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Nonparametric Econometrics: Theory and Practice

By Qi Li and Jeffrey Scott Racine

Abstract

Until recently, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data--nominal and ordinal--in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types--continuous, nominal, and ordinal--within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables.nonparametric, semiparametric, statistics, econometrics, estimators, analysis

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  1. 1.10 Uniform Rates
  2. 1.12 Proof of Theorem 1.4 (Uniform Almost Sure Convergence) The
  3. 24 1. DENSITY ESTIMATION (see Exercise 1.9) E[CVF(h)] = � F(1 − F)dx + 1 � F(1 − F)dx − C1hn−1 + C2h4 + o
  4. Bandwidth Selection: Cross-Validation Methods
  5. Exercise 1.12 shows that the leading term of CVf(h1,...,hq) is given by (ignoring a term unrelated to the hs’s) q CVf0(h1,...,hq) = � � � Bs(x)h2 s �2 dx + κq , (1.39) nh1 ...hq s=1 where Bs(x)
  6. Figure 1.2 plots the second, fourth, and sixth order Epanechnikov kernels defined above. Clearly, for ν > 2, the kernels indeed assign negative weights which can result
  7. h2 . s s=1 x∈S Using the results of (1.36) and (1.37), we can establish the following uniform MSE rate.
  8. modifications
  9. n h i=1 −∞ where G(x) = � x k(v)dv is a CDF (which follows directly because k( ) −∞ · is a PDF; see (1.10)). The next theorem provides the MSE of F ˆ(x).
  10. Theorem 1.5. Assuming that f(x) is twice differentiable with bounded second derivatives, then we have q

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