Testing Conditional Independence Restrictions

REFERENCES

• Agresti , A. ( 1990 ). Categorical Data Analysis . New York : John Wiley .
   Google Scholar
• Andrews , D. W. K. ( 1994 ). Empirical process methods in econometrics . In: Handbook of Econometrics . Vol. IV . Engle , R. F. , McFadden , D. L. , eds. Amsterdam : Elsevier Science B.V .
   Google Scholar
• Andrews , D. W. K. ( 1997 ). A conditional Kolmogorov test . Econometrica 65 : 1097 – 1128 .
   Web of Science ®Google Scholar
• Bai , J. ( 1994 ). Weak convergence of the sequential residual empirical process in ARMA models . The Annals of Statistics 22 : 2051 – 2061 .
   Web of Science ®Google Scholar
• Beran , R. , Millar , P. W. ( 1986 ). Confidence sets for a multivariate distribution . The Annals of Statistics 14 : 431 – 443 .
   Web of Science ®Google Scholar
• Bierens , H. J. , Ploberger , W. ( 1997 ). Asymptotic theory of integrated conditional moment tests . Econometrica 65 : 1129 – 1151 .
   Web of Science ®Google Scholar
• Blum , J. R. , Kiefer , J. , Rosenblatt , M. (1961). Distribution free tests of independence based on the sample distribution function. Annals of Mathematical Statistics 32:485–498.
   Google Scholar
• Canepa , A. , Godfrey , L. ( 2007 ). Improvement of the quasi-likelihood ratio test in ARMA models: some results for bootstrap methods . Journal of Times Series Analysis 28 : 434 – 453 .
   Web of Science ®Google Scholar
• Chamberlain , G. ( 1987 ). Asymptotic efficiency in estimation with conditional moment restrictions . Journal of Econometrics 34 : 305 – 334 .
   Web of Science ®Google Scholar
• Chow , Y. S. , Teicher , H. ( 1988 ). Probability Theory. , 2nd ed. Berlin : Springer Texts in Statistics .
   Google Scholar
• Csörgó , S. , Faraway , J. J. ( 1996 ). The exact and asymptotic distribution of Cramér von Mises statistics . Journal of the Royal Statistical Society Series B 58 : 221 – 234 .
   Google Scholar
• Dawid , A. P. ( 1979 ). Conditional independence in statistical theory . Journal of the Royal Statistical Society, Series B. 41 : 1 – 31 .
   Google Scholar
• Delgado , M. ( 1996 ). Testing serial independence using the sample distribution function . Journal of Time Series Analysis 17 : 271 – 287 .
   Google Scholar
• Durbin , J. ( 1973 ). Weak convergence of the sample distribution function when parameters are estimated . The Annals of Statistics 1 : 279 – 290 .
   Web of Science ®Google Scholar
• Fan , Y. , Li , Q. ( 1996 ). Consistent model specification tests: Omitted variables and semiparametric functional forms . Econometrica 64 : 865 – 890 .
   Web of Science ®Google Scholar
• Fernandes , M. , Flores , R. G. ( 2001 ). Tests for Conditional Independence, Markovian Dynamics, and Noncausality. http://www.vwl.uni-mannheim.de/brownbag/flores.pdf. Last accessed 9 September 2013 .
   Google Scholar
• Godfrey , L. ( 1988 ). Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Approaches . ix + pp. 252. Econometric Society Monograph No. 16 . Cambridge : Cambridge University Press, 1988, reprinted 1989 .
   Google Scholar
• Linton , O. , Gozalo , P. ( 1997 ). Conditional Independence Restrictions: Testing and Estimation. Discussion Paper 1140, Cowles Foundation for Research in Economics, Yale Univ .
   Google Scholar
• Härdle , W. , Janssen , P. , Serfling , R. ( 1988 ). Strong uniform consistency rates for estimators of conditional functionals . Annals of Statistics 16 : 1428 – 1449 .
   Web of Science ®Google Scholar
• Härdle , W. , Linton , O. B. ( 1994 ). Applied nonparametric methods . The Handbook of Econometrics . Vol. IV . McFadden , D. F. , Engle III , R. F. , eds. Amsterdam : North Holland .
   Google Scholar
• Han , A. K. ( 1987 ). A non-parametric analysis of transformations . Journal of Econometrics 35 : 191 – 209 .
   Web of Science ®Google Scholar
• Heckman , J. J. , Ichimura , H. , Smith , J. , Todd , P. ( 1998 ). Characterizing Selection Bias Using Experimental Data. Econometrica. Vol. 66, No. 5 (Sep., 1998), pp. 1017–1098 .
   Google Scholar
• Hoeffding , W. ( 1948 ). A non-parametric test of independence . The Annals of Mathematical Statistics 58 : 546 – 557 .
   Google Scholar
• Hong , Y. , White , H. ( 1995 ). Consistent specification testing via nonparametric series regression . Econometrica 63 : 1133 – 1159 .
   Web of Science ®Google Scholar
• Horowitz , J. ( 1992 ). A smoothed maximum score estimator for the binary response model . Econometrica 60 : 505 – 531 .
   Web of Science ®Google Scholar
• Horowitz , J. ( 1997 ). Bootstrap methods in econometrics: Theory and numerical performance . In: Kreps , D. , Wallis , K. W. , eds. Advances in Economics and Econometrics: 7th World Congress . Cambridge : Cambridge University Press , pp. 188 – 222 .
   Google Scholar
• Ichimura , H. ( 1993 ). Semiparametric least squares (SLS) and weighted SLS estimation of single-index models . Journal of Econometrics 58 : 71 – 120 .
   Web of Science ®Google Scholar
• Joag-Dev , K. ( 1984 ). Measures of dependence . In: Krishnaiah , P. R. , Sen , P. K. , eds. Handbook of Statistics . Vol. 4 , pp. 296 – 307 .
   Google Scholar
• Kim , J. , Pollard , D. ( 1990 ). Cube root asymptotics . The Annals of Statistics 18 : 191 – 219 .
   Web of Science ®Google Scholar
• Klein , R. W. , Spady , R. H. ( 1993 ). An efficient semiparametric estimator for discrete choice models . Econometrica 61 : 387 – 421 .
   Web of Science ®Google Scholar
• Koul , H. L. ( 1996 ). Asymptotics of some estimators and sequential residual empiricals in nonlinear time series models . The Annals of Statistics 24 : 380 – 404 .
   Web of Science ®Google Scholar
• Linton , O. B. , Gozalo , P. L. ( 1995 ). A nonparametric test of conditional independence. Cowles Foundation Discussion Paper no 1106 .
   Google Scholar
• Manski , C. F. ( 1975 ). The maximum score estimation of the stochastic utility model of choice . Journal of Econometrics 3 : 205 – 228 .
   Google Scholar
• Manski , C. ( 1994 ). Analog estimation of econometric models . In: Engle III , R. F. , McFadden , D. F. , eds. The Handbook of Econometrics , vol. IV . North Holland .
   Google Scholar
• Nikitin , Y. (1995). Asymptotic Efficiency of Nonparametric Tests . Cambridge : Cambridge University Press.
   Google Scholar
• Pakes , A. , Pollard , D. ( 1989 ). Simulation and the asymptotics of optimization estimators . Econometrica 57 : 1027 – 1057 .
   Web of Science ®Google Scholar
• Phillips , P. C. B. ( 1988 ). Conditional and unconditional statistical independence . Journal of Econometrics 38 : 341 – 348 .
   Web of Science ®Google Scholar
• Pierce , D. A. , Kopecky , K. J. ( 1979 ). Testing goodness of fit for the distribution of errors in regression model . Biometrika 66 : 1 – 5 .
   Web of Science ®Google Scholar
• Powell , J. L. ( 1994 ). Estimation in semiparametric models . In: Engle III , R. F. , McFadden , D. F. , eds. The Handbook of Econometrics . Vol. IV . North Holland .
   Google Scholar
• Robinson , P. M. ( 1991 ). Consistent nonparametric entropy-based testing . Review of Economic Studies 58 : 437 – 453 .
   Web of Science ®Google Scholar
• Rosenbaum , P. R. , Rubin , D. B. ( 1983 ). The central role of the propensity score in observational studies for causal effects . Biometrika 70 : 41 – 55 .
   Web of Science ®Google Scholar
• Sherman , R. P. ( 1993 ). The limiting distribution of the maximum rank correlation estimator . Econometrica 61 : 123 – 138 .
   Web of Science ®Google Scholar
• Shorack , G. R. , Wellner , J. A. ( 1986 ). Empirical Processes with Applications to Statistics . New York : John Wiley .
   Google Scholar
• Skaug , H. J. , Tjøstheim , D. ( 1993 ). A nonparametric test of serial independence based on the empirical distribution function . Biometrika 80 : 591 – 602 .
   Web of Science ®Google Scholar
• Song , K. ( 2009 ). Testing conditional independence via rosenblatt transforms . The Annals of Statistics 37 ( 6B ): 4011 – 4045 .
   Web of Science ®Google Scholar
• Su , L. , White , H. ( 2008 ). A nonparametric Hellinger metric test for conditional independence . Econometric Theory 24 : 829 – 864 .
   Web of Science ®Google Scholar
• Van der Vaart , A. W. , Wellner , J. A. ( 1996 ). Weak Convergence and Empirical Processes . Springer-Verlag : Berlin .
   Google Scholar
• Zheng , J. Z. ( 1997 ). A consistent specification test of independence . Journal of Nonparametric Statistics 7 ( 4 ).
   Google Scholar