×

zbMATH — the first resource for mathematics

\(k\)-nearest neighbor estimation of inverse-density-weighted expectations with dependent data. (English) Zbl 1419.62072
Summary: This paper considers the problem of estimating expected values of functions that are inversely weighted by an unknown density using the \(k\)-nearest neighbor (\(k\)-NN) method. It establishes the \(\sqrt T \)-consistency and the asymptotic normality of an estimator that allows for strictly stationary time-series data. The consistency of the Bartlett estimator of the derived asymptotic variance is also established. The proposed estimator is also shown to be asymptotically semiparametric efficient in the independent random sampling scheme. Monte Carlo experiments show that the proposed estimator performs well in finite sample applications.

MSC:
62G07 Density estimation
60G10 Stationary stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1080/07474939708800396 · Zbl 0914.62028
[2] DOI: 10.1214/aoms/1177700079 · Zbl 0132.38905
[3] DOI: 10.1016/j.jeconom.2005.08.005 · Zbl 1418.62138
[4] Boente, Sankhyā: Series A 53 pp 194– (1991)
[5] DOI: 10.1214/aos/1176347631 · Zbl 0703.62025
[6] DOI: 10.1016/j.jeconom.2010.11.006 · Zbl 1441.62792
[7] DOI: 10.1111/j.1467-9892.1987.tb00435.x · Zbl 0615.62115
[8] DOI: 10.1016/0047-259X(88)90154-6 · Zbl 0664.62038
[9] DOI: 10.1016/j.jeconom.2006.11.004 · Zbl 1418.62507
[10] White, Asymptotic Theory for Econometricians (2001)
[11] DOI: 10.1214/aos/1176350487 · Zbl 0643.62027
[12] DOI: 10.1016/S0304-4076(00)00015-4 · Zbl 0970.62082
[13] DOI: 10.2307/2938229 · Zbl 0732.62052
[14] DOI: 10.2307/2998542 · Zbl 1055.62574
[15] DOI: 10.1214/aos/1176348513 · Zbl 0764.62038
[16] DOI: 10.1198/jbes.2009.07333 · Zbl 1214.62031
[17] DOI: 10.1017/S0266466600005636 · Zbl 04537809
[18] DOI: 10.1006/jmva.1993.1002 · Zbl 0764.62076
[19] DOI: 10.1111/j.1468-0262.2006.00655.x · Zbl 1112.62042
[20] Khan, Econometrica 78 pp 2021– (2011)
[21] DOI: 10.1214/aos/1176349163 · Zbl 0790.62037
[22] DOI: 10.1090/S0002-9947-96-01681-9 · Zbl 0863.60032
[23] DOI: 10.1017/S0266466607070132 · Zbl 1237.62047
[24] DOI: 10.1017/S0266466605050103 · Zbl 1072.62081
[25] DOI: 10.1016/S0304-4076(00)00090-7 · Zbl 1130.62336
[26] DOI: 10.1016/j.jeconom.2009.02.005 · Zbl 1431.62188
[27] DOI: 10.1080/07362998708809108 · Zbl 0619.60022
[28] DOI: 10.1017/S0266466609090549 · Zbl 1284.62419
[29] DOI: 10.1214/aoms/1177728190 · Zbl 0073.14602
[30] DOI: 10.1017/S0266466609090628 · Zbl 1183.62063
[31] DOI: 10.1073/pnas.42.1.43 · Zbl 0070.13804
[32] Jacho-Chávez, Economics Bulletin 3 pp 1– (2008)
[33] DOI: 10.1080/10485259508832632 · Zbl 0873.62043
[34] Ibragimov, Independent and stationary sequences of random variables (1971)
[35] DOI: 10.2307/1911033 · Zbl 0651.62107
[36] DOI: 10.1111/1468-0262.00363 · Zbl 1141.62360
[37] DOI: 10.1007/s10463-007-0152-2 · Zbl 1314.60054
[38] DOI: 10.1111/j.1468-0262.2005.00597.x · Zbl 1152.91729
[39] Rao, Semimartingales and their Statistical Inference (1999) · Zbl 0960.62090
[40] DOI: 10.1111/1467-937X.00044 · Zbl 0908.90059
[41] DOI: 10.2307/2171777 · Zbl 0840.90044
[42] DOI: 10.2307/1913237 · Zbl 0613.62109
[43] DOI: 10.2307/2297912 · Zbl 0815.62063
[44] Härdle, Journal of the American Statistical Association 84 pp 986– (1989)
[45] DOI: 10.2307/2951575 · Zbl 0746.62088
[46] DOI: 10.2307/1913610 · Zbl 0658.62139
[47] DOI: 10.1016/j.jeconom.2004.08.005 · Zbl 1334.62080
[48] DOI: 10.1017/CBO9780511614491.024
[49] Hall, Martingale Limit Theory and Its Application (1980) · Zbl 0462.60045
[50] Newey, Handbook of Econometrics IV pp 2111– (1994)
[51] DOI: 10.1016/j.csda.2008.05.016 · Zbl 05689618
[52] DOI: 10.1016/S0304-4076(97)00011-0 · Zbl 0873.62049
[53] DOI: 10.2307/2297982 · Zbl 0805.62097
[54] DOI: 10.2307/2938351 · Zbl 0728.62107
[55] DOI: 10.1017/S0266466600012767 · Zbl 04508527
[56] DOI: 10.1007/BF00532611 · Zbl 0288.60034
[57] DOI: 10.1016/0304-4149(94)00063-Y · Zbl 0817.62027
[58] McFadden, Trade, Theory and Econometrics 15 pp 253– (1999)
[59] DOI: 10.1103/PhysRevD.10.526
[60] Wheeden, Measure and Integral (1977)
[61] DOI: 10.1016/0047-259X(79)90065-4 · Zbl 0406.62023
[62] Bradley, Introduction to Strong Mixing Conditions 1 (2007)
[63] DOI: 10.1007/BF02880000 · Zbl 0916.62039
[64] DOI: 10.1006/jmva.1995.1045 · Zbl 0898.62043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.