orthoDr_reg: Semiparametric dimension reduction method from Ma & Zhu...

In orthoDr: Semi-Parametric Dimension Reduction Models Using Orthogonality Constrained Optimization

Semiparametric dimension reduction method from Ma & Zhu (2012).

Description

Performs the semiparametric dimension reduction method associated with Ma & Zhu (2012).

Usage

orthoDr_reg(
  x,
  y,
  method = "sir",
  ndr = 2,
  B.initial = NULL,
  bw = NULL,
  keep.data = FALSE,
  control = list(),
  maxitr = 500,
  verbose = FALSE,
  ncore = 0
)

Arguments

x	A matrix or data.frame for features (continous only). The algorithm will not scale the columns to unit variance
y	A vector of continuous outcome
method	Dimension reduction methods (semi-): "sir", "save", "phd", "local" or "seff". Currently only "sir" and "phd" are available.
ndr	The number of directions
B.initial	Initial B values. If specified, must be a matrix with ncol(x) rows and ndr columns. Will be processed by Gram-Schmidt if not orthogonal. If the initial value is not given, three initial values ("sir", "save" and "phd") using the traditional method will be tested. The one with smallest l2 norm of the estimating equation will be used.
bw	A Kernel bandwidth, assuming each variables have unit variance
keep.data	Should the original data be kept for prediction. Default is FALSE.
control	A list of tuning variables for optimization. epsilon is the size for numerically approximating the gradient. For others, see Wen and Yin (2013).
maxitr	Maximum number of iterations
verbose	Should information be displayed
ncore	Number of cores for parallel computing. The default is the maximum number of threads.

Value

A orthoDr object consisting of list with named elements:

B	The optimal B value
fn	The final functional value
itr	The number of iterations
converge	convergence code

References

Ma, Y., & Zhu, L. (2012). A semiparametric approach to dimension reduction. Journal of the American Statistical Association, 107(497), 168-179. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2011.646925")}

Ma, Y., & Zhu, L. (2013). Efficient estimation in sufficient dimension reduction. Annals of statistics, 41(1), 250. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/12-AOS1072")}

Examples

# generate some regression data
set.seed(1)
N <- 100
P <- 4
dataX <- matrix(rnorm(N * P), N, P)
Y <- -1 + dataX[, 1] + rnorm(N)

# fit the semi-sir model
orthoDr_reg(dataX, Y, ndr = 1, method = "sir")

# fit the semi-phd model
Y <- -1 + dataX[, 1]^2 + rnorm(N)
orthoDr_reg(dataX, Y, ndr = 1, method = "phd")

orthoDr documentation built on April 30, 2023, 5:12 p.m.