intervalSystem: Interval systems

In stepR: Multiscale Change-Point Inference

Interval systems

Description

Overview about the supported interval systems. More details are given in section 6 of the vignette.

Details

The following interval systems (set of intervals on which tests will be performed) are available. Intervals are given as indices of observations / sample points.

"all"

all intervals. More precisely, the set \{[i, j], 1 \leq i \leq j \leq n\}. This system allows all lengths 1:n.

"dyaLen"

all intervals of dyadic length. More precisely, the set \{[i, j], 1 \leq i \leq j \leq n\ s.t.\ j - i + 1 = 2^k,\ k\in N_0\}. This system allows all lengths of dyadic length 2^(0:as.integer(floor(log2(n)) + 1e-6)).

"dyaPar"

the dyadic partition, i.e. all disjoint intervals of dyadic length. More precisely, the set \{[(i - 1) * 2^k + 1, i * 2^k], i = 1,\ldots, \lfloor n / 2^k\rfloor,\ k = 0, \ldots, \lfloor\log_2(n)\rfloor\}. This system allows all lengths of dyadic length 2^(0:as.integer(floor(log2(n)) + 1e-6)).

The interval system is selected via the intervalSystem argument, providing the corresponding string. By default (NULL) the default interval system of the specified parametric family will be used, which one this will be is described in parametricFamily. With the additional argument lengths it is possible to specify a set of lengths such that only tests on intervals with a length contained in this set will be performed. The set of lengths has to be a subset of all lengths that are allowed by the interval system and the parametric family. By default (NULL) all lengths allowed by the interval system and the parametric family are used.

See Also

parametricFamily

Examples

y <- c(rnorm(50), rnorm(50, 2))

# interval system of all intervals and all lengths
fit <- stepFit(y, alpha = 0.5, intervalSystem = "all", lengths = 1:100,
               jumpint = TRUE, confband = TRUE)

# default for family "gauss" if number of observations is 1000 or less
identical(stepFit(y, alpha = 0.5, jumpint = TRUE, confband = TRUE), fit)

# intervalSystem "dyaLen" and a subset of lengths
!identical(stepFit(y, alpha = 0.5, intervalSystem = "dyaLen", lengths = c(2, 4, 16),
                   jumpint = TRUE, confband = TRUE), fit)

# default for lengths are all possible lengths of the interval system
# and the parametric family
identical(stepFit(y, alpha = 0.5, intervalSystem = "dyaPar",
                  jumpint = TRUE, confband = TRUE),
          stepFit(y, alpha = 0.5, intervalSystem = "dyaPar", lengths = 2^(0:6),
                  jumpint = TRUE, confband = TRUE))

# interval system "dyaPar" is default for parametric family "hsmuce"
# length 1 is not possible for this parametric family
identical(stepFit(y, alpha = 0.5, family = "hsmuce",
                  jumpint = TRUE, confband = TRUE),
          stepFit(y, alpha = 0.5, family = "hsmuce", intervalSystem = "dyaPar",
                  lengths = 2^(1:6), jumpint = TRUE, confband = TRUE))

# interval system "dyaLen" is default for parametric family "mDependentPS"
identical(stepFit(y, alpha = 0.5, family = "mDependentPS", covariances = c(1, 0.5),
                  jumpint = TRUE, confband = TRUE),
          stepFit(y, alpha = 0.5, family = "mDependentPS", covariances = c(1, 0.5),
                  intervalSystem = "dyaLen", lengths = 2^(0:6),
                  jumpint = TRUE, confband = TRUE))

stepR documentation built on Nov. 14, 2023, 1:09 a.m.