T. (1997 b). Data driven smooth tests when the hypothesis is composite. \eqn{ J. Amer. Statist. Assoc.} \bold{ 92}, 1094--1104.
#'
#' @examples
#' set.seed(7)
#' # H0 is true
#' z <- rexp(80,4)
#' \dontrun{
#' t <- ddst.exp.test (z, compute.p = TRUE, d.n = 10)
#' t
#' plot(t)
#'
#' # H0 is false
#' z = rchisq(80,4)
#' (t = ddst.exp.test (z, compute.p = TRUE, d.n = 10))
#' t$p.value
#' plot(t)
#' }
#' @keywords htest
#' @aliases ddst.exp.Nk
#'
`ddst.exp.test` <-
function(x,
base = ddst.base.legendre,
d.n = 10,
c = 100,
nr = 100000,
compute.p = TRUE,
alpha = 0.05,
compute.cv = TRUE,
...) {
# method.name = as.character(substitute(base))
base = ddst.base.legendre
method.name = "ddst.base.legendre"
n = length(x)
if (n < 5)
stop("length(x) should be at least 5")
er = mean(x)
maxN = max(min(d.n, n - 2, 20), 1)
coord = numeric(maxN)
u = numeric(maxN)
for (j in 1:maxN) {
u[j] = ddst.phi(pexp(x, 1 / er), j, base)
coord[j] = t(u[1:j]) %*% MMexp[[j]] %*% u[1:j] * n
}
l = ddst.IIC(coord, n, c)
attr(l, "names") = "T*"
t = coord[l]
attr(t, "names") = "W*T*"
result = list(statistic = t,
parameter = l,
coordinates = coord - c(0, coord[-d.n]),
method = "Data Driven Smooth Test for Expotentiality")
result$data.name = paste(paste(as.character(substitute(x)), collapse = ""),
", base: ",
method.name,
", c: ",
c,
", d.n: ",
d.n,
sep = "")
class(result) = c("htest", "ddst.test")
if (compute.p | compute.cv) {
tmp = numeric(nr)
for (i in 1:nr) {
y = rexp(length(x))
tmpC = ddst.exp.Nk(y, base, Dmax = d.n, n = length(y))
l = ddst.IIC(tmpC, n, c)
tmp[i] = tmpC[l]
}
p.val = mean(tmp > t)
if (compute.p) {
result$p.value = mean(tmp > t)
}
if (compute.cv) {
result$cv = quantile(tmp, alpha)
}
}
result
}
`MMexp` <-
list(
structure(4, .Dim = c(1L, 1L)),
structure(
c(7.75, 2.90473750965556,
2.90473750965556, 2.25),
.Dim = c(2L, 2L)
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-0.0141540454380189,
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),
.Dim = c(20L, 20L)
)
)
`ddst.exp.Nk` <-
function(x,
base = ddst.base.legendre,
Dmax = 5,
n = length(x)) {
er = mean(x)
maxN = max(min(Dmax, n - 2, 20), 1)
coord = numeric(maxN)
u = numeric(maxN)
for (j in 1:maxN) {
u[j] = ddst.phi(pexp(x, 1 / er), j, base)
coord[j] = t(u[1:j]) %*% MMexp[[j]] %*% u[1:j] * n
}
coord
}
pbiecek/ddst documentation built on Aug. 22, 2023, 7:44 p.m.
R Package Documentation
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Defines functions `ddst.exp.Nk` `ddst.exp.test`
#' Data Driven Smooth Test for Exponentiality
#'
#' Performs data driven smooth test for composite hypothesis of exponentiality.
#' Null density is given by \eqn{f(z;gamma) = exp(-z/gamma)} for z >= 0 and 0 otherwise.
#' Modelling alternatives similarly as in Kallenberg and Ledwina (1997 a,b).
#'
#' @param x a (non-empty) numeric vector of data values
#' @param base a function which returns an orthonormal system, possible choice: \code{ddst.base.legendre} for the Legendre polynomials and \code{ddst.base.cos} for the cosine system
#' @param d.n an integer specifying the maximum dimension considered, only for advanced users
#' @param c a calibrating parameter in the penalty in the model selection rule
#' @param nr an integer specifying the number of runs for a p-value and a critical value computation if any
#' @param compute.p a logical value indicating whether to compute a p-value or not
#' @param alpha a significance level
#' @param compute.cv a logical value indicating whether to compute a critical value corresponding to the significance level alpha or not
#' @param ... further arguments
#'
#' @return An object of class \code{htest}
#' \item{statistic }{the value of the test statistic.}
#' \item{parameter }{the number of choosen coordinates (k).}
#' \item{method }{a character string indicating the parameters of performed test. }
#' \item{data.name }{a character string giving the name(s) of the data. }
#' \item{p.value }{the p-value for the test, computed only if \code{compute.p=T}.}
#'
#' @export
#'
#' @references
#' Kallenberg, W.C.M., Ledwina, T. (1997 a). Data driven smooth tests for composite hypotheses: Comparison of powers. \eqn{ J. Statist. Comput. Simul.} \bold{ 59}, 101--121.
#'
#' Kallenberg, W.C.M., Ledwina, T. (1997 b). Data driven smooth tests when the hypothesis is composite. \eqn{ J. Amer. Statist. Assoc.} \bold{ 92}, 1094--1104.
#'
#' @examples
#' set.seed(7)
#' # H0 is true
#' z <- rexp(80,4)
#' \dontrun{
#' t <- ddst.exp.test (z, compute.p = TRUE, d.n = 10)
#' t
#' plot(t)
#'
#' # H0 is false
#' z = rchisq(80,4)
#' (t = ddst.exp.test (z, compute.p = TRUE, d.n = 10))
#' t$p.value
#' plot(t)
#' }
#' @keywords htest
#' @aliases ddst.exp.Nk
#'
`ddst.exp.test` <-
function(x,
base = ddst.base.legendre,
d.n = 10,
c = 100,
nr = 100000,
compute.p = TRUE,
alpha = 0.05,
compute.cv = TRUE,
...) {
# method.name = as.character(substitute(base))
base = ddst.base.legendre
method.name = "ddst.base.legendre"
n = length(x)
if (n < 5)
stop("length(x) should be at least 5")
er = mean(x)
maxN = max(min(d.n, n - 2, 20), 1)
coord = numeric(maxN)
u = numeric(maxN)
for (j in 1:maxN) {
u[j] = ddst.phi(pexp(x, 1 / er), j, base)
coord[j] = t(u[1:j]) %*% MMexp[[j]] %*% u[1:j] * n
}
l = ddst.IIC(coord, n, c)
attr(l, "names") = "T*"
t = coord[l]
attr(t, "names") = "W*T*"
result = list(statistic = t,
parameter = l,
coordinates = coord - c(0, coord[-d.n]),
method = "Data Driven Smooth Test for Expotentiality")
result$data.name = paste(paste(as.character(substitute(x)), collapse = ""),
", base: ",
method.name,
", c: ",
c,
", d.n: ",
d.n,
sep = "")
class(result) = c("htest", "ddst.test")
if (compute.p | compute.cv) {
tmp = numeric(nr)
for (i in 1:nr) {
y = rexp(length(x))
tmpC = ddst.exp.Nk(y, base, Dmax = d.n, n = length(y))
l = ddst.IIC(tmpC, n, c)
tmp[i] = tmpC[l]
}
p.val = mean(tmp > t)
if (compute.p) {
result$p.value = mean(tmp > t)
}
if (compute.cv) {
result$cv = quantile(tmp, alpha)
}
}
result
}
`MMexp` <-
list(
structure(4, .Dim = c(1L, 1L)),
structure(
c(7.75, 2.90473750965556,
2.90473750965556, 2.25),
.Dim = c(2L, 2L)
),
structure(
c(
13.0000000000001,
5.16397779494326,
3.05505046330393,
5.16397779494326,
3.22222222222224,
1.31468439624438,
3.05505046330393,
1.31468439624438,
1.77777777777779
),
.Dim = c(3L, 3L)
),
structure(
c(
19.7499999999998,
8.06871530459869,
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3.24759526419154,
8.06871530459869,
4.47222222222218,
2.05419436913180,
1.39754248593732,
4.7735163489123,
2.05419436913180,
2.21527777777777,
0.826797284707661,
3.24759526419154,
1.39754248593732,
0.826797284707661,
1.56249999999997
),
.Dim = c(4L, 4L)
),
structure(
c(
28.0000000000111,
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6.87386354243662,
4.67653718043779,
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2.95803989155104,
2.01246117975060,
1.48323969742047,
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2.75000000000074,
1.19058808997954,
0.877496438740007,
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2.01246117975060,
1.19058808997954,
1.8100000000003,
0.596992462264497,
3.44673758792592,
1.48323969742047,
0.877496438740007,
0.596992462264497,
1.44000000000061
),
.Dim = c(5L, 5L)
),
structure(
c(
37.7499999996889,
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4.02622096346428,
2.73918327241400,
2.01885403258216,
1.56766122880296,
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3.3819444444243,
1.62052267801332,
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0.927440890247034,
6.3652867177616,
2.73918327241400,
1.62052267801332,
2.10249999999062,
0.812573073630574,
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4.69139282796864,
2.01885403258216,
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1.59888888888440,
0.465043473333310,
3.64291549898935,
1.56766122880296,
0.927440890247034,
0.630971473192956,
0.465043473333310,
1.36111111109903
),
.Dim = c(6L, 6L)
),
structure(
c(
49.0000000062404,
20.6559111824583,
12.2202018548044,
8.3138438774113,
6.12753349044019,
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20.6559111824583,
9.88888889004452,
5.25873758566114,
3.57770876446472,
2.63687057353367,
2.04755752361801,
1.64957219827918,
12.2202018548044,
5.25873758566114,
4.11111111151561,
2.11660104912681,
1.55999366907329,
1.21135136702101,
0.975900073300267,
8.3138438774113,
3.57770876446472,
2.11660104912681,
2.44000000018715,
1.06131993305220,
0.824126005917164,
0.663940002446266,
6.12753349044019,
2.63687057353367,
1.55999366907329,
1.06131993305220,
1.78222222232468,
0.607403720356187,
0.489342193649563,
4.75809371362456,
2.04755752361801,
1.21135136702101,
0.824126005917164,
0.607403720356187,
1.47165532884771,
0.379979321051083,
3.83325939138121,
1.64957219827918,
0.975900073300267,
0.663940002446266,
0.489342193649563,
0.379979321051083,
1.30612244916046
),
.Dim = c(7L, 7L)
),
structure(
c(
61.7499999643167,
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4.01705348301015,
26.1426375715444,
12.249999993392,
6.65558975207775,
4.52803765177731,
3.33728931723443,
2.59143998896998,
2.08773981194937,
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6.65558975207775,
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1.9743669860045,
1.53311657278613,
1.23512352938459,
1.02269175869889,
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2.67882320087937,
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1.34323303930558,
1.04303447549065,
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6.02196235198601,
2.59143998896998,
1.53311657278613,
1.04303447549065,
0.768745333024312,
1.59693877514465,
0.480911327860278,
0.398198269214986,
4.85146891373646,
2.08773981194937,
1.23512352938459,
0.840299064993236,
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1.02269175869889,
0.695774072929495,
0.512804786392375,
0.398198269214986,
0.320800166404736,
1.26562499909206
),
.Dim = c(8L, 8L)
),
structure(
c(
75.9999998148397,
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19.0940653485099,
12.9903810246956,
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4.19435243809508,
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14.8888888546000,
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7.43452140821745,
3.19930862233875,
1.89273650605146,
1.28769688089909,
0.949068310590093,
1.73696144940933,
0.593717687599357,
0.491602800575069,
0.415773374288155,
5.98946778346764,
2.57745655311289,
1.52484386056889,
1.03740625112627,
0.764597175590399,
0.593717687599357,
1.47831632557016,
0.396049587408857,
0.334959184833341,
4.95932527833625,
2.13415380126909,
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0.334959184833341,
0.277348774984669,
1.23456789891182
),
.Dim = c(9L, 9L)
),
structure(
c(
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)
)
`ddst.exp.Nk` <-
function(x,
base = ddst.base.legendre,
Dmax = 5,
n = length(x)) {
er = mean(x)
maxN = max(min(Dmax, n - 2, 20), 1)
coord = numeric(maxN)
u = numeric(maxN)
for (j in 1:maxN) {
u[j] = ddst.phi(pexp(x, 1 / er), j, base)
coord[j] = t(u[1:j]) %*% MMexp[[j]] %*% u[1:j] * n
}
coord
}
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