directional_quantile function

Compute directional quantile outlyingness for a sample of discretely observed curves

The directional quantile is a measure of outlyingness based on a scaled pointwise deviation from the mean. These deviations are usually scaled by the deviation of the mean from the 2.5% upper and lower quantiles depending on if the (pointwise) observed value of a function is above or below the (pointwise) mean. Directional quantile was mentioned in Myllymäki et al. (2015) tools:::Rd_expr_doi("10.1016/j.spasta.2014.11.004") , Myllymäki et al. (2017) tools:::Rd_expr_doi("10.1111/rssb.12172") and Dai et al. (2020) tools:::Rd_expr_doi("10.1016/j.csda.2020.106960") .

directional_quantile(dt, quantiles = c(0.025, 0.975))

Arguments

• dt: A matrix or dataframe of size $n$ observations/curves by $p$ domain/evaluation points.
• quantiles: A numeric vector of length 2 specifying the probabilities of the lower and upper quantiles. Values must be between 0 and 1. Defaults to c(0.025, 0.975) as specified in Dai et al. (2020) tools:::Rd_expr_doi("10.1016/j.csda.2020.106960") .

Returns

A numeric vector containing the the directional quantiles of each observation of dt.

Details

The method computes the directional quantile of a sample of curves discretely observed on common points. The directional quantile of a function/curve $X_i(t)$ is the maximum pointwise scaled outlyingness of $X_i(t)$. The scaling is done using the pointwise absolute difference between the 2.5% mean and the lower (and upper) quantiles. See Dai et al. (2020) tools:::Rd_expr_doi("10.1016/j.csda.2020.106960") and Myllymäki et al. (2017) tools:::Rd_expr_doi("10.1111/rssb.12172") for more details.

Examples

dt1 <- simulation_model1()
dq <- directional_quantile(dt1$data)

References

Dai, W., Mrkvička, T., Sun, Y., & Genton, M. G. (2020). Functional outlier detection and taxonomy by sequential transformations. Computational Statistics & Data Analysis, 106960.

Myllymäki, M., Mrkvička, T., Grabarnik, P., Seijo, H., & Hahn, U. (2017). Global envelope tests for spatial processes. J. R. Stat. Soc. B, 79:381-404.

Author(s)

Oluwasegun Taiwo Ojo