Data Driven Smooth Tests with ddst package

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) and Towards data driven selection of a penalty function for data driven Neyman tests by Inglot and Ledwina (2006).

• 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).
• DDST for Exponentiality - ddst.exp.test(); see Data driven smooth tests for composite hypotheses: Comparison of powers by Kallenberg and Ledwina (1997).
• DDST for Normality; Bounded Basis Functions - ddst.normbounded.test(); see Data-driven tests for a location-scale family revisited by Janic and Ledwina (2009).
• DDST for Normality; Unbounded Basis Functions - ddst.normunbounded.test(); see Detection of non-Gaussianity by Ledwina and Wyłupek (2015).
• DDST for Extreme Value Distribution - ddst.evd.test(); see Data-driven tests for a location-scale family revisited by Janic and Ledwina (2009).

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) and Towards data driven selection of a penalty function for data driven Neyman tests by Inglot and Ledwina (2006).

• DDST for Two-Sample Problem - ddst.twosample.test(); see Data-driven k-sample tests by Wyłupek (2010).
• DDST for k-Sample Problem - ddst.ksample.test(); see Data-driven k-sample tests by Wyłupek (2010).
• 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).
• DDST for Stochastic Dominance in Two Samples - ddst.forstochdom.test(); see Nonparametric tests for stochastic ordering by Ledwina and Wyłupek (2012).
• DDST Against Stochastic Dominance - ddst.againststochdom.test(); see Two-sample test against one-sided alternatives by Ledwina and Wyłupek (2012).
• DDST for Upward Trend Alternatives - ddst.upwardtrend.test(); see Data-driven tests for trend by Wyłupek (2013).
• DDST for Umbrella Alternatives; Known Peak - ddst.umbrellaknownp.test(); see An automatic test for the umbrella alternatives by Wyłupek (2016).
• DDST for Umbrella Alternatives; Unknown Peak - ddst.umbrellaunknownp.test(); see An automatic test for the umbrella alternatives by Wyłupek (2016).

A more detailed overview is contained in Data Driven Smooth Tests - Introductory Material. Full details on the above procedures can be found in the related papers.

Installation

# 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")