is a normalization factor to ensure that gp(r)is a PDF for each p.The unknown pa- rameters (can be estimated from the sample via the maximum likelihood estimation (MLE)method.For example,suppose {Xt}is an IID sample.Then T 3=arg max∑n9p(X) t=1 To ensure that p(m)=Cg()∑-o3,H) is asymptotically unbiased,we must let p =p(T)oo as T-oo.However,p must grow more slowly than the sample size T grows to infinity so that the sampling variation of B will not be too large. For the use of Hermite Polynomial series expansions,see (e.g.)Gallant and Tauchen (1996,Econometric Theory),Ait-Sahalia (2002,Econometrica),and Cui,Hong and Li (2020) Question:What are the advantages of nonparametric smoothing methods? They require few assumptions or restrictions on the data generating process.In particular,they do not assume a specific functional form for the function of interest (of course certain smoothness condition such as differentiability is required).They can deliver a consistent estimator for the unknown function,no matter whether it is linear or nonlinear.Thus,nonparametric methods can effectively reduce potential systematic bi- ases due to model misspecification,which is more likely to be encountered for parametric modeling. Question:What are the disadvantages of nonparametric methods? Nonparametric methods require a large data set for reasonable estimation.Fur- thermore,there exists a notorious problem of "curse of dimensionality,"when the function of interest contains multiple explanatory variables.This will be explained below. There exists another notorious "boundary effect"problem for nonparametric esti- mation near the boundary regions of the support.This occurs due to asymmetric coverage of data in the boundary regions. 9is a normalization factor to ensure that gp(x) is a PDF for each p: The unknown pa￾rameters fjg can be estimated from the sample fXtg T t=1 via the maximum likelihood estimation (MLE) method. For example, suppose fXtg is an IID sample. Then ^ = arg max  X T t=1 ln ^gp(Xt) To ensure that g^p(x) = C^￾1 p (x) Xp j=0^ jHj (x) is asymptotically unbiased, we must let p = p(T) ! 1 as T ! 1: However, p must grow more slowly than the sample size T grows to inÖnity so that the sampling variation of ^ will not be too large. For the use of Hermite Polynomial series expansions, see (e.g.) Gallant and Tauchen (1996, Econometric Theory), AÔt-Sahalia (2002, Econometrica), and Cui, Hong and Li (2020). Question: What are the advantages of nonparametric smoothing methods? They require few assumptions or restrictions on the data generating process. In particular, they do not assume a speciÖc functional form for the function of interest (of course certain smoothness condition such as di§erentiability is required). They can deliver a consistent estimator for the unknown function, no matter whether it is linear or nonlinear. Thus, nonparametric methods can e§ectively reduce potential systematic bi￾ases due to model misspeciÖcation, which is more likely to be encountered for parametric modeling. Question: What are the disadvantages of nonparametric methods?  Nonparametric methods require a large data set for reasonable estimation. Fur￾thermore, there exists a notorious problem of ìcurse of dimensionality,îwhen the function of interest contains multiple explanatory variables. This will be explained below.  There exists another notorious ìboundary e§ectîproblem for nonparametric esti￾mation near the boundary regions of the support. This occurs due to asymmetric coverage of data in the boundary regions. 9