R/rjb.test.R

In lawstat: Tools for Biostatistics, Public Policy, and Law

#' Test of Normailty -- Robust Jarque--Bera Test
#' 
#' The robust and classical Jarque--Bera tests of normality.
#' 
#' @details The test is based on a joint statistic using skewness and kurtosis
#' coefficients. The Robust Jarque--Bera (RJB) is the robust version of
#' the Jarque--Bera (JB) test of normality. The RJB (default option) utilizes
#' the robust standard deviation (specifically, 
#' the Average Absolute Deviation from the Median; MAAD) 
#' to estimate sample kurtosis and skewness. For more details, see 
#' \insertCite{Gel_Gastwirth_2008;textual}{lawstat}. Users can also choose to 
#' perform the classical Jarque--Bera test \insertCite{Jarque_Bera_1980}{lawstat}.
#' 
#' @note Modified from \code{\link[tseries]{jarque.bera.test}} 
#' (\code{tseries} package).
#'
#'
#' @param x a numeric vector of data values.
#' @param option the choice of whether to perform the robust test, \code{"RJB"} 
#' (default) or classic test, \code{"JB"}.
#' @param crit.values a character string specifying how the critical values 
#' should be obtained: approximated by the Chi-square distribution (default) 
#' or empirically.
#' @param N number of Monte Carlo simulations for the empirical critical values.
#'
#'
#' @return A list of class \code{"htest"} with the following components:
#' \item{statistic}{the value of the test statistic.}
#' \item{parameter}{the degrees of freedom.}
#' \item{p.value}{the \eqn{p}-value of the test.}
#' \item{method}{type of test was performed.}
#' \item{data.name}{a character string giving the name of the data.}
#' 
#' @references
#' \insertAllCited{}
#' 
#' @seealso \code{\link{sj.test}}, \code{\link{rqq}}, 
#' \code{\link[tseries]{jarque.bera.test}}
#' 
#' @keywords distribution robust htest
#' 
#' @author W. Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth, Weiwen Miao
#' 
#' @export
#' @examples
#' ## Normally distributed data
#' x = rnorm(100)
#' rjb.test(x)
#' 
#' ## Using zuni data
#' data(zuni)
#' rjb.test(zuni[, "Revenue"])
#' 
rjb.test <- function(x,
                       option = c("RJB", "JB"),
                       crit.values = c("chisq.approximation", "empirical"),
                       N = 0)
{
    option <- match.arg(option)
    crit.values = match.arg(crit.values)
    if (NCOL(x) > 1) {
        stop("x is not a vector or univariate time series")
    }
    if (any(is.na(x))) {
        stop("NAs in x")
    }
    if ((crit.values == "empirical") & (N == 0)) {
        stop(
            "number of Monte Carlo simulations N should be provided for the empirical critical values"
        )
    }
    DNAME <- deparse(substitute(x))
    ### Calculate the first 4 central moments ###
    n <- length(x)
    m1 <- sum(x) / n
    m2 <- sum((x - m1) ^ 2) / n
    m3 <- sum((x - m1) ^ 3) / n
    m4 <- sum((x - m1) ^ 4) / n
    ### User can choose the Standard Jarque Bera Test or Robust Jarque Bera Test ###
    ### Robust Jarque Bera Test is default ###
    if (option == "JB") {
        b1 <- (m3 / m2 ^ (3 / 2)) ^ 2
        b2 <- (m4 / m2 ^ 2)
        METHOD <- "Standard Jarque Bera Test"
        statistic <- n * b1 / 6 + n * (b2 - 3) ^ 2 / 24
    } else {
        option = "RJB"
        J <- sqrt(pi / 2) * mean(abs(x - median(x)))
        J2 <- J ^ 2
        b1 <- (m3 / (J2) ^ (3 / 2)) ^ 2
        b2 <- (m4 / (J2) ^ 2)
        vk <- 64 / n
        METHOD <- "Robust Jarque Bera Test"
        vs <- 6 / n
        ek <- 3
        statistic <- b1 / vs + (b2 - ek) ^ 2 / vk
    }
    if (crit.values == "empirical") {
        if (option == "JB"){
            #### computes empirical critical values for the JB statistic####
            jb <- double(N)
            for (k in 1:N) {
                e <- rnorm(length(x), mean = 0, sd = sqrt(1))
                m1 <- sum(e) / n
                m2 <- sum((e - m1) ^ 2) / n
                m3 <- sum((e - m1) ^ 3) / n
                m4 <- sum((e - m1) ^ 4) / n
                b1 <- (m3 / m2 ^ (3 / 2)) ^ 2
                b2 <- (m4 / m2 ^ 2)
                vk <- 24 / n
                vs <- 6 / n
                ek <- 3
                jb[k] <- b1 / vs + (b2 - ek) ^ 2 / vk
            }
            y <- sort(jb)
            if (statistic >= max(y)) {
                p.value = 0
            } else if (statistic <= min(y)) {
                p.value = 1
            } else {
                bn <- which(y == min(y[I(y >= statistic)]))
                an <- which(y == max(y[I(y < statistic)]))
                a <- max(y[I(y < statistic)])
                b <- min(y[I(y >= statistic)])
                pa <- (an - 1) / (N - 1)
                pb <- (bn - 1) / (N - 1)
                alpha <- (statistic - a) / (b - a)
                p.value = 1 - alpha * pb - (1 - alpha) * pa
            }
        } else {
            #### computes empirical critical values for the RJB statistic####
            rjb <- double(N)
            for (k in 1:N) {
                e <- rnorm(length(x), mean = 0, sd = sqrt(1))
                J <- sqrt(pi / 2) * mean(abs(e - median(e)))
                J2 <- J ^ 2
                m1 <- sum(e) / n
                m2 <- sum((e - m1) ^ 2) / n
                m3 <- sum((e - m1) ^ 3) / n
                m4 <- sum((e - m1) ^ 4) / n
                b1 <- (m3 / (J2) ^ (3 / 2)) ^ 2
                b2 <- (m4 / (J2) ^ 2)
                vk <- 64 / n
                vs <- 6 / n
                ek <- 3
                rjb[k] <- b1 / vs + (b2 - ek) ^ 2 / vk
            }
            y <- sort(rjb)
            if (statistic >= max(y)) {
                p.value = 0
            } else if (statistic <= min(y)) {
                p.value = 1
            } else {
                bn <- which(y == min(y[I(y >= statistic)]))
                an <- which(y == max(y[I(y < statistic)]))
                a <- max(y[I(y < statistic)])
                b <- min(y[I(y >= statistic)])
                pa <- (an - 1) / (N - 1)
                pb <- (bn - 1) / (N - 1)
                alpha <- (statistic - a) / (b - a)
                p.value = 1 - alpha * pb - (1 - alpha) * pa
            }
        }
    } else {
        p.value <- 1 - pchisq(statistic, df = 2)
    }
    if (option == "JB") {
        METHOD <- "Jarque Bera Test"
    } else {
        METHOD <- "Robust Jarque Bera Test"
    }
    ### Display Output ###
    STATISTIC = statistic
    names(STATISTIC) <- "X-squared"
    PARAMETER <- 2
    names(PARAMETER) <- "df"
    structure(
        list(
            statistic = STATISTIC,
            parameter = PARAMETER,
            p.value = p.value,
            method = METHOD,
            data.name = DNAME
        ),
        class = "htest"
    )
}