Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

1 | ```
MD_OLS(type_inference, level_significance, null_value, X, Y, V, W)
``` |

`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 |

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

`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 |

NA

Xiao Guo and Guang Cheng

Moderate-Dimensional Inferences on Quadratic Functionals in Ordinary Least Squares

NA

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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)
``` |

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