Testing Parametric versus Semiparametric Modeling in Generalized Linear Models

Semiparametric Inference in Generalized Mixed Effects Models

“…First note that the covariances between the {m.t dj / −m.t dj /} are asymptotically negligible for different observations of t dj . Given the maximum likelihood estimator and the resulting asymptotic expansions indicated (up to first order) in corollary 1 and 2, the proof of corollary 3 can be derived from the proof in Härdle et al (1998). They considered the more general quasilikelihood so our case is even easier and we can follow line by line their proof.…”

“…, and denote the log-likelihood estimators for this model by .γ c ,ũ,δ/. Following the arguments of Härdle et al (1998), a direct comparison ofm.T/ withc + T Tγ may be misleading, becausem.·/ has a smoothing bias which is typically non-negligible. To avoid this effect, we add a bias tõ c + T Tγ that will compensate for the bias ofm.T/, procedure B: A most traditional testing approach would be based on the likelihood ratio.…”

“…In semiparametrics, these kinds of test statistic are quite popular. On the one hand they imitate the likelihood ratio in the semiparametric world; see Härdle et al (1998) and Müller (2001).…”

“…For a general discussion of the validation of bootstrap methods see Shao and Tu (1995), page 76. The proof follows by using the same process as in Härdle et al (1998) (see the proof of their theorem 2), taking into account the asymptotics results above and that |Y Å dj | has a bounded conditional Laplace transform in a neighbourhood of 0. For more details see Mammen and van de Geer (1997), section 5, who studied the asymptotic distribution of the parametric component of a regression model using the wild bootstrap.…”

Partially Linear Additive Models with Unknown Link Functions

“…For example, Engle et al (1986) and Heckman (1986) studied estimation using smoothing splines to estimate the nonparametric part, and Robinson (1988) and Speckman (1988) considered the same problem with kernel smoothing, while Chen (1988) studied estimation based on piecewise polynomial. Härdle et al (2000) gave a comprehensive review for PLM. When the link function in partially linear additive models (PLAMs) is the identity, we have partially additive models (Li, 2000;Liu et al, 2011).…”