Bagidis (version 1.0)

BD.plot: B-D representation of the Bottom Up Unbalanced Haar Wavelet Expansion of a series

Description

Function for graphical representation of the Bottom Up Unbalanced Haar Wavelet Expansion (here after BUUHWE) of a series, in the Breakpoints-Details plane (B-D plane).

Usage

BD.plot(x, y = NULL, BUUHWE.out.x = BUUHWE(x), BUUHWE.out.y = BUUHWE(y), 
French = FALSE, col = c('black','red'))

Arguments

x

a numeric vector (a series) whose BUUHWE expansion has to be computed and represented and the B-D plane

y

an optional second numeric vector (a series) whose BUUHWE expansion has to be computed and superimposed to the one of x in the B-D plane. length(y) must be equal to length(x).

BUUHWE.out.x

output of BUUHWE(x), included as an optional argument for saving computation time within the function if it has already been computed and saved outside the function; otherwise BUUHWE transform of x is compute at the call of function BD.plot.

BUUHWE.out.y

output of BUUHWE(y), included as an optional argument for saving computation time within the function if it has already been computed and saved outside the function; otherwise the BUUHWE transform of y is computed by BUUHWE at the call of function BD.plot.

French

logical. Should labels be written in french ? (default=english)

col

vector of size one or two, indicating the colors for representing series x and - if needed -series y in the B-D plane. Default is black for series x and red for series y.

Value

This function is invoked for its side effect which is to produce a graphical representation of the expansion of a series in its unbalanced Haar wavelet basis. The series is plotted in the plane that is defined by the values of its breakpoints and its detail coefficients. Points are numbered according to their rank in the hierarchy.

Details

See References below, in particular Timmermans (2012), Chapter 1, or Timmermans and von Sachs (2010).

References

The main references are

• Timmermans C., 2012, Bases Giving Distances. A new paradigm for investigating functional data with applications for spectroscopy. PhD thesis, Universite catholique de Louvain. http://hdl.handle.net/2078.1/112451
• Timmermans C. and von Sachs R., 2015, A novel semi-distance for investigating dissimilarities of curves with sharp local patterns, Journal of Statistical Planning and Inference, 160, 35-50. http://hdl.handle.net/2078.1/154928
• Fryzlewicz P. and Timmermans C., 2015, SHAH: Shape Adaptive Haar wavelets for image processing. Journal of Computational and Graphical Statistics. (accepted - published online 27 May 2015) http://stats.lse.ac.uk/fryzlewicz/shah/shah.pdf
• Timmermans C., Delsol L. and von Sachs R., 2013, Using BAGIDIS in nonparametric functional data analysis: predicting from curves with sharp local features, Journal of Multivariate Analysis, 115, p. 421-444. http://hdl.handle.net/2078.1/118369

Other references include

• Girardi M. and Sweldens W., 1997, A new class of unbalanced Haar wavelets that form an unconditional basis for Lp on general measure spaces, J. Fourier Anal. Appl. 3, 457-474
• Fryzlewicz P., 2007, Unbalanced Haar Technique for Non Parametric Function Estimation, Journal of the American Statistical Association, 102, 1318-1327.
• Timmermans C., von Sachs, R. , 2010, BAGIDIS, a new method for statistical analysis of differences between curves with sharp patterns (ISBA Discussion Paper 2010/30). Url : http://hdl.handle.net/2078.1/91090
• Timmermans, C. , Fryzlewicz, P., 2012, SHAH: Shape-Adaptive Haar Wavelet Transform For Images With Application To Classification (ISBA Discussion Paper 2012/15). Url: http://hdl.handle.net/2078.1/110529

See Also

BUUHWE, BUUHWE.plot

Examples

 x= c(1,7,3,0,-2,6,4,0,2)
 BD.plot(x)