Package 'SIHR' reference manual

Title:	Statistical Inference in High Dimensional Regression
Description:	The goal of SIHR is to provide inference procedures in the high-dimensional generalized linear regression setting for: (1) linear functionals <doi:10.48550/arXiv.1904.12891> <doi:10.48550/arXiv.2012.07133>, (2) conditional average treatment effects, (3) quadratic functionals <doi:10.48550/arXiv.1909.01503>, (4) inner product, (5) distance.
Authors:	Zhenyu Wang [aut], Prabrisha Rakshit [aut], Tony Cai [aut], Zijian Guo [aut, cre]
Maintainer:	Zijian Guo <[email protected]>
License:	GPL-3
Version:	2.1.0
Built:	2024-11-26 04:53:05 UTC
Source:	https://github.com/zywang0701/sihr

Inference for difference of linear combinations of the regression vectors in high dimensional generalized linear regressions

Description

Computes the bias-corrected estimator of the difference of linear combinations of the regression vectors for the high dimensional generalized linear regressions and the corresponding standard error.

Usage

CATE(
  X1,
  y1,
  X2,
  y2,
  loading.mat,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  intercept.loading = FALSE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  verbose = FALSE
)
CATE(
  X1,
  y1,
  X2,
  y2,
  loading.mat,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  intercept.loading = FALSE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  verbose = FALSE
)

Arguments

`X1`	Design matrix for the first sample, of dimension $n_1$ x $p$
`y1`	Outcome vector for the first sample, of length $n_1$
`X2`	Design matrix for the second sample, of dimension $n_2$ x $p$
`y2`	Outcome vector for the second sample, of length $n_1$
`loading.mat`	Loading matrix, nrow= $p$ , each column corresponds to a loading of interest
`model`	The high dimensional regression model, either `"linear"` or `"logistic"` or `"logistic_alter"`
`intercept`	Should intercept(s) be fitted for the initial estimators (default = `TRUE`)
`intercept.loading`	Should intercept term be included for the `loading` (default = `FALSE`)
`beta.init1`	The initial estimator of the regression vector for the 1st data (default = `NULL`)
`beta.init2`	The initial estimator of the regression vector for the 2nd data (default = `NULL`)
`lambda`	The tuning parameter in fitting initial model. If `NULL`, it will be picked by cross-validation. (default = `NULL`)
`mu`	The dual tuning parameter used in the construction of the projection direction. If `NULL` it will be searched automatically. (default = `NULL`)
`prob.filter`	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
`rescale`	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
`verbose`	Should intermediate message(s) be printed (default = `FALSE`)

Value

A list consists of plugin estimators, debiased estimators, and confidence intervals. For logistic regression, it also returns those items after probability transformation.

`est.plugin.vec`	The vector of plugin(biased) estimators for the linear combination of regression coefficients, length of `ncol(loading.mat)`; corresponding to different column in `loading.mat`
`est.debias.vec`	The vector of bias-corrected estimators for the linear combination of regression coefficients, length of `ncol(loading.mat)`; corresponding to different column in `loading.mat`
`se.vec`	The vector of standard errors of the bias-corrected estimators, length of `ncol(loading.mat)`; corresponding to different column in `loading.mat`
`prob.debias.vec`	The vector of bias-corrected estimators after probability transformation, length of `ncol(loading.mat)`; corresponding to different column in `loading.mat`.
`prob.se.vec`	The vector of standard errors of the bias-corrected estimators after probability transformation, length of `ncol(loading.mat)`; corresponding to different column in `loading.mat`.

Examples

X1 <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y1 <- -0.5 + X1[, 1] * 0.5 + X1[, 2] * 1 + rnorm(100)
X2 <- matrix(rnorm(90 * 5), nrow = 90, ncol = 5)
y2 <- -0.4 + X2[, 1] * 0.48 + X2[, 2] * 1.1 + rnorm(90)
loading1 <- c(1, 1, rep(0, 3))
loading2 <- c(-0.5, -1, rep(0, 3))
loading.mat <- cbind(loading1, loading2)
Est <- CATE(X1, y1, X2, y2, loading.mat, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)
X1 <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y1 <- -0.5 + X1[, 1] * 0.5 + X1[, 2] * 1 + rnorm(100)
X2 <- matrix(rnorm(90 * 5), nrow = 90, ncol = 5)
y2 <- -0.4 + X2[, 1] * 0.48 + X2[, 2] * 1.1 + rnorm(90)
loading1 <- c(1, 1, rep(0, 3))
loading2 <- c(-0.5, -1, rep(0, 3))
loading.mat <- cbind(loading1, loading2)
Est <- CATE(X1, y1, X2, y2, loading.mat, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)

Inference for weighted quadratic functional of difference of the regression vectors (excluding the intercept term) in high dimensional generalized linear regressions.

Description

Inference for weighted quadratic functional of difference of the regression vectors (excluding the intercept term) in high dimensional generalized linear regressions.

Usage

Dist(
  X1,
  y1,
  X2,
  y2,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  verbose = FALSE
)
Dist(
  X1,
  y1,
  X2,
  y2,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  verbose = FALSE
)

Arguments

`X1`	Design matrix for the first sample, of dimension $n_1$ x $p$
`y1`	Outcome vector for the first sample, of length $n_1$
`X2`	Design matrix for the second sample, of dimension $n_2$ x $p$
`y2`	Outcome vector for the second sample, of length $n_1$
`G`	The set of indices, `G` in the quadratic form
`A`	The matrix A in the quadratic form, of dimension $\|G\|\times$ $\|G\|$ . If `NULL` A would be set as the $\|G\|\times$ $\|G\|$ submatrix of the population covariance matrix corresponding to the index set `G` (default = `NULL`)
`model`	The high dimensional regression model, either `"linear"` or `"logistic"` or `"logistic_alter"`
`intercept`	Should intercept(s) be fitted for the initial estimators (default = `TRUE`)
`beta.init1`	The initial estimator of the regression vector for the 1st data (default = `NULL`)
`beta.init2`	The initial estimator of the regression vector for the 2nd data (default = `NULL`)
`split`	Sampling splitting or not for computing the initial estimators. It take effects only when `beta.init1 = NULL` or `beta.init2 = NULL`. (default = `TRUE`)
`lambda`	The tuning parameter in fitting initial model. If `NULL`, it will be picked by cross-validation. (default = `NULL`)
`mu`	The dual tuning parameter used in the construction of the projection direction. If `NULL` it will be searched automatically. (default = `NULL`)
`prob.filter`	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
`rescale`	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
`tau`	The enlargement factor for asymptotic variance of the bias-corrected estimator to handle super-efficiency. It allows for a scalar or vector. (default = `c(0.25,0.5, 1)`)
`verbose`	Should intermediate message(s) be printed. (default = `FALSE`)

Value

`est.plugin`	The plugin(biased) estimator for the quadratic form of the regression vectors restricted to `G`
`est.debias`	The bias-corrected estimator of the quadratic form of the regression vectors
`se`	Standard errors of the bias-corrected estimator, length of `tau`; corrsponding to different values of `tau`

Examples

X1 <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y1 <- -0.5 + X1[, 1] * 0.5 + X1[, 2] * 1 + rnorm(100)
X2 <- matrix(rnorm(90 * 5), nrow = 90, ncol = 5)
y2 <- -0.4 + X2[, 1] * 0.48 + X2[, 2] * 1.1 + rnorm(90)
G <- c(1, 2)
A <- matrix(c(1.5, 0.8, 0.8, 1.5), nrow = 2, ncol = 2)
Est <- Dist(X1, y1, X2, y2, G, A, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)
X1 <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y1 <- -0.5 + X1[, 1] * 0.5 + X1[, 2] * 1 + rnorm(100)
X2 <- matrix(rnorm(90 * 5), nrow = 90, ncol = 5)
y2 <- -0.4 + X2[, 1] * 0.48 + X2[, 2] * 1.1 + rnorm(90)
G <- c(1, 2)
A <- matrix(c(1.5, 0.8, 0.8, 1.5), nrow = 2, ncol = 2)
Est <- Dist(X1, y1, X2, y2, G, A, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)

Inference for weighted inner product of the regression vectors in high dimensional generalized linear regressions

Description

Inference for weighted inner product of the regression vectors in high dimensional generalized linear regressions

Usage

InnProd(
  X1,
  y1,
  X2,
  y2,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  verbose = FALSE
)
InnProd(
  X1,
  y1,
  X2,
  y2,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init1 = NULL,
  beta.init2 = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  verbose = FALSE
)

Arguments

`X1`	Design matrix for the first sample, of dimension $n_1$ x $p$
`y1`	Outcome vector for the first sample, of length $n_1$
`X2`	Design matrix for the second sample, of dimension $n_2$ x $p$
`y2`	Outcome vector for the second sample, of length $n_1$
`G`	The set of indices, `G` in the quadratic form
`A`	The matrix A in the quadratic form, of dimension $\|G\|\times$ $\|G\|$ . If `NULL` A would be set as the $\|G\|\times$ $\|G\|$ submatrix of the population covariance matrix corresponding to the index set `G` (default = `NULL`)
`model`	The high dimensional regression model, either `"linear"` or `"logistic"` or `"logistic_alter"`
`intercept`	Should intercept(s) be fitted for the initial estimators (default = `TRUE`)
`beta.init1`	The initial estimator of the regression vector for the 1st data (default = `NULL`)
`beta.init2`	The initial estimator of the regression vector for the 2nd data (default = `NULL`)
`split`	Sampling splitting or not for computing the initial estimators. It take effects only when `beta.init1 = NULL` or `beta.init2 = NULL`. (default = `TRUE`)
`lambda`	The tuning parameter in fitting initial model. If `NULL`, it will be picked by cross-validation. (default = `NULL`)
`mu`	The dual tuning parameter used in the construction of the projection direction. If `NULL` it will be searched automatically. (default = `NULL`)
`prob.filter`	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
`rescale`	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
`tau`	The enlargement factor for asymptotic variance of the bias-corrected estimator to handle super-efficiency. It allows for a scalar or vector. (default = `c(0.25,0.5, 1)`)
`verbose`	Should intermediate message(s) be printed. (default = `FALSE`)

Value

`est.plugin`	The plugin(biased) estimator for the inner product form of the regression vectors restricted to `G`
`est.debias`	The bias-corrected estimator of the inner product form of the regression vectors
`se`	Standard errors of the bias-corrected estimator, length of `tau`; corrsponding to different values of `tau`

Examples

X1 <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y1 <- -0.5 + X1[, 1] * 0.5 + X1[, 2] * 1 + rnorm(100)
X2 <- matrix(rnorm(90 * 5), nrow = 90, ncol = 5)
y2 <- -0.4 + X2[, 1] * 0.48 + X2[, 2] * 1.1 + rnorm(90)
G <- c(1, 2)
A <- matrix(c(1.5, 0.8, 0.8, 1.5), nrow = 2, ncol = 2)
Est <- InnProd(X1, y1, X2, y2, G, A, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)
X1 <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y1 <- -0.5 + X1[, 1] * 0.5 + X1[, 2] * 1 + rnorm(100)
X2 <- matrix(rnorm(90 * 5), nrow = 90, ncol = 5)
y2 <- -0.4 + X2[, 1] * 0.48 + X2[, 2] * 1.1 + rnorm(90)
G <- c(1, 2)
A <- matrix(c(1.5, 0.8, 0.8, 1.5), nrow = 2, ncol = 2)
Est <- InnProd(X1, y1, X2, y2, G, A, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)

Inference for linear combination of the regression vector in high dimensional generalized linear regression

Description

Inference for linear combination of the regression vector in high dimensional generalized linear regression

Usage

LF(
  X,
  y,
  loading.mat,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  intercept.loading = FALSE,
  beta.init = NULL,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  verbose = FALSE
)
LF(
  X,
  y,
  loading.mat,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  intercept.loading = FALSE,
  beta.init = NULL,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  verbose = FALSE
)

Arguments

`X`	Design matrix, of dimension $n$ x $p$
`y`	Outcome vector, of length $n$
`loading.mat`	Loading matrix, nrow= $p$ , each column corresponds to a loading of interest
`model`	The high dimensional regression model, either `"linear"` or `"logistic"` or `"logistic_alter"`
`intercept`	Should intercept be fitted for the initial estimator (default = `TRUE`)
`intercept.loading`	Should intercept term be included for the loading (default = `FALSE`)
`beta.init`	The initial estimator of the regression vector (default = `NULL`)
`lambda`	The tuning parameter in fitting initial model. If `NULL`, it will be picked by cross-validation. (default = `NULL`)
`mu`	The dual tuning parameter used in the construction of the projection direction. If `NULL` it will be searched automatically. (default = `NULL`)
`prob.filter`	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
`rescale`	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
`verbose`	Should intermediate message(s) be printed. (default = `FALSE`)

Value

`est.plugin.vec`	The vector of plugin(biased) estimators for the linear combination of regression coefficients, length of `ncol(loading.mat)`; each corresponding to a loading of interest
`est.debias.vec`	The vector of bias-corrected estimators for the linear combination of regression coefficients, length of `ncol(loading.mat)`; each corresponding to a loading of interest
`se.vec`	The vector of standard errors of the bias-corrected estimators, length of `ncol(loading.mat)`; each corresponding to a loading of interest
`proj.mat`	The matrix of projection directions; each column corresponding to a loading of interest.

Examples

X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y <- -0.5 + X[, 1] * 0.5 + X[, 2] * 1 + rnorm(100)
loading1 <- c(1, 1, rep(0, 3))
loading2 <- c(-0.5, -1, rep(0, 3))
loading.mat <- cbind(loading1, loading2)
Est <- LF(X, y, loading.mat, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)
X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y <- -0.5 + X[, 1] * 0.5 + X[, 2] * 1 + rnorm(100)
loading1 <- c(1, 1, rep(0, 3))
loading2 <- c(-0.5, -1, rep(0, 3))
loading.mat <- cbind(loading1, loading2)
Est <- LF(X, y, loading.mat, model = "linear")

## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)

Inference for quadratic forms of the regression vector in high dimensional generalized linear regressions

Description

Inference for quadratic forms of the regression vector in high dimensional generalized linear regressions

Usage

QF(
  X,
  y,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  verbose = FALSE
)
QF(
  X,
  y,
  G,
  A = NULL,
  model = c("linear", "logistic", "logistic_alter"),
  intercept = TRUE,
  beta.init = NULL,
  split = TRUE,
  lambda = NULL,
  mu = NULL,
  prob.filter = 0.05,
  rescale = 1.1,
  tau = c(0.25, 0.5, 1),
  verbose = FALSE
)

Arguments

`X`	Design matrix, of dimension $n$ x $p$
`y`	Outcome vector, of length $n$
`G`	The set of indices, `G` in the quadratic form
`A`	The matrix A in the quadratic form, of dimension $\|G\|\times$ $\|G\|$ . If `NULL` A would be set as the $\|G\|\times$ $\|G\|$ submatrix of the population covariance matrix corresponding to the index set `G` (default = `NULL`)
`model`	The high dimensional regression model, either `"linear"` or `"logistic"` or `"logistic_alter"`
`intercept`	Should intercept be fitted for the initial estimator (default = `TRUE`)
`beta.init`	The initial estimator of the regression vector (default = `NULL`)
`split`	Sampling splitting or not for computing the initial estimator. It take effects only when `beta.init = NULL`. (default = `TRUE`)
`lambda`	The tuning parameter in fitting initial model. If `NULL`, it will be picked by cross-validation. (default = `NULL`)
`mu`	The dual tuning parameter used in the construction of the projection direction. If `NULL` it will be searched automatically. (default = `NULL`)
`prob.filter`	The threshold of estimated probabilities for filtering observations in logistic regression. (default = 0.05)
`rescale`	The factor to enlarge the standard error to account for the finite sample bias. (default = 1.1)
`tau`	The enlargement factor for asymptotic variance of the bias-corrected estimator to handle super-efficiency. It allows for a scalar or vector. (default = `c(0.25,0.5,1)`)
`verbose`	Should intermediate message(s) be printed. (default = `FALSE`)

Value

`est.plugin`	The plugin(biased) estimator for the quadratic form of the regression vector restricted to `G`
`est.debias`	The bias-corrected estimator of the quadratic form of the regression vector
`se`	Standard errors of the bias-corrected estimator, length of `tau`; corrsponding to different values of `tau`

Examples

X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y <- X[, 1] * 0.5 + X[, 2] * 1 + rnorm(100)
G <- c(1, 2)
A <- matrix(c(1.5, 0.8, 0.8, 1.5), nrow = 2, ncol = 2)
Est <- QF(X, y, G, A, model = "linear")
## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)
X <- matrix(rnorm(100 * 5), nrow = 100, ncol = 5)
y <- X[, 1] * 0.5 + X[, 2] * 1 + rnorm(100)
G <- c(1, 2)
A <- matrix(c(1.5, 0.8, 0.8, 1.5), nrow = 2, ncol = 2)
Est <- QF(X, y, G, A, model = "linear")
## compute confidence intervals
ci(Est, alpha = 0.05, alternative = "two.sided")

## summary statistics
summary(Est)

Package 'SIHR'

Help Index

Inference for difference of linear combinations of the regression vectors in high dimensional generalized linear regressions

Description

Usage

Arguments

Value

Examples

Inference for weighted quadratic functional of difference of the regression vectors (excluding the intercept term) in high dimensional generalized linear regressions.

Description

Usage

Arguments

Value

Examples

Inference for weighted inner product of the regression vectors in high dimensional generalized linear regressions

Description

Usage

Arguments

Value

Examples

Inference for linear combination of the regression vector in high dimensional generalized linear regression

Description

Usage

Arguments

Value

Examples

Inference for quadratic forms of the regression vector in high dimensional generalized linear regressions

Description

Usage

Arguments

Value

Examples