MD_OLS {MDOLS}

R Package for Quadratic Functional of Moderate-Dimensional OLS

Description

This package conduct statistical inference for quadratic functional of the moderate-dimensional linear model in Guo and Cheng (2020).

Usage

MD_OLS(type_inference, level_significance, null_value, X, Y, V, W)

Arguments

type_inference

the type of inference: 0-confidence interval for quadratic functional; 1-signal detection; 2-FVE; 3-error variance; 4-equality of two parameters; 5-co-heritability; 6-confidence ball; 7-inference for quadratic functional

level_significance

nominal significance level, default value is 0.05

null_value

the null value for hypothesis testing

X

n by p matrix of predictor for model 1

Y

n by 1 vector of response for model 1

V

n by p matrix of predictor for model 2

W

n by 1 vector of response for model 2

Details

"type_inference", "X" and "Y" are required inputs.

Value

eta_hat_proposed

proposed estimator for eta

rho_hat_proposed

proposed estimator for rho

var_proposed_test

proposed estimator for the variance part

var_convnetional_test

conventional estimator for the variance part

CI_proposed_method_lower

lower bound of the confidence interval

CI_proposed_method_upper

upper bound of the confidence interval

test_stat_proposed

proposed test statistic

test_stat_conventional

conventional test statistic

p_value_proposed

p-value of the proposed test

p_value_conventional

p-value of the conventional test

norm_beta_estimated

estimated norm of beta

norm_gamma_estimated

estimated norm of gamma

co_herit_hat_proposed

proposed estimate of co-heritability

co_herit_hat_conventional

conventional estimate of co-heritability

sigma_star_hat_square

sigma star hat square

ID_correctly_covered_by_confidence_ball_two_sided

indicator that the parameter is covered by the two-sided confidence ball

ID_correctly_covered_by_confidence_ball_one_sided

indicator that the parameter is covered by the one-sided confidence ball

Note

NA

Author(s)

Xiao Guo and Guang Cheng

References

Moderate-Dimensional Inferences on Quadratic Functionals in Ordinary Least Squares

See Also

NA

Examples

type<-4
level<-0.05
null_value<-0
n_1 <- 500
p <-100
n_2 <- 600
X<-matrix(rnorm(n_1*p),nrow=n_1,ncol=p)
eps<-matrix(rnorm(n_1),nrow=n_1,ncol=1)
Y <- X[,1] + eps
V<-matrix(rnorm(n_2*p),nrow=n_2,ncol=p)
delta<-matrix(rnorm(n_2),nrow=n_2,ncol=1)
W<-V[,1] + delta
MD_OLS(type, level, null_value, X, Y,V,W)