*! version 1.0.0 24/jul2020

help critiband1 [Salgado-Ugarte, I.H. 2002]

Title

critiband1 -- Critical bandwidth search for WARPing density estimation (Updated version)

Syntax

critiband1 varname [if] [in] , bwhigh(#)
bwlow(#)
stsize(#)
mval(#)
[nograph
graph_options]

Description

critiband1 calculates the kde's and count the modes in order to
find the critical bandwidths in the specified range of bandwidths
for use with the Silverman multimodality smoothed bootstrapped test.
As in the silvtest.ado program, to estimate the KDE it uses the WARPing
procedure based on the algorithms described in Haerdle (1991), Scott (1992; 2016),
Salgado-Ugarte & Saito-Quezada (2020). The program produces a graph and a text
in the Results window with the bandwidths and number of modes in the analyzed
range.

Options

bwhigh(#) is the high value for the range of smoother parameter h
(bandwidth for kernel density estimators).

bwlow(#) is the low value for the range of smoother parameter h

stsize(#) specifies size of the step for the specified bandwidth range

mval(#) is the number of histograms to average for the kde estimation

nograph suppresses the graph drawing.

graph_options are any of the options allowed with graph, twoway
except top label options.

Remarks

bwhigh, bwlow, stsize and mval, are not optional. If the user does not
provide them, the program halts and displays an error message on screen.

As the warpdenm.ado program, this program is an all Stata command. Due to the
requirement of larger precision, a value of at least 40 for the number of histograms
to average ({opt mval) is necessary.

The kde graphics display the effect of varying the bandwidth: "smooth" results
being gradualy becoming noisy estimations, with the corresponding increment in
the number of modes.

Because this program is intended to use in combination with the silvtest.ado
program (Silverman's multimodality smoothed bootstrap test) only the Gaussian
kernel is implemented.

The number of KDEs calculated is round((bwhigh - bwlow)/stsize) + 1. If this
number is large, it is recommended to divide the total range of interest in several
shorter intervals in order to fit the size of the Results window.

This procedure permit to observe the gradual increment of the modes and to
locate the last bandwidth value compatible with a given number of modes.
The graphics give and animated presentation of the increasing number of
modes with the bandwidth decreasing, procedure very instructive and
recommended by Izenman and Sommer (1988).

Examples

. use silica

. critiband1 silica, bwhigh(2.5) bwlow(.5) stsize(0.01) mval(40)

Will display the KDEs for silica using bandwidths from 2.5 to 0.5 in steps
of 0.01 and a text report of the bandwidths and the corresponding number of
modes

. critiband1 silica, bwh(2.5) bwl(.5) st(.01) m(40) nog

Will display only the text of bandwidth and number of modes on the "Results"
window for the silica variable.

References

Haerdle, W. (1991) Smoothing Techniques with Implementation in S.
Springer-Verlag Chapter 2: 43-84; Chapters 1-2: 1-84.
Izenman, A.J. and C. Sommer (1988) Philatelic mixtures and multimodal
densities. Journal of the American Statistical Association,
83(404): 941-953.
Salgado-Ugarte, I.H. (2002) Suavización no paramétrica para análisis de
datos. DGAPA and FES Zaragoza, UNAM. Mexico. 139 p.
Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1993) snp6: Exploring
the shape of univariate data using kernel density estimators. Stata
Technical Bulletin 16: 8-19.
Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1995a) snp6.1: ASH,
WARPing, and kernel density estimation for univariate data. Stata
Technical Bulletin 26: 23-31.
Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1995b) snp6.2: Practical
Rules for bandwidth selection in univariate density estimation. Stata
Technical Bulletin 27: 5-19.
Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1997) snp13:
Nonparametric assessment of multimodality for univariate data. Stata
Technical Bulletin 38: 27-35.
Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice,
and Visualization. John Wiley, Chapter 9: 256-257.
Scott, D.W. (2016) Multivariate Density Estimation: Theory, Practice, and
Visualization. 2nd. ed. John Wiley, Hoboken, NJ, USA: Chapter 9: 275-276
Silverman, B.W. (1986) Density Estimation for Statistics and Data
Analysis. Chapman and Hall.

Authors

Original version:
Isaias H. Salgado-Ugarte, Makoto Shimizu and Toru Taniuchi
University of Tokyo, Faculty of Agriculture,
Department of Fisheries, Yayoi 1-1-1, Bunkyo-ku
Tokyo 113, Japan.(Fax 81-3-3812-0529)
Updated version:
Isaías H. Salgado-Ugarte & V. Mitsui Saito-Quezada
Laboratorio de Biometría y Biología Pesquera
Facultad de Estudios Superiores Zaragoza
Universidad Nacional Autónoma de México
isalgado@unam.mx

Also see

STB: snp6 (STB-16); snp6.1 (STB-26); snp6.2 (STB-27); snp6.4 (STB-38)

On-line: help for warpdenm1, kerneld, bandw1, l2cvwarpy, bcvwarpy, kernrpy, numode