Package 'MissCP'

BIC

Description

BIC and HBIC function

Usage

BIC(residual, phi)

Arguments

residual	residual matrix
phi	estimated coefficient matrix of the model

Value

A list object, which contains the followings

BIC

BIC value

HBIC

HBIC value

---

BIC_threshold

Description

BIC threshold for final parameter estimation

Usage

BIC_threshold(
  beta.final,
  k,
  m.hat,
  brk,
  data_y,
  data_x = NULL,
  b_n = 2,
  nlam = 20
)

Arguments

beta.final	estimated parameter coefficient matrices
k	dimensions of parameter coefficient matrices
m.hat	number of estimated change points
brk	vector of estimated change points
data_y	input data matrix (response), with each column representing the time series component
data_x	input data matrix (predictor), with each column 1
b_n	the block size
nlam	number of hyperparameters for grid search

Value

lambda.val.best, the tuning parameter lambda selected by BIC.

---

BTIE

Description

Perform the BTIE algorithm to detect the structural breaks in large scale high-dimensional mean shift models.

Usage

BTIE(
  data_y,
  lambda.1.cv = NULL,
  lambda.2.cv = NULL,
  max.iteration = 100,
  tol = 10^(-2),
  block.size = NULL,
  refit = FALSE,
  optimal.block = TRUE,
  optimal.gamma.val = 1.5,
  block.range = NULL
)

Arguments

data_y	input data matrix (response), with each column representing the time series component
lambda.1.cv	tuning parmaeter lambda_1 for fused lasso
lambda.2.cv	tuning parmaeter lambda_2 for fused lasso
max.iteration	max number of iteration for the fused lasso
tol	tolerance for the fused lasso
block.size	the block size
refit	logical; if TRUE, refit the model, if FALSE, use BIC to find a thresholding value and then output the parameter estimates without refitting. Default is FALSE.
optimal.block	logical; if TRUE, grid search to find optimal block size, if FALSE, directly use the default block size. Default is TRUE.
optimal.gamma.val	hyperparameter for optimal block size, if optimal.blocks == TRUE. Default is 1.5.
block.range	the search domain for optimal block size.

Value

A list object, which contains the followings

Examples

set.seed(1)
n <- 1000;
p <- 50;
brk <-  c(333, 666, n+1)
m <- length(brk)
d <- 5
constant.full <- constant_generation(n, p, d, 50, brk)
e.sigma <- as.matrix(1*diag(p))
data_y <- data_generation(n = n, mu = constant.full, sigma = e.sigma, brk = brk)
data_y <- as.matrix(data_y, ncol = p.y)
data_y_miss <- MCAR(data_y, 0.3)
temp <- BTIE(data_y_miss, optimal.block = FALSE, block.size = 30)
temp$cp.final

---

constant_generation

Description

function to generate constant given jump size and break points

Usage

constant_generation(n, p, d, vns, brk)

Arguments

n	the sample size
p	the data dimension
d	the number of nonzero coeddficients
vns	the jump size. It can be a vector or a single value. If single value, it is same for all break points
brk	the break points' locations

Value

the parameter matrix used to generate data

---

data_generation

Description

The function to generate mean shift data

Usage

data_generation(n, mu, sigma, brk = n + 1)

Arguments

n	the number of data points
mu	the matrix of mean parameter
sigma	covariance matrix of the white noise
brk	vector of change points

Value

data_y matrix of generated mean shift data

---

first.step

Description

Perform the block fused lasso with thresholding to detect candidate break points.

Usage

first.step(
  data_y,
  data_x,
  lambda1,
  lambda2,
  max.iteration = max.iteration,
  tol = tol,
  blocks,
  cv.index,
  fixed_index = NULL,
  nonfixed_index = NULL
)

Arguments

data_y	input data matrix Y, with each column representing the time series component
data_x	input data matrix X
lambda1	tuning parmaeter lambda_1 for fused lasso
lambda2	tuning parmaeter lambda_2 for fused lasso
max.iteration	max number of iteration for the fused lasso
tol	tolerance for the fused lasso
blocks	the blocks
cv.index	the index of time points for cross-validation
fixed_index	index for linear regression model with only partial compoenents change.
nonfixed_index	index for linear regression model with only partial compoenents change.

Value

A list object, which contains the followings

jump.l2

estimated jump size in L2 norm

jump.l1

estimated jump size in L1 norm

pts.list

estimated change points in the first step

beta.full

estimated parameters in the first step

---

Heter_missing

Description

function to do the missing assuming the missing completely at random

Usage

Heter_missing(data, alpha)

Arguments

data	data before the missing case
alpha	the list of percentage of missing compared to whole data

Value

the data matrix with missing values

---

imputation

Description

function to do the imputation based on block size

Usage

imputation(data, block.size)

Arguments

data	data before the imputation
block.size	the block size that are used to impute the missing

Value

the data matrix without missing values after imputation

---

imputation2

Description

function to do the imputation based on change point candidate

Usage

imputation2(data, cp.candidate)

Arguments

data	data before the imputation
cp.candidate	the change point candidate that are used to impute the missing

Value

the data matrix without missing values after imputation

---

MCAR

Description

function to do the missing assuming the missing completely at random

Usage

MCAR(data, alpha)

Arguments

data	data before the missing case
alpha	the percentage of missing compared to whole data

Value

the data matrix with missing values

---

pred

Description

function to do the prediction

Usage

pred(X, phi, j, p.x, p.y, h = 1)

Arguments

X	data for prediction
phi	parameter matrix
j	the start time point for prediction
p.x	the dimension of data X
p.y	the dimension of data Y
h	the length of observation to predict

Value

prediction matrix

---

pred.block

Description

Prediction function (block)

Usage

pred.block(X, phi, j, p.x, p.y, h)

Arguments

X	data for prediction
phi	parameter matrix
j	the start time point for prediction
p.x	the dimension of data X
p.y	the dimension of data Y
h	the length of observation to predict

Value

prediction matrix

---

second.step

Description

Reimputate the missing values and perform the exhaustive search to "thin out" redundant break points.

Usage

second.step(
  data_y,
  data_x,
  max.iteration = max.iteration,
  tol = tol,
  cp.first,
  beta.est,
  blocks,
  data_y_miss
)

Arguments

data_y	input data matrix, with each column representing the time series component
data_x	input data matrix
max.iteration	max number of iteration for the fused lasso
tol	tolerance for the fused lasso
cp.first	the selected break points after the first step
beta.est	the estiamted parameters by block fused lasso
blocks	the blocks
data_y_miss	the data y matrix before the first imputation

Value

A list object, which contains the followings

cp.final

a set of selected break point after the exhaustive search step

beta.hat.list

the estimated coefficient matrix for each segmentation

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