skedastic: Handling Heteroskedasticity in the 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 The most novel contribution of the package is found in the functions that implement the as-yet-unpublished auxiliary linear variance models and auxiliary nonlinear variance models that are designed to estimate error variances in a heteroskedastic linear regression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>.

install.packages("skedastic")

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