Studentization in Edgeworth expansions for estimates of semiparametric index models

Nishiyama, Yoshihiko; Robinson, Peter

doi:10.1017/cbo9781139175203.009

Cited by 6 publications

(16 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is no results on higher order refinement for semiparametric conditional moment models containing functions of endogenous variables yet. There are some second order theories for semiparametric models without nonparametric endogeneity, such as Robinson (1995), Linton (1995), Nishiyama and Robinson (2000), Nishiyama and Robinson (2001) and Nishiyama and Robinson (2005), to name a few. We hope to study the higher order refinement of the weighted bootstrap procedure in another paper.…”

Section: Resultsmentioning

confidence: 99%

Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

Chen

Pouzo

2008

112

View full text Add to dashboard Cite

For semi/nonparametric conditional moment models containing unknown parametric components (θ) and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (θ, h) and derive the large sample properties. This paper greatly extends their results by establishing the followings: (1) The penalized SMD (PSMD) estimator (θ,ĥ) can simultaneously achieve root-n asymptotic normality ofθ and nonparametric optimal convergence rate ofĥ, allowing for models with possibly nonsmooth residuals and/or noncompact infinite dimensional parameter spaces. (2) A simple weighted bootstrap procedure can consistently estimate the limiting distribution of the PSMDθ. (3) The semiparametric efficiency bound results of Ai and Chen (2003) remain valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bounds. (4) The profiled optimally weighted PSMD criterion is asymptotically Chi-square distributed, which implies an alternative consistent estimation of confidence region of the efficient PSMD estimator of θ. All the theoretical results are stated in terms of any consistent nonparametric estimator of conditional mean functions. We illustrate our general theories using a partially linear quantile instrumental variables regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile Engel curves with endogenous total expenditure. JEL classification: C14; C22

show abstract

Section: Resultsmentioning

confidence: 99%

Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

Chen

Pouzo

2008

112

View full text Add to dashboard Cite

show abstract

“…Assumptions 3(a) and 3(b) are natural and in agreement with those imposed in Powell and Stoker (1996) and Nishiyama andRobinson (2000, 2005), while Assumption 3(c) is slightly stronger than the analogue restriction imposed in those papers. Assumption 3(d) is used to ensure that the higher-order mean squared expansion is valid up to the order needed.…”

Section: Mse Expansion and "Optimal" Bandwidth Selectorsmentioning

confidence: 54%

“…For the case of the density-weighted average derivative there exist three bandwidth selectors of the plug-in variety. Härdle and Tsybakov (1993) and Powell and Stoker (1996) construct a bandwidth selector based on the minimization of the mean squared error of^ n , while Nishiyama andRobinson (2000, 2005) construct two plug-in bandwidth selectors based on an Edgeworth expansion for the one-sided and two-sided corresponding test statistics. See Ichimura and Todd (2007, Section 6.3) for a general discussion on these results and their implementation.…”

Section: Mse Expansion and "Optimal" Bandwidth Selectorsmentioning

confidence: 99%

“…This new bandwidth selector may be compared to the two competing plug-in bandwidth selectors available in the literature, proposed by Powell and Stoker (1996) and Nishiyama and Robinson (2005), and given by…”

Section: Mse Expansion and "Optimal" Bandwidth Selectorsmentioning

confidence: 99%

“…Powell, Stock, and Stoker (1989) study the …rst-order large sample properties of this estimator and provide su¢ cient (but not necessary) conditions for root-n consistency and asymptotic normality. Nishiyama and Robinson (2000, 2001, 2005) study its second-order large sample properties by deriving valid Edgeworth expansions for this estimator (see also Robinson (1995)), while Härdle and Tsybakov (1993) and Powell and Stoker (1996) provide second-order mean squared error expansions for this estimator (see also Newey, Hsieh, and Robins (2004)). Both types of higher-order expansions provide simple plug-in bandwidth selectors targeting di¤erent properties of this estimator, and are compatible with the classical large sample theory available in the literature.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Data-Driven Inference for Density-Weighted Average Derivatives

Cattaneo

Crump

Jansson

2010

Journal of the American Statistical Association

View full text Add to dashboard Cite

Abstract. This paper presents a new data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for densityweighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidthdependent robust inference procedure proposed by Cattaneo, Crump, and Jansson (2009) is coupled with this new data-driven bandwidth selector. The resulting robust data-driven con…-dence intervals compare favorably to the alternative procedures available in the literature.

show abstract

Minimum normal approximation error bandwidth selection for averaged derivatives

Nishiyama

2004

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

Studentization in Edgeworth expansions for estimates of semiparametric index models

Cited by 6 publications

References 26 publications

Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

Robust Data-Driven Inference for Density-Weighted Average Derivatives

Minimum normal approximation error bandwidth selection for averaged derivatives

Contact Info

Product

Resources

About