critical.value {hrt} | R Documentation |
Critical Values for Heteroskedasticity Robust Testing
Description
This function provides an implementation of
Algorithm 3 in Pötscher and Preinerstorfer (2021), based on
Algorithm 1 (if q = 1
) or Algorithm 2
(if q > 1
) in the same reference as the auxiliary algorithm \mathsf{A}
.
Which of the two algorithms is used is automatically
determined as a function of q
, the number of rows of R
.
The user is referred to Pötscher and Preinerstorfer (2021) for definitions, a detailed description of the problems solved by the algorithms, and for a detailed description of the algorithms themselves.
Most of the input parameters to critical.value
are actually used
in the auxiliary Algorithm 1 or 2, respectively.
Algorithm 1 is based on the function
davies
from the package CompQuadForm. The parameters
lim
and acc
for davies
can be supplemented by the user.
Algorithms 1 and 2 are implemented using the function constrOptim
from stats in Stages 1 and 2; this function
is used with default parameters, but control parameters can be supplied by the user.
After determining a critical value for a given testing
problem via the function critical.value
, it is recommended that: (i) the user
applies the function size
to compute the size of the test corresponding to the critical value obtained;
and (ii) to check whether the size obtained does coincide with (or is close to) the targeted level of
significance (that is alpha
). If (ii) is not the case, this is an indication
of numerical issues, which potentially can be avoided by changing the input parameters
responsible for the accuracy of the computations.
Usage
critical.value(alpha, R, X, hcmethod, restr.cov, Mp, M1, M2,
N0 = NULL, N1 = NULL, N2 = NULL, tol = 1e-08,
control.1 = list("reltol" = 1e-02, "maxit" = dim(X)[1]*20),
control.2 = list("reltol" = 1e-03, "maxit" = dim(X)[1]*30),
cores = 1, lower = 0, eps.close = .0001, lim = 30000, acc = 0.001,
size.tol = .001, maxit = 25, as.tol = 1e-08)
Arguments
alpha |
Significance level. A real number in the interval |
R |
The restriction matrix. |
X |
The design matrix |
hcmethod |
Integer in [-1, 4]. Determines the method applied in the construction of the covariance estimator
used in the test statistic. The value -1 corresponds to unadjusted (i.e., classical) F statistic without df adjustment; the value 0
corresponds to the HC0 estimator; ...; the value 4 corresponds to the HC4 estimator. Note that in case |
restr.cov |
TRUE or FALSE. Covariance matrix estimator based on null-restricted (TRUE) or unrestricted (FALSE) residuals. |
Mp |
This input is used in Algorithm 1 or 2, respectively.
|
M1 |
This input is used in Algorithm 1 or 2, respectively. A positive integer
(should be chosen large, e.g., 500; but the feasibility depends on the dimension of |
M2 |
This input is used in Algorithm 1 or 2, respectively.
A positive integer. Corresponds to |
N0 |
This input is needed in Algorithm 2.
Only used in case |
N1 |
This input is needed in Algorithm 2.
Only used in case |
N2 |
This input is needed in Algorithm 2.
Only used in case |
tol |
This input is used in Algorithm 1 or 2, respectively. (Small) positive real number. Tolerance parameter used in checking invertibility of the covariance matrix in the test statistic. Default is 1e-08. |
control.1 |
This input is used in Algorithm 1 or 2, respectively.
Control parameters passed to the |
control.2 |
This input is used in Algorithm 1 or 2, respectively.
Control parameters passed to the |
cores |
The number of CPU cores used in the (parallelized) computations. Default is 1. Parallelized computation is enabled only if the compiler used to build hrt supports OpenMP. |
lower |
Number in |
eps.close |
(Small) positive real number. This determines the size of the dominant entry in the choice of the
initial values as discussed in the description of the input |
lim |
This input is needed in Algorithm 1. Only used in case |
acc |
This input is needed in Algorithm 1. Only used in case |
size.tol |
(Small) positive real number. |
maxit |
Maximum number of iterations in the while loop of Algorithm 3. Default is 25. |
as.tol |
(Small) positive real number. Tolerance parameter used in checking rank
conditions for verifying Assumptions 1, 2, and for checking a non-constancy condition
on the test statistic in case |
Details
For details see the relevant sections in Pötscher and Preinerstorfer (2021), in particular the description of Algorithms 1 and 2 in the Appendix.
Value
The output of critical.value
is the following:
critical.value |
The critical value obtained by Algorithm 3. |
approximate.size |
The approximate size of the test based on the returned critical value. |
iter |
The number of iterations performed. If |
References
Pötscher, B. M. and Preinerstorfer, D. (2021). Valid Heteroskedasticity Robust Testing. <arXiv:2104.12597>
See Also
Examples
#critical value for the classical (uncorrected) F-test in a location model
#with unrestricted heteroskedasticity
#it is known that (in this very special case) the conventional critical value
#C <- qt(.975, df = 9)^2
#is size-controlling (thus the resulting size should be 5% (approximately))
R <- matrix(1, nrow = 1)
X <- matrix(rep(1, length = 10), nrow = 10, ncol = 1)
hcmethod <- -1
restr.cov <- FALSE
Mp <- 1000
M1 <- 5
M2 <- 1
#here, the parameters are chosen such that the run-time is low
#to guarantee a high accuracy level in the computation,
#Mp, M1 and M2 should be chosen much higher
critical.value(alpha = .05, R, X, hcmethod, restr.cov, Mp, M1, M2)