Package unbalhaar. February 20, 2015
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1 Type Package Package unbalhaar February 20, 2015 Title Function estimation via Unbalanced Haar wavelets Version 2.0 Date Author Maintainer The package implements top-down and bottom-up algorithms for nonparametric function estimation in Gaussian noise using Unbalanced Haar wavelets. License GPL-2 LazyLoad yes Repository CRAN Date/Publication :59:57 NeedsCompilation no R topics documented: unbalhaar-package best.unbal.haar best.unbal.haar.bu hard.thresh hard.thresh.bu inner.prod.iter inner.prod.ma inner.prod.ma.p med reconstr reconstr.bu uh uh.bu unbal.haar.vector Inde 13 1
2 2 best.unbal.haar unbalhaar-package Function estimation via Unbalanced Haar wavelets Details The package implements top-down and bottom-up algorithms for nonparametric function estimation in Gaussian noise using Unbalanced Haar wavelets. Package: unbalhaar Type: Package Version: 2.0 Date: License: GPL-2 LazyLoad: yes The main functions of the package are uh and uh.bu. Maintainer: References P. Fryzlewicz (2007) Unbalanced Haar technique for nonparametric function estimation. Journal of the American Statistical Association, 102, <- c(rep(0, 100), rep(1, 200)) + rnorm(300) est.topdown <- uh() est.bottomup <- uh.bu() best.unbal.haar Best top-down Unbalanced Haar decomposition The function finds the best top-down Unbalanced Haar (UH) decomposition of the input vector, according to a selection rule (criterion) which specifies which UH vector gets chosen at each scale and location.
3 best.unbal.haar.bu 3 best.unbal.haar(, criterion = inner.prod.ma) criterion a vector a function which takes a vector of length n and returns an integer between 1 and n-1 tree smooth A list of J matrices, where J represents the number of scales. Each matri is of size 5 (the number of UH coefficients at a given scale). Each column (= vector of length 5) contains an Unbalanced Haar coefficient in the following format: 1st component - an inde of the coefficient; 2nd component - the value of the coefficient; 3rd component - time point where the corresponding UH vector starts; 4th component - last time point before the breakpoint of the UH vector; 5th component - end point of the UH vector. the smooth component of, equal to sum() / sqrt(n), where n is the length of inner.prod.ma, inner.prod.ma.p, best.unbal.haar.bu best.unbal.haar(rnorm(100), inner.prod.ma.p) best.unbal.haar.bu Best bottom-up Unbalanced Haar decomposition The function finds the best bottom-up Unbalanced Haar (UH) decomposition of the input vector. best.unbal.haar.bu(, stretch = length())
4 4 hard.thresh stretch a vector at each iteration, only the first 1:stretch elements of the current input vector (whose length decreases by one with each iteration) get scanned in the search for the worst-fitting fine-scale Unbalanced Haar wavelet detail smooth A matri of size 3 n-1, where n is the length of, containing the detail coefficients of in the order they were chosen. Each column corresponds to a single coefficient and contains, from top to bottom: location of the coefficient, the associated weight, and the value of the coefficient. the smooth component of, equal to sum() / sqrt(n), where n is the length of best.unbal.haar best.unbal.haar.bu(rnorm(100)) hard.thresh Hard thresholding of a top-down Unbalanced Haar decomposition Presented with an object returned by best.unbal.haar, the function sets to zero those Unbalanced Haar coefficients which fall below a certain threshold sigma. hard.thresh(buh, sigma = 1) buh sigma an object returned by best.unbal.haar containing the decomposition to be thresholded the threshold (a positive scalar)
5 hard.thresh.bu 5 a thresholded object, of the same class as buh best.unbal.haar, hard.thresh.bu <- rnorm(1000).uh <- best.unbal.haar().uh.th <- hard.thresh(.uh).uh.th.r <- reconstr(.uh.th) ts.plot(.uh.th.r) hard.thresh.bu Hard thresholding of a bottom-up Unbalanced Haar decomposition Presented with an object returned by best.unbal.haar.bu, the function sets to zero those Unbalanced Haar coefficients which fall below a certain threshold sigma. hard.thresh.bu(buh.bu, sigma = 1) buh.bu sigma an object returned by best.unbal.haar.bu containing the decomposition to be thresholded the threshold (a positive scalar) a thresholded object, of the same class as buh.bu best.unbal.haar.bu, hard.thresh
6 6 inner.prod.iter <- rnorm(1000).uh <- best.unbal.haar.bu().uh.th <- hard.thresh.bu(.uh).uh.th.r <- reconstr.bu(.uh.th) ts.plot(.uh.th.r) inner.prod.iter Inner products with Unbalanced Haar wavelets For an input vector of length n, the function computes inner products between the input vector and all possible n-1 Unbalanced Haar vectors of length n. inner.prod.iter() a vector of length n Details The computation is iterative and is performed in computational time O(n). a vector of length n-1, containing inner products between and consecutive Unbalanced Haar wavelets of length n inner.prod.iter(rnorm(100))
7 inner.prod.ma 7 inner.prod.ma Unbalanced Haar wavelet which maimises the inner product The function finds the Unbalanced Haar vector which yields the largest (in absolute value) inner product with the input vector. inner.prod.ma() a vector The inde where abs(inner.prod.iter()) is maimised. If two or more maima are found, the med of their locations is returned. inner.prod.iter, med, inner.prod.ma.p inner.prod.ma(c(rep(0, 100), rep(1, 200))) inner.prod.ma.p Unbalanced Haar wavelet which maimises the inner product The function finds the Unbalanced Haar vector which yields the largest (in absolute value) inner product with the input vector, amongst those Unbalanced Haar vectors whose breakpoint is located between 100(1-p)% and 100p% of their support. inner.prod.ma.p(, p = 0.8)
8 8 med a vector p a scalar in (0.5, 1] The inde where abs(inner.prod.iter()) is maimised on the subinterval (1+floor((1-p)*n)):ceiling(p*n), where n is the length of. If two or more maima are found, the med of their locations is returned. inner.prod.iter, med, inner.prod.ma inner.prod.ma.p(c(rep(0, 100), rep(1, 200)),.55) med Median The function computes the median of a vector. Unlike median, it is guaranteed to return a value which is a component of the input vector. med() a vector a scalar defined as quantile(,.5, type=3)[[1]] med(1:4) median(1:4)
9 reconstr 9 reconstr Reconstruct a top-down Unbalanced Haar decomposition Reconstructs a vector from its top-down Unbalanced Haar decomposition stored in an object returned by best.unbal.haar or hard.thresh. reconstr(buh) buh an object of the type returned by best.unbal.haar and hard.thresh the inverse Unbalanced Haar transform of buh best.unbal.haar, hard.thresh, reconstr.bu <- rnorm(1000).uh <- best.unbal.haar().uh.th <- hard.thresh(.uh).uh.th.r <- reconstr(.uh.th) ts.plot(.uh.th.r) reconstr.bu Reconstruct a bottom-up Unbalanced Haar decomposition Reconstructs a vector from its bottom-up Unbalanced Haar decomposition stored in an object returned by best.unbal.haar.bu or hard.thresh.bu. reconstr.bu(buh.bu)
10 10 uh buh.bu an object of the type returned by best.unbal.haar.bu and hard.thresh.bu the inverse Unbalanced Haar transform of buh.bu best.unbal.haar.bu, hard.thresh.bu, reconstr <- rnorm(1000).uh <- best.unbal.haar.bu().uh.th <- hard.thresh.bu(.uh).uh.th.r <- reconstr.bu(.uh.th) ts.plot(.uh.th.r) uh Denoising via top-down Unbalanced Haar Given an input vector of the form signal + iid Gaussian noise, the function estimates the noise level via Median Absolute Deviation, finds the best top-down Unbalanced Haar decomposition (according to the selection rule criterion), thresholds it with the universal threshold, and performs the inverse Unbalanced Haar transform to yield an estimate of the signal. uh(, criterion = inner.prod.ma) criterion a vector of the form signal + iid Gaussian noise a function which takes a vector of length n and returns an integer between 1 and n-1 an estimate of the signal
11 uh.bu 11 References P. Fryzlewicz (2007) Unbalanced Haar technique for nonparametric function estimation. Journal of the American Statistical Association, 102, uh.bu, best.unbal.haar, inner.prod.ma, inner.prod.ma.p, hard.thresh, reconstr <- c(rep(0, 100), rep(1, 200)) + rnorm(300) est <- uh() uh.bu Denoising via bottom-up Unbalanced Haar Given an input vector of the form signal + iid Gaussian noise, the function estimates the noise level via Median Absolute Deviation, finds the best bottom-up Unbalanced Haar decomposition, thresholds it with the universal threshold, and performs the inverse Unbalanced Haar transform to yield an estimate of the signal. uh.bu(, stretch = length()) stretch a vector of the form signal + iid Gaussian noise at each iteration, only the first 1:stretch elements of the current input vector (whose length decreases by one with each iteration) get scanned in the search for the worst-fitting fine-scale Unbalanced Haar wavelet an estimate of the signal
12 12 unbal.haar.vector References P. Fryzlewicz (2007) Unbalanced Haar technique for nonparametric function estimation. Journal of the American Statistical Association, 102, uh, best.unbal.haar.bu, hard.thresh.bu, reconstr.bu <- c(rep(0, 100), rep(1, 200)) + rnorm(300) est <- uh.bu() unbal.haar.vector Unbalanced Haar vector Computes the non-zero part of an Unbalanced Haar vector with a given start-, break- and end-point. unbal.haar.vector(a) a a three-component vector of integers such that a[1] <= a[2] < a[3]. The three components specify, respectively, the start point, the time point just before the breakpoint, and the endpoint of the desired Unbalanced Haar vector. the non-zero part of the corresponding Unbalanced Haar vector unbal.haar.vector(c(1, 1, 2)) unbal.haar.vector(c(2, 5, 12))
13 Inde Topic math best.unbal.haar, 2 best.unbal.haar.bu, 3 hard.thresh, 4 hard.thresh.bu, 5 inner.prod.iter, 6 inner.prod.ma, 7 inner.prod.ma.p, 7 med, 8 reconstr, 9 reconstr.bu, 9 uh, 10 uh.bu, 11 unbal.haar.vector, 12 Topic package unbalhaar-package, 2 best.unbal.haar, 2, 4, 5, 9, 11 best.unbal.haar.bu, 3, 3, 5, 10, 12 hard.thresh, 4, 5, 9, 11 hard.thresh.bu, 5, 5, 10, 12 inner.prod.iter, 6, 7, 8 inner.prod.ma, 3, 7, 8, 11 inner.prod.ma.p, 3, 7, 7, 11 med, 7, 8, 8 reconstr, 9, 10, 11 reconstr.bu, 9, 9, 12 uh, 2, 10, 12 uh.bu, 2, 11, 11 unbal.haar.vector, 12 unbalhaar (unbalhaar-package), 2 unbalhaar-package, 2 13
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Package babar. R topics documented: February 24, Type Package
Type Package Package babar February 24, 2015 Title Bayesian Bacterial Growth Curve Analysis in R Version 1.0 Date 2014-11-13 Author Maintainer Matthew Hartley Babar is designed
Package CovSel. September 25, 2013
Type Package Title Model-Free Covariate Selection Version 1.0 Date 2013-06-24 Author Jenny Häggström, Emma Persson, Package CovSel September 25, 2013 Maintainer Jenny Häggström
Package EMVS. April 24, 2018
Type Package Package EMVS April 24, 2018 Title The Expectation-Maximization Approach to Bayesian Variable Selection Version 1.0 Date 2018-04-23 Author Veronika Rockova [aut,cre], Gemma Moran [aut] Maintainer
Package ENA. February 15, 2013
Package ENA February 15, 2013 Type Package Title Ensemble Network Aggregation Version 1.2-4 Date 2013-02-14 Author Maintainer Depends R (>= 2.13.0), space (>= 0.1), WGCNA (>= 1.20), GeneNet(>= 1.2.5),
Package ICGOR. January 13, 2017
Package ICGOR January 13, 2017 Type Package Title Fit Generalized Odds Rate Hazards Model with Interval Censored Data Version 2.0 Date 2017-01-12 Author Jie Zhou, Jiajia Zhang, Wenbin Lu Maintainer Jie
Package RcppSMC. March 18, 2018
Type Package Title Rcpp Bindings for Sequential Monte Carlo Version 0.2.1 Date 2018-03-18 Package RcppSMC March 18, 2018 Author Dirk Eddelbuettel, Adam M. Johansen and Leah F. South Maintainer Dirk Eddelbuettel
Package crossreg. February 19, 2015
Package crossreg February 19, 2015 Type Package Title Confidence intervals for crossover points of two simple regression lines Version 1.0 Date 2014-07-08 Author Maintainer This package
Package gsarima. February 20, 2015
Package gsarima February 20, 2015 Version 0.1-4 Date 2013-06-17 Title Two functions for Generalized SARIMA time series simulation Author Olivier Briet Maintainer Olivier Briet
Package TruncatedNormal
Package TruncatedNormal November 10, 2015 Type Package Title Truncated Multivariate Normal Version 1.0 Date 2015-11-08 Author Zdravko I. Botev Maintainer Zdravko Botev A collection
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Version 2.0-7 Type Package Package leiv February 20, 2015 Title Bivariate Linear Errors-In-Variables Estimation Date 2015-01-11 Maintainer David Leonard Depends R (>= 2.9.0)
Package OSCV. March 18, 2017
Title One-Sided Cross-Validation Version 1.0 Author Olga Savchuk Package OSCV March 18, 2017 Maintainer Olga Savchuk Functions for implementing different versions of the OSCV
Package idmtpreg. February 27, 2018
Type Package Package idmtpreg February 27, 2018 Title Regression Model for Progressive Illness Death Data Version 1.1 Date 2018-02-23 Author Leyla Azarang and Manuel Oviedo de la Fuente Maintainer Leyla
Package mar. R topics documented: February 20, Title Multivariate AutoRegressive analysis Version Author S. M. Barbosa
Title Multivariate AutoRegressive analysis Version 1.1-2 Author S. M. Barbosa Package mar February 20, 2015 R functions for multivariate autoregressive analysis Depends MASS Maintainer S. M. Barbosa
Package rela. R topics documented: February 20, Version 4.1 Date Title Item Analysis Package with Standard Errors
Version 4.1 Date 2009-10-25 Title Item Analysis Package with Standard Errors Package rela February 20, 2015 Author Michael Chajewski Maintainer Michael Chajewski
Package mhsmm. January 15, 2017
Type Package Package mhsmm January 15, 2017 Title Inference for Hidden Markov and Semi-Markov Models Version 0.4.16 Date 2017-01-15 Author Jared O'Connell , SÃ ren HÃ jsgaard
Wild Binary Segmentation for multiple change-point detection
for multiple change-point detection Piotr Fryzlewicz p.fryzlewicz@lse.ac.uk Department of Statistics, London School of Economics, UK Isaac Newton Institute, 14 January 2014 Segmentation in a simple function
Package RTransferEntropy
Type Package Package RTransferEntropy March 12, 2019 Title Measuring Information Flow Between Time Series with Shannon and Renyi Transfer Entropy Version 0.2.8 Measuring information flow between time series