bootstrapFP {bootstrapFP}

Bootstrap algorithms for Finite Population sampling

Description

Bootstrap variance estimation for finite population sampling.

Usage

bootstrapFP(
  y,
  pik,
  B,
  D = 1,
  method,
  design,
  x = NULL,
  s = NULL,
  distribution = "uniform"
)

Arguments

y

vector of sample values

pik

vector of sample first-order inclusion probabilities

B

scalar, number of bootstrap replications

D

scalar, number of replications for the double bootstrap (when applicable)

method

a string indicating the bootstrap method to be used, see Details for more

design

sampling procedure to be used for sample selection. Either a string indicating the name of the sampling design or a function; see section "Details" for more information.

x

vector of length N with values of the auxiliary variable for all population units, only required if method "ppHotDeck" is chosen

s

logical vector of length N, TRUE for units in the sample, FALSE otherwise. Alternatively, a vector of length n with the indices of the sample units. Only required for "ppHotDeck" method.

distribution

required only for method='generalised', a string indicating the distribution to use for the Generalised bootstrap. Available options are "uniform", "normal", "exponential" and "lognormal"

Details

Argument design accepts either a string indicating the sampling design to use to draw samples or a function. Accepted designs are "brewer", "tille", "maxEntropy", "poisson", "sampford", "systematic", "randomSystematic". The user may also pass a function as argument; such function should take as input the parameters passed to argument design_pars and return either a logical vector or a vector of 0 and 1, where TRUE or 1 indicate sampled units and FALSE or 0 indicate non-sample units. The length of such vector must be equal to the length of x if units is not specified, otherwise it must have the same length of units.

method must be a string indicating the bootstrap method to use. A list of the currently available methods follows, the sampling design they they should be used with is indicated in square brackets. The prefix "pp" indicates a pseudo-population method, the prefix "d" represents a direct method, and the prefix "w" inicates a weights method. For more details on these methods see Mashreghi et al. (2016).

• "ppGross" [SRSWOR]

• "ppBooth" [SRSWOR]

• "ppChaoLo85" [SRSWOR]

• "ppChaoLo94" [SRSWOR]

• "ppBickelFreedman" [SRSWOR]

• "ppSitter" [SRSWOR]

• "ppHolmberg" [UPSWOR]

• "ppChauvet" [UPSWOR]

• "ppHotDeck" [UPSWOR]

• "dEfron" [SRSWOR]

• "dMcCarthySnowden" [SRSWOR]

• "dRaoWu" [SRSWOR]

• "dSitter" [SRSWOR]

• "dAntalTille_UPS" [UPSWOR]

• "wRaoWuYue" [SRSWOR]

• "wChipperfieldPreston" [SRSWOR]

• "wGeneralised" [any]

Value

The bootstrap variance of the Horvitz-Thompson estimator.

References

Mashreghi Z.; Haziza D.; Léger C., 2016. A survey of bootstrap methods in finite population sampling. Statistics Surveys 10 1-52.

Examples

library(bootstrapFP)

### Generate population data ---
N   <- 20; n <- 5
x   <- rgamma(N, scale=10, shape=5)
y   <- abs( 2*x + 3.7*sqrt(x) * rnorm(N) )
pik <- n * x/sum(x)

### Draw a dummy sample ---
s  <- sample(N, n)

### Estimate bootstrap variance ---
bootstrapFP(y = y[s], pik = n/N, B=100, method = "ppSitter")
bootstrapFP(y = y[s], pik = pik[s], B=10, method = "ppHolmberg", design = 'brewer')
bootstrapFP(y = y[s], pik = pik[s], B=10, D=10, method = "ppChauvet")
bootstrapFP(y = y[s], pik = n/N, B=10, method = "dRaoWu")
bootstrapFP(y = y[s], pik = n/N, B=10, method = "dSitter")
bootstrapFP(y = y[s], pik = pik[s], B=10, method = "dAntalTille_UPS", design='brewer')
bootstrapFP(y = y[s], pik = n/N, B=10, method = "wRaoWuYue") 
bootstrapFP(y = y[s], pik = n/N, B=10, method = "wChipperfieldPreston")
bootstrapFP(y = y[s], pik = pik[s], B=10, method = "wGeneralised", distribution = 'normal')