T_alpha

A matrix of \(2 ^ 14\) rows and 16 columns. Each column contains
\(2 ^ 14\) Monte Carlo replicates from the distribution of
\(T_{\alpha}\) for a particular value of \(\alpha\), \(\alpha=i/32\),
\(i=0,1,\ldots,15\). The values were generated by first generating a
Brownian Bridge using \(m = 2 ^ 17\) standard normal variates and then
applying Equation (11) from Rackauskas07;textualskedastic.
It can be used to compute empirical approximate \(p\)-values for
implementation of the Rackauskas-Zuokas Test for heteroskedasticity. This
is a time-saving measure because, while <code><a rd-options="" href="/link/rackauskas_zuokas?package=skedastic&version=1.0.0" data-mini-rdoc="skedastic::rackauskas_zuokas">rackauskas_zuokas</a></code>
contains an option for simulating the \(p\)-value directly, this would be
computationally intensive for the authors' recommended \(m\) of
\(2 ^ 17\). Passing the argument <code>pvalmethod = "data"</code> to
<code><a rd-options="" href="/link/rackauskas_zuokas?package=skedastic&version=1.0.0" data-mini-rdoc="skedastic::rackauskas_zuokas">rackauskas_zuokas</a></code> instructs the function to use the
pre-generated values in this data set to compute the empirical approximate
\(p\)-value for the test.

datasets

Implements numerous methods for detecting heteroskedasticity
(sometimes called heteroscedasticity) in the classical linear regression
model. These include a test based on Anscombe (1961)
<https://projecteuclid.org/ euclid.bsmsp/1200512155>, Ramsey's (1969)
BAMSET Test <doi:10.1111/j.2517-6161.1969.tb00796.x>, the tests of Bickel
(1978) <doi:10.1214/aos/1176344124>, Breusch and Pagan (1979)
<doi:10.2307/1911963> with and without the modification
proposed by Koenker (1981) <doi:10.1016/0304-4076(81)90062-2>, Carapeto and
Holt (2003) <doi:10.1080/0266476022000018475>, Cook and Weisberg (1983)
<doi:10.1093/biomet/70.1.1> (including their graphical methods), Diblasi
and Bowman (1997) <doi:10.1016/S0167-7152(96)00115-0>, Dufour, Khalaf,
Bernard, and Genest (2004) <doi:10.1016/j.jeconom.2003.10.024>, Evans and
King (1985) <doi:10.1016/0304-4076(85)90085-5> and Evans and King (1988)
<doi:10.1016/0304-4076(88)90006-1>, Glejser (1969)
<doi:10.1080/01621459.1969.10500976> as formulated by
Mittelhammer, Judge and Miller (2000, ISBN: 0-521-62394-4), Godfrey and
Orme (1999) <doi:10.1080/07474939908800438>, Goldfeld and Quandt
(1965) <doi:10.1080/01621459.1965.10480811>, Harvey (1976)
<doi:10.2307/1913974>, Honda (1989)
<doi:10.1111/j.2517-6161.1989.tb01749.x>, Horn (1981)
<doi:10.1080/03610928108828074>, Li and Yao (2019)
<doi:10.1016/j.ecosta.2018.01.001> with and without the modification of
Bai, Pan, and Yin (2016) <doi:10.1007/s11749-017-0575-x>, Rackauskas and
Zuokas (2007) <doi:10.1007/s10986-007-0018-6>, Simonoff and Tsai (1994)
<doi:10.2307/2986026> with and without the modification of Ferrari,
Cysneiros, and Cribari-Neto (2004) <doi:10.1016/S0378-3758(03)00210-6>,
Szroeter (1978) <doi:10.2307/1913831>, Verbyla (1993)
<doi:10.1111/j.2517-6161.1993.tb01918.x>, White (1980)
<doi:10.2307/1912934>, Wilcox and Keselman (2006)
<doi:10.1080/10629360500107923>, and Zhou, Song, and Thompson (2015)
<doi:10.1002/cjs.11252>. Besides these heteroskedasticity tests, there are
supporting functions that compute the BLUS residuals of Theil (1965)
<doi:10.1080/01621459.1965.10480851>, the conditional two-sided p-values of
Kulinskaya (2008) <arXiv:0810.2124v1>, and probabilities for the
nonparametric trend statistic of Lehmann (1975, ISBN: 0-816-24996-1).
Homoskedasticity refers to the assumption of constant variance that is
imposed on the model errors (disturbances); heteroskedasticity is the
violation of this assumption.

Thomas Farrar

skedastic

Heteroskedasticity Diagnostics for Linear Regression Models

University of the Western Cape 

T_alpha function

An object of class <code>matrix</code> (inherits from <code>array</code>) with 16384 rows and 16 columns.

Format

A matrix of \(2 ^ 14\) rows and 16 columns. Each column contains
\(2 ^ 14\) Monte Carlo replicates from the distribution of
\(T_{\alpha}\) for a particular value of \(\alpha\), \(\alpha=i/32\),
\(i=0,1,\ldots,15\). The values were generated by first generating a
Brownian Bridge using \(m = 2 ^ 17\) standard normal variates and then
applying Equation (11) from Rackauskas07;textualskedastic.
It can be used to compute empirical approximate \(p\)-values for
implementation of the Rackauskas-Zuokas Test for heteroskedasticity. This
is a time-saving measure because, while <code><a rd-options='' href='rackauskas_zuokas'>rackauskas_zuokas</a></code>
contains an option for simulating the \(p\)-value directly, this would be
computationally intensive for the authors' recommended \(m\) of
\(2 ^ 17\). Passing the argument <code>pvalmethod = "data"</code> to
<code><a rd-options='' href='rackauskas_zuokas'>rackauskas_zuokas</a></code> instructs the function to use the
pre-generated values in this data set to compute the empirical approximate
\(p\)-value for the test.

T_alpha: Pseudorandom numbers from Asymptotic Null Distribution of Test Statistic for Method of Rackauskas07;textualskedastic

Description

Usage

Arguments

Format