https://github.com/egarpor/rotasym

Tests for rotational symmetry on the hypersphere. Software companion for "On optimal tests for rotational symmetry against new classes of hyperspherical distributions"

https://github.com/egarpor/rotasym

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Tests for rotational symmetry on the hypersphere. Software companion for "On optimal tests for rotational symmetry against new classes of hyperspherical distributions"

README.Rmd

---
output:
  md_document:
    variant: gfm
---

```{r, echo = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE, comment = "#>", fig.path = "README/README-",
  message = FALSE, warning = FALSE, fig.asp = 1, fig.align = 'center'
)
```

rotasym
=======

```{r, echo = FALSE, results = 'asis'}
cat(
  badger::badge_license(license = "GPLv3", color = "blue",
                        url = "https://www.gnu.org/licenses/gpl-3.0"),
  badger::badge_github_actions(action = "R-CMD-check"),
  badger::badge_cran_release(color = "green"),
  badger::badge_cran_download(pkg = NULL, type = "grand-total"),
  badger::badge_cran_download(pkg = NULL, type = "last-month")
)
```



## Overview

Software companion for the paper "*On optimal tests for rotational symmetry against new classes of hyperspherical distributions*" (García-Portugués, Paindaveine and Verdebout, 2020). It implements the proposed tests for rotational symmetry of hyperspherical data and allows to replicate the data application presented.

## Installation

Get the released version from CRAN:

```{r, install-CRAN, eval = FALSE}
# Install the package
install.packages("rotasym")

# Load package
library(rotasym)
```

Alternatively, get the latest version from GitHub:

```{r, install-GitHub, eval = FALSE}
# Install the package
library(devtools)
install_github("egarpor/rotasym")

# Load package
library(rotasym)
```

```{r, load, echo = FALSE}
# Load package
library(rotasym)
```

## Tests usage

The following are some simple examples of the usage of the main function of the package, `test_rotasym`, with simulated data. More examples are available in `?test_rotasym`.

```{r, sample}
# Sample data from a vMF (rotational symmetric distribution about mu)
n <- 200
p <- 10
theta <- c(1, rep(0, p - 1))
set.seed(123456789)
data_0 <- r_vMF(n = n, mu = theta, kappa = 1)
```

### Specified-θ case

```{r, specified}
# theta known
test_rotasym(data = data_0, theta = theta, type = "sc")
test_rotasym(data = data_0, theta = theta, type = "loc_vMF")
test_rotasym(data = data_0, theta = theta, type = "hyb_vMF")
```

### Unspecified-θ case

```{r, unspecified}
# theta unknown (employs the spherical mean as estimator)
test_rotasym(data = data_0, type = "sc")
test_rotasym(data = data_0, type = "loc_vMF")
test_rotasym(data = data_0, type = "hyb_vMF")
```

## Data application: test for the rotational symmetry of sunspots

The data used in García-Portugués, Paindaveine and Verdebout (2020) is available in the object `sunspot_births`, which is created through the script [sunspots.R](https://github.com/egarpor/rotasym/blob/master/data-raw/sunspots.R). The code snippet below reproduces the main results in the paper.

```{r, sunspots_births, fig.show = 'hold'}
# Load data
data("sunspots_births")
sunspots_births$X <-
  cbind(cos(sunspots_births$phi) * cos(sunspots_births$theta),
        cos(sunspots_births$phi) * sin(sunspots_births$theta),
        sin(sunspots_births$phi))

# Test rotational symmetry for the 23rd cycle
sunspots_23 <- subset(sunspots_births, cycle == 23)
test_rotasym(data = sunspots_23$X, type = "sc", theta = c(0, 0, 1))
test_rotasym(data = sunspots_23$X, type = "loc", theta = c(0, 0, 1))
test_rotasym(data = sunspots_23$X, type = "hyb", theta = c(0, 0, 1))

# Test rotational symmetry for the 22nd cycle
sunspots_22 <- subset(sunspots_births, cycle == 22)
test_rotasym(data = sunspots_22$X, type = "sc", theta = c(0, 0, 1))
test_rotasym(data = sunspots_22$X, type = "loc", theta = c(0, 0, 1))
test_rotasym(data = sunspots_22$X, type = "hyb", theta = c(0, 0, 1))

# More analyses in ?sunspots_births
example("sunspots_births")
```

## References

García-Portugués, E., Paindaveine, D., and Verdebout, T. (2020). On optimal tests for rotational symmetry against new classes of hyperspherical distributions. *Journal of the American Statistical Association*, 115(532):1873--1887. [doi:10.1080/01621459.2019.1665527](https://doi.org/10.1080/01621459.2019.1665527).

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