bootmode

% Function file: [H, P, h] = bootmode (x, m, B, kernel)
%
% This function tests whether the distribution underlying the univariate
% data in vector x has m modes. The method employs the smooth bootstrap
% as described [1].
%
% The parsimonious approach is to consider a successively increasing
% number of modes until the null hypothesis (H0) is accepted (i.e. H=0),
% where H0 corresponds to the number of modes being equal to m.
%
% x is the vector of data
%
% m is the number of modes for hypothesis testing
%
% B is the number of bootstrap replicates
%
% kernel can be 'Gaussian' (default) or 'Epanechnikov'
%
% H=0 indicates that the null hypothesis cannot be rejected at the 5%
% significance level. H=1 indicates that the null hypothesis can be
% rejected at the 5% level.
%
% P is the achieved significance level using the bootstrap test.
%
% h is the critical bandwidth (i.e. the smallest bandwidth achievable to
% obtain a kernel density estimate with m modes)
%
% Bibliography:
% [1] Efron and Tibshirani. Chapter 16 Hypothesis testing with the
% bootstrap in An introduction to the bootstrap (CRC Press, 1994)
%
% bootmode v1.1 (22/04/2019)
% Author: Andrew Charles Penn
% https://www.researchgate.net/profile/Andrew_Penn/