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Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. (English) Zbl 1431.62646
Summary: We consider nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. Most of the existing works on asymptotic distributions of a nonparametric/semiparametric estimator or a test statistic are based on some deterministic smoothing parameters, while in practice it is important to use data-driven methods to select the smoothing parameters. In this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters. We also allow for general weakly dependent data.

MSC:
62P20 Applications of statistics to economics
62G05 Nonparametric estimation
62G07 Density estimation
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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[1] Bai, J., Weak convergence of sequential empirical processes of residuals in ARMA models, Annals of statistics, 22, 2051-2061, (1994) · Zbl 0826.60016
[2] Bai, J., Testing for parameter consistency in linear regressions: an empirical distribution function approach, Econometrica, 64, 597-622, (1996) · Zbl 0844.62032
[3] Billingsley, P., Convergence of probability measures, (1968), Wiley New York · Zbl 0172.21201
[4] Billingsley, P., Convergence of probability measures, (1999), Wiley New York · Zbl 0172.21201
[5] Cai, Z., Regression quantile for time series data, Econometric theory, 18, 169-192, (2002) · Zbl 1181.62124
[6] Chen, X.; Fan, Y., Consistent model specification test in semiparametric and nonparametric models for econometric time series, Journal of econometrics, 91, 373-401, (1999) · Zbl 1041.62506
[7] Chen, X.; Shen, X., Sieve extremum estimates for weakly dependent data, Econometrica, 66, 289-314, (1998) · Zbl 1055.62544
[8] Fan, Y.; Li, Q., Consistent model specification tests: omitted variables and semiparametric functional forms, Econometrica, 64, 865-890, (1996) · Zbl 0854.62038
[9] Fan, Y.; Li, Q., Root-N-consistent estimation of partially linear time series models, Journal of nonparametric statistics, 11, 251-269, (1999) · Zbl 0953.62094
[10] Fan, Y.; Li, Q., Central limit theorem for degenerate U-statistics of absolute regular processes with applications to model specification testing, Journal of nonparametric statistics, 10, 245-271, (1999) · Zbl 0974.62044
[11] Hahn, J., On the role of the propensity score in efficient semiparametric estimation, Econometrica, 66, 315-331, (1998) · Zbl 1055.62572
[12] Hall, P.; Li, Q.; Racine, J., Nonparametric estimation of regression functions in the presence of irrelevant regressors, Review of economic and statistics, 89, 784-789, (2007)
[13] Hall, P.; Racine, J.; Li, Q., Cross-validation and the estimation of conditional probability densities, Journal of the American statistical association, 99, 1015-1026, (2004) · Zbl 1055.62035
[14] Hall, P.; Wolff, R.C.L.; Yao, Q., Methods for estimating a conditional distribution function, Journal of the American statistical association, 94, 154-163, (1999) · Zbl 1072.62558
[15] Härdle, W.; Hall, P.; Marron, J.S., How far are automatically chosen regression smoothing parameters from their optimum?, Journal of American statistical association, 83, 86-99, (1988) · Zbl 0644.62048
[16] Härdle, W.; Hall, P.; Marron, J.S., Regression smoothing parameters that are not far from their optimum, Journal of American statistical association, 87, 227-233, (1992) · Zbl 0850.62352
[17] Härdle, W.; Marron, J.S., Optimal bandwidth selection in nonparametric regression function estimation, The annals of statistics, 13, 1465-1481, (1985) · Zbl 0594.62043
[18] Horowitz, J., A smoothed maximum score estimator for the binary response model, Econometrica, 60, 505-531, (1992) · Zbl 0761.62166
[19] Hsiao, C.; Li, Q.; Racine, J., A consistent model specification test with mixed categorical and continuous data, Journal of econometrics, 140, 802-826, (2007) · Zbl 1247.62126
[20] Ichimura, H., Semiparametric least squares (SLS) and weighted SLS estimation of single-index models, Journal of econometrics, 58, 71-120, (1993) · Zbl 0816.62079
[21] Ichimura, H., 2000. Asymptotic distribution of nonparametric and semiparametric estimators with data dependent smoothing parameters. Unpublished manuscript
[22] Lavergne, P.; Vuong, Q., Nonparametric significance test, Econometric theory, 16, 576-601, (2000) · Zbl 0968.62047
[23] Li, K.C., Asymptotic optimality for \(C_p\), \(C_L\), cross-validation and generalized cross-validation: discrete index set, Annals of statistics, 15, 958-975, (1987) · Zbl 0653.62037
[24] Li, Q., Consistent model specification tests for time series econometric models, Journal of econometrics, 92, 101-147, (1999) · Zbl 0929.62054
[25] Li, Q.; Racine, J., Nonparametric estimation of conditional CDF and quantile functions with mixed categorical and continuous data, Journal of business and economic statistics, 26, 423-434, (2008)
[26] Mammen, E., When does bootstrap work? asymptotic results and simulations, (1992), Springer-Verlag New York · Zbl 0760.62038
[27] Newey, W.K., Convergence rates and asymptotic normality for series estimators, Journal of econometrics, 79, 147-168, (1997) · Zbl 0873.62049
[28] Ossiander, M., A central limit theorem under metric entropy with \(L_2\) bracketing, Annals of probability, 15, 186-211, (1987)
[29] Pollard, D., Convergence of stochastic process, (1984), Springer-Verlag New York
[30] Pollard, D., Empirical processes: theory and applications, (1990), IMS Hayward, California · Zbl 0741.60001
[31] Powell, J.; Stock, J.H.; Stoker, T.M., Semiparametric estimation of weighted average derivatives, Econometrica, 57, 1403-1430, (1989) · Zbl 0683.62070
[32] Racine, J.; Li, Q., Nonparametric estimation of regression functions with both categorical and continuous data, Journal of econometrics, 119, 99-130, (2004) · Zbl 1337.62062
[33] Robinson, P., Root-N consistent semiparametric regression, Econometrica, 56, 931-954, (1988) · Zbl 0647.62100
[34] Sherman, R., Maximal inequalities for degenerate u-processes with applications to optimization estimators, Annals of statistics, 22, 239-459, (1994) · Zbl 0798.60021
[35] Sherman, R., U-processes in the analysis of a generalized semiparametric regression estimator, Econometric theory, 10, 372-395, (1994)
[36] Stone, C., An asymptotically optimal window selection rule for kernel density estimates, Annals of statistics, 12, 1285-1297, (1984) · Zbl 0599.62052
[37] Volkonskii, V.A.; Rozanov, Y.A., Some limit theorems for random functions, Theory of probability and applications, 4, 178-197, (1959) · Zbl 0092.33502
[38] Zheng, J.X., A consistent test of functional form via nonparametric estimation techniques, Journal of econometrics, 75, 236-289, (1996) · Zbl 0865.62030
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