我的一般理解是AIC处理模型的拟合优度和模型的复杂性之间的权衡。

$AIC =2k -2ln(L)$

$k$ = 模型中的参数数量

$L$ = 可能性

贝叶斯信息准则BIC与 AIC 密切相关。AIC 对参数数量的惩罚不如 BIC 强。我可以看到这两个在历史上无处不在。但是广义交叉验证（GCV）对我来说是新的。GCV 如何与 BIC 或 AIC 相关联？这些标准是如何一起或单独用于在像脊这样的面板回归中选择惩罚项的？

编辑： 这是一个思考和讨论的例子：

    require(lasso2)
    data(Prostate)
    require(rms)

    ridgefits = ols(lpsa~lcavol+lweight+age+lbph+svi+lcp+gleason+pgg45,
           method="qr", data=Prostate,se.fit = TRUE, x=TRUE, y=TRUE)
    p <- pentrace(ridgefits, seq(0,1,by=.01))
    effective.df(ridgefits,p)
    out <- p$results.all
    par(mfrow=c(3,2))
    plot(out$df, out$aic, col = "blue", type = "l", ylab = "AIC", xlab = "df"  )
    plot(out$df, out$bic, col = "green4", type = "l", ylab = "BIC",  xlab = "df" )
    plot(out$penalty, out$df,  type = "l", col = "red", 
     xlab = expression(paste(lambda)), ylab = "df" )
    plot(out$penalty, out$aic, col = "blue", type = "l",  
      ylab = "AIC", xlab = expression(paste(lambda))  )
    plot(out$penalty, out$bic, col = "green4", type = "l", ylab = "BIC", 
      xlab= expression(paste(lambda))

require(glmnet)
y <- matrix(Prostate$lpsa, ncol = 1)
x <- as.matrix (Prostate[,- length(Prostate)])
cv <- cv.glmnet(x,y,alpha=1,nfolds=10)
plot(cv$lambda, cv$cvm, col = "red", type = "l", 
      ylab = "CVM",   xlab= expression(paste(lambda))