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https://github.com/pbiecek/ddst

R package for Data driven smooth tests
https://github.com/pbiecek/ddst

data-driven r smooth-test statistics test

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R package for Data driven smooth tests

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# Data Driven Smooth Tests with ddst package

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## Overview

DDST (ddst) stands for Data Driven Smooth Test (data driven smooth test). The test characterizes data-dependent choice of the number of components in a smooth test statistic.

In this package you will find two groups of selected data driven smooth tests: goodness-of-fit tests and nonparametric tests for comparing distributions.

### Data Driven Smooth Tests for Selected Goodness-of-Fit Problems

These tests were inspired by the results from: [*Data driven smooth tests for composite hypotheses* by Inglot, Kallenberg, and Ledwina (1997)](https://projecteuclid.org/euclid.aos/1069362746) and [*Towards data driven selection of a penalty function for data driven Neyman tests* by Inglot and Ledwina (2006)](https://www.sciencedirect.com/science/article/pii/S0024379505005082).

* DDST for Uniformity - `ddst.uniform.test()`; see [*Towards data driven selection of a penalty function for data driven Neyman tests* by Inglot and Ledwina (2006)](https://www.sciencedirect.com/science/article/pii/S0024379505005082).
* DDST for Exponentiality - `ddst.exp.test()`; see [*Data driven smooth tests for composite hypotheses: Comparison of powers* by Kallenberg and Ledwina (1997)](https://www.tandfonline.com/doi/abs/10.1080/00949659708811850).
* DDST for Normality; Bounded Basis Functions - `ddst.normbounded.test()`; see [*Data-driven tests for a location-scale family revisited* by Janic and Ledwina (2009)](https://link.springer.com/article/10.1080/15598608.2009.10411952).
* DDST for Normality; Unbounded Basis Functions - `ddst.normunbounded.test()`; see [*Detection of non-Gaussianity* by Ledwina and Wyłupek (2015)](https://www.tandfonline.com/doi/abs/10.1080/00949655.2014.983110?journalCode=gscs20).
* DDST for Extreme Value Distribution - `ddst.evd.test()`; see [*Data-driven tests for a location-scale family revisited* by Janic and Ledwina (2009)](https://link.springer.com/article/10.1080/15598608.2009.10411952).

### Nonparametric Data Driven Smooth Tests for Comparing Distributions

A starting point of the constructions were the papers: [*Data driven rank test for two-sample problem* by Janic-Wróblewska and Ledwina (2000)](https://www.jstor.org/stable/4616603?seq=1#page_scan_tab_contents) and [*Towards data driven selection of a penalty function for data driven Neyman tests* by Inglot and Ledwina (2006)](https://www.sciencedirect.com/science/article/pii/S0024379505005082).

* DDST for Two-Sample Problem - `ddst.twosample.test()`; see [*Data-driven k-sample tests* by Wyłupek (2010)](https://www.jstor.org/stable/40586684?seq=1).
* DDST for k-Sample Problem - `ddst.ksample.test()`; see [*Data-driven k-sample tests* by Wyłupek (2010)](https://www.jstor.org/stable/40586684?seq=1).
* DDST for Change-Point Problem - `ddst.changepoint.test()`; see [*Data driven rank test for the change point problem* by Antoch, Hušková, Janic and Ledwina (2008)](https://link.springer.com/article/10.1007/s00184-007-0139-2).
* DDST for Stochastic Dominance in Two Samples - `ddst.forstochdom.test()`; see [*Nonparametric tests for stochastic ordering* by Ledwina and Wyłupek (2012) ](https://link.springer.com/article/10.1007/s11749-011-0278-7).
* DDST Against Stochastic Dominance - `ddst.againststochdom.test()`; see [*Two-sample test against one-sided alternatives* by Ledwina and Wyłupek (2012)](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9469.2011.00787.x).
* DDST for Upward Trend Alternatives - `ddst.upwardtrend.test()`; see [*Data-driven tests for trend* by Wyłupek (2013)](https://www.tandfonline.com/doi/abs/10.1080/03610926.2012.697967).
* DDST for Umbrella Alternatives; Known Peak - `ddst.umbrellaknownp.test()`; see [*An automatic test for the umbrella alternatives* by Wyłupek (2016)](https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12231).
* DDST for Umbrella Alternatives; Unknown Peak - `ddst.umbrellaunknownp.test()`; see [*An automatic test for the umbrella alternatives* by Wyłupek (2016)](https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12231).

A more detailed overview is contained in [Data Driven Smooth Tests - Introductory Material](http://www.biecek.pl/R/ddst/description.pdf). Full details on the above procedures can be found in the related papers.

## Installation

```{r}
# the easiest way to get ddst is to install it from CRAN:
install.packages("ddst")

# Or the the development version from GitHub:
# install.packages("devtools")
devtools::install_github("pbiecek/ddst")
```