diblasi_bowman

This function implements the nonparametric test of
 Diblasi97;textualskedastic for testing for heteroskedasticity
 in a linear regression model.

Implements numerous methods for testing for, modelling, and
correcting for heteroskedasticity in the classical linear regression
model. The most novel contribution of the
package is found in the functions that implement the as-yet-unpublished
auxiliary linear variance models and auxiliary nonlinear variance
models that are designed to estimate error variances in a heteroskedastic
linear regression model. These models follow principles of statistical
learning described in Hastie (2009) <doi:10.1007/978-0-387-21606-5>.
The nonlinear version of the model is estimated using quasi-likelihood
methods as described in Seber and Wild (2003, ISBN: 0-471-47135-6).
Bootstrap methods for approximate confidence intervals for error variances
are implemented as described in Efron and Tibshirani
(1993, ISBN: 978-1-4899-4541-9), including also the expansion technique
described in Hesterberg (2014) <doi:10.1080/00031305.2015.1089789>. The
wild bootstrap employed here follows the description in Davidson and
Flachaire (2008) <doi:10.1016/j.jeconom.2008.08.003>. Tuning of
hyper-parameters makes use of a golden section search function that is
modelled after the MATLAB function of Zarnowiec (2022)
<https://www.mathworks.com/matlabcentral/fileexchange/25919-golden-section-method-algorithm>.
A methodological description of the algorithm can be found in Fox (2021,
ISBN: 978-1-003-00957-3).
There are 25 different functions that implement hypothesis tests for
heteroskedasticity. 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>, Harrison and McCabe (1979)
<doi:10.1080/01621459.1979.10482544>, 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>, Yuce (2008)
<https://dergipark.org.tr/en/pub/iuekois/issue/8989/112070>, 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). For handling heteroskedasticity, in addition to the
new auxiliary variance model methods, there is a function
to implement various existing Heteroskedasticity-Consistent Covariance
Matrix Estimators from the literature, such as those of White (1980)
<doi:10.2307/1912934>, MacKinnon and White (1985)
<doi:10.1016/0304-4076(85)90158-7>, Cribari-Neto (2004)
<doi:10.1016/S0167-9473(02)00366-3>, Cribari-Neto et al. (2007)
<doi:10.1080/03610920601126589>, Cribari-Neto and da Silva (2011)
<doi:10.1007/s10182-010-0141-2>, Aftab and Chang (2016)
<doi:10.18187/pjsor.v12i2.983>, and Li et al. (2017)
<doi:10.1080/00949655.2016.1198906>.

Thomas Farrar

skedastic

Handling Heteroskedasticity in the Linear Regression Model

University of the Western Cape 

diblasi_bowman function

<dl><dt>mainlm</dt>
<dd>Either an object of <code><a href="/link/class?package=skedastic&version=2.0.2" data-mini-rdoc="skedastic::class">class</a></code> <code>"lm"</code>
(e.g., generated by <code><a href="/link/lm?package=skedastic&version=2.0.2" data-mini-rdoc="skedastic::lm">lm</a></code>), or
a list of two objects: a response vector and a design matrix. The objects
are assumed to be in that order, unless they are given the names
<code>"X"</code> and <code>"y"</code> to distinguish them. The design matrix passed
in a list must begin with a column of ones if an intercept is to be
included in the linear model. The design matrix passed in a list should
not contain factors, as all columns are treated 'as is'. For tests that
use ordinary least squares residuals, one can also pass a vector of
residuals in the list, which should either be the third object or be
named <code>"e"</code>.</dd>
<dt>distmethod</dt>
<dd>A character specifying the method by which to estimate
the \(p\)-values, either <code>"moment.match"</code> or <code>"bootstrap"</code>.</dd>
<dt>H</dt>
<dd>A hyperparameter denoting the bandwidth matrix in the kernel
function used for weights in nonparametric smoothing. If a double of
length 1 (the default), <code>H</code> is set to \(h I_{p^\prime}\) where
\(h\) is the scalar bandwidth value entered and \(I_{p^\prime}\)
is the \(p^\prime \times p^\prime\) identity matrix (where
\(p^\prime\) is the number of columns in the \(X\) matrix, excluding
an intercept if present). If a double of length \(p^\prime\), <code>H</code>
is set to \(diag(h)\) where \(h\) is the bandwidth vector entered.
If <code>H</code> is a \(p^\prime\times p^\prime\) matrix it is used as is.
Any other dimensionality of <code>H</code> results in an error.</dd>
<dt>ignorecov</dt>
<dd>A logical. If <code>TRUE</code> (the default), the
variance-covariance matrix of \(s\) is assumed to be diagonal. (This
assumption is, strictly speaking, invalid, but usually yields a reasonable
approximation. Computation time is
prohibitive for large sample sizes if set to <code>FALSE</code>).</dd>
<dt>B</dt>
<dd>An integer specifying the number of nonparametric bootstrap
replications to be used, if <code>distmethod="bootstrap"</code>.</dd>
<dt>seed</dt>
<dd>An integer specifying a seed to pass to
<code><a href="/link/set.seed?package=skedastic&version=2.0.2" data-mini-rdoc="skedastic::set.seed">set.seed</a></code> for random number generation. This allows
reproducibility of bootstrap results. The value <code>NA</code>
results in not setting a seed.</dd>
<dt>statonly</dt>
<dd>A logical. If <code>TRUE</code>, only the test statistic value
is returned, instead of an object of <code><a href="/link/class?package=skedastic&version=2.0.2" data-mini-rdoc="skedastic::class">class</a></code>
<code>"htest"</code>. Defaults to <code>FALSE</code>.</dd></dl>

Arguments

Diblasi and Bowman's Test for Heteroskedasticity in a Linear Regression Model — diblasi_bowman

<dl>

<dt>mainlm</dt>
<dd>Either an object of <code><a href='https://rdrr.io/r/base/class.html'>class</a></code> <code>"lm"</code>
(e.g., generated by <code><a href='https://rdrr.io/r/stats/lm.html'>lm</a></code>), or
a list of two objects: a response vector and a design matrix. The objects
are assumed to be in that order, unless they are given the names
<code>"X"</code> and <code>"y"</code> to distinguish them. The design matrix passed
in a list must begin with a column of ones if an intercept is to be
included in the linear model. The design matrix passed in a list should
not contain factors, as all columns are treated 'as is'. For tests that
use ordinary least squares residuals, one can also pass a vector of
residuals in the list, which should either be the third object or be
named <code>"e"</code>.</dd>


<dt>distmethod</dt>
<dd>A character specifying the method by which to estimate
the \(p\)-values, either <code>"moment.match"</code> or <code>"bootstrap"</code>.</dd>


<dt>H</dt>
<dd>A hyperparameter denoting the bandwidth matrix in the kernel
function used for weights in nonparametric smoothing. If a double of
length 1 (the default), <code>H</code> is set to \(h I_{p^\prime}\) where
\(h\) is the scalar bandwidth value entered and \(I_{p^\prime}\)
is the \(p^\prime \times p^\prime\) identity matrix (where
\(p^\prime\) is the number of columns in the \(X\) matrix, excluding
an intercept if present). If a double of length \(p^\prime\), <code>H</code>
is set to \(diag(h)\) where \(h\) is the bandwidth vector entered.
If <code>H</code> is a \(p^\prime\times p^\prime\) matrix it is used as is.
Any other dimensionality of <code>H</code> results in an error.</dd>


<dt>ignorecov</dt>
<dd>A logical. If <code>TRUE</code> (the default), the
variance-covariance matrix of \(s\) is assumed to be diagonal. (This
assumption is, strictly speaking, invalid, but usually yields a reasonable
approximation. Computation time is
prohibitive for large sample sizes if set to <code>FALSE</code>).</dd>


<dt>B</dt>
<dd>An integer specifying the number of nonparametric bootstrap
replications to be used, if <code>distmethod="bootstrap"</code>.</dd>


<dt>seed</dt>
<dd>An integer specifying a seed to pass to
<code><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></code> for random number generation. This allows
reproducibility of bootstrap results. The value <code>NA</code>
results in not setting a seed.</dd>


<dt>statonly</dt>
<dd>A logical. If <code>TRUE</code>, only the test statistic value
is returned, instead of an object of <code><a href='https://rdrr.io/r/base/class.html'>class</a></code>
<code>"htest"</code>. Defaults to <code>FALSE</code>.</dd>

</dl>

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diblasi_bowman: Diblasi and Bowman's Test for Heteroskedasticity in a Linear Regression Model

Description

Usage

Value

Arguments

Details

References

Examples