TPC_pl {TPCselect}

Variable Selection via Thresholded Partial Correlation

Description

These are the main selection functions with fixed significance level s and constant. The function TPC implements the thresholded partial correlation (TPC) approach to selecting important variables in linear models of Li et al. (2017). The function TPC_pl implements the thresholded partial correlation approach to selecting important variables in partial linear models of Liu et al. (2018). This function also extends the PC-simple algorithm of Bühlmann et al. (2010) to partial linear models.

Usage

TPC_pl(y, x, u = NULL, s = 0.05, constant = 1, method = "threshold", ...)

Arguments

y

response vector;

x

covariate matrix;

u

non-parametric variable, should be a vector;

s

s is a numeric value or vector that used as the significance level(s) for the partial correlation tests

constant

a value that used as the tuning constant for partial correlation test. constant is treated as 1 when method is "simple".

method

the method to be used; default set as method = "threshold"; "simple" is also available.

...

smoothing parameters and functions: kernel, degree, and bandwidth h.

Value

TPC.object a TPC object, which extends the lm object. New attributes are:

• beta - the fitted coefficients

• selected_index - the selected coefficients indices

Examples

#generate partial linear data
samples <- generate_toy_pldata()
y <- samples[[1]]
x <- samples[[2]]
times <- samples[[3]]

#perform variable selection via partial correlation
TPC.fit = TPC_pl(y,x,times,0.05,1,method="threshold")
TPC.fit$beta