What Are Degrees of Freedom

By Shanta Pandey, C. Bright. 2008

411 citations recorded by the source corpus.

Subfields: History, Sociology and Political Science

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Citations in the corpus

Degrees of freedom and model search (2014, background): “Theorem 1 (Zou et al. 2007, Tibshirani & Taylor 2012).”
Regression coefficient and autoregressive order shrinkage and selection via the lasso (2007, methodology): “This motivates us to adapt the BIC-type tuning parameter selector of Zou et al. (2004): BIC= log.σ̂2/+ d̂f log.n/=n, .6/ where σ̂2 =n−1 n0∑ t=q+1 { yt −x′t β̂ − q∑ j=1 φ̂j.yt−j −x′t−jβ̂/ }2 and d̂f is the number of non-zero coefficients of θ̂.”
A Model-Averaging Approach for High-Dimensional Regression (2014, methodology): “These include the lasso method (Tibshirani 1996; Zou, Hastie, and Tibshirani 2007) and its variants (Yuan and Lin 2006; Zou 2006), Bayesian lasso (Park and Casella 2008), least-angle regression (Efron et al. 2004), elastic net (Zou and Hastie 2005), the smoothly clipped absolute deviation penalty…”
Penalized Wavelets: Embedding Wavelets into Semiparametric Regression (2011, background): “Another option for selection of λ is k-fold cross-validation, where k is a small number such as 5 or 10 (e.g. Hastie, Tibshirani and Friedman [37], Section 7.10.1).”
SparseNet: Coordinate Descent With Nonconvex Penalties (2011, methodology): “For a LASSO fit, the df is estimated by the number of nonzero coefficients (Zou, Hastie, and Tibshirani 2007).”
Penalized Model-Based Clustering with Application to Variable Selection (2007, methodology): “Based on the new results on degrees of freedom in the context of L 1 -penalized regression (Efron et al., 2004; Zou et al., 2004), we propose counting only non-zero components of the maximum penalized likelihood estimate when calculating the effective number of parameters in BIC.”
On Model Selection Consistency of Lasso (2006, methodology): “We also make connections to previous theoretical studies and simulations on Lasso (e.g. Donoho et al., 2004; Zou et al., 2004; Tibshirani, 1996).”
Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso (2007, methodology): “…cross-validation, generalized cross-validation (Craven and Wahba 1979; Tibshirani 1996; Fan and Li 2001), AIC, AICc, and BIC (Hurvich and Tsai 1989; Zou, Hastie, and Tibshirani 2004) methods can be used to select the optimal regularization parameter λj after appropriate modification, for example,…”
Very short term irradiance forecasting using the lasso (2015, methodology): “Alternatively, information criteria can be used (see Zou et al., 2007; Tibshirani and Taylor, 2012).100 We use the implementation by Hastie and Efron (2013) for lasso computation.”
Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models (2013, methodology): “In particular, based on lemma 2 by Zou, Hastie, and Tibshirani (2007), the Lasso satisfies this relationship and the same sufficient conditions provided by ZLT for (A4) can be used.”
Electronic medical records for discovery research in rheumatoid arthritis (2010, positive): “We used penalized logistic regression to develop a classification algorithm to predict the probability of having RA (23,24).”
Same data, different conclusions: Radical dispersion in empirical results when independent analysts operationalize and test the same hypothesis (2021, background): “To that end, Delios et al. (2020a) have recruited over 80 analysts to test four hypotheses from the field of strategic management using the same complex longitudinal dataset, assessing both statistical and topic expertise as potential moderators. Further individual-differences that may shape researc”