Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data

References

• Abramson I.S. (1982), ‘On Bandwidth Variation in Kernel Estimates – A Square Root Law’, Annals of Statistics, 10, 1217–1223. doi: 10.1214/aos/1176345986
   Web of Science ®Google Scholar
• Ahn D.H., and Gao B. ( 1999), ‘A Parametric Nonlinear Model of Term Structure Dynamics’, Review of Financial Studies, 12, 721–762. doi: 10.1093/rfs/12.4.721
   Web of Science ®Google Scholar
• Bouezmarni T., and Rombouts J.V.K. ( 2010), ‘Nonparametric Density Estimation for Positive Time Series’, Computational Statistics & Data Analysis, 54, 245–261. doi: 10.1016/j.csda.2009.08.016
   Web of Science ®Google Scholar
• Bouezmarni T., and Scaillet O. ( 2005), ‘Consistency of Asymmetric Kernel Density Estimators and Smoothed Histograms with Application to Income Data’, Econometric Theory, 21, 390–412. doi: 10.1017/S0266466605050218
   Web of Science ®Google Scholar
• Buch-Larsen T., Nielsen J.P., Guillén M., and Bolancé C. ( 2005), ‘Kernel Density Estimation for Heavy-Tailed Distributions Using the Champernowne Transformation’, Statistics, 39, 503–518. doi: 10.1080/02331880500439782
   Web of Science ®Google Scholar
• Carrasco M., and Chen X. ( 2002), ‘Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models’, Econometric Theory, 18, 17–39. doi: 10.1017/S0266466602181023
   Web of Science ®Google Scholar
• Chen S.X. (2000), ‘Probability Density Function Estimation Using Gamma Kernels’, Annals of the Institute of Statistical Mathematics, 52, 471–480. doi: 10.1023/A:1004165218295
   Web of Science ®Google Scholar
• Chen X., Hansen L.P., and Carrasco M. ( 2010), ‘Nonlinearity and Temporal Dependence’, Journal of Econometrics, 155, 155–169. doi: 10.1016/j.jeconom.2009.10.001
   Web of Science ®Google Scholar
• Cox J.C., Ingersoll Jr J.E., and Ross S.A. ( 1985), ‘A Theory of the Term Structure of Interest Rates’, Econometrica, 53, 385–408. doi: 10.2307/1911242
   Web of Science ®Google Scholar
• Fernandes M., and Grammig J. ( 2005), ‘Nonparametric Specification Tests for Conditional Duration Models’, Journal of Econometrics, 127, 35–68. doi: 10.1016/j.jeconom.2004.06.003
   Web of Science ®Google Scholar
• Fernandes M., Mendes E.F., and Scaillet O. ( 2011), ‘Testing for Symmetry and Conditional Symmetry Using Asymmetric Kernels’, Swiss Finance Institute Occasional Paper Series No.11-32.
   Google Scholar
• Gospodinov N., and Hirukawa M. ( 2012), ‘Nonparametric Estimation of Scalar Diffusion Models of Interest Rates Using Asymmetric Kernels’, Journal of Empirical Finance, 19, 595–609. doi: 10.1016/j.jempfin.2012.04.001
   Web of Science ®Google Scholar
• Gustafsson J., Hagmann M., Nielsen J.P., and Scaillet O. ( 2009), ‘Local Transformation Kernel Density Estimation of Loss Distributions’, Journal of Business & Economic Statistics, 27, 161–175. doi: 10.1198/jbes.2009.0011
   Web of Science ®Google Scholar
• Hagmann M., and Scaillet O. ( 2007), ‘Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators’, Journal of Econometrics, 141, 213–249. doi: 10.1016/j.jeconom.2007.01.018
   Web of Science ®Google Scholar
• Hirukawa M. (2010), ‘Nonparametric Multiplicative Bias Correction for Kernel-Type Density Estimation on the Unit Interval’, Computational Statistics & Data Analysis, 54, 473–495. doi: 10.1016/j.csda.2009.09.017
   Web of Science ®Google Scholar
• Hirukawa M., and Sakudo M. ( 2014), ‘Nonnegative Bias Reduction Methods for Density Estimation Using Asymmetric Kernels’, Computational Statistics & Data Analysis, 75, 112–123. doi: 10.1016/j.csda.2014.01.012
   Web of Science ®Google Scholar
• Jin X., and Kawczak J. ( 2003), ‘Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data’, Annals of Economics and Finance, 4, 103–124.
   Google Scholar
• Jones M.C. (1993), ‘ Simple Boundary Correction for Kernel Density Estimation’, Statistics and Computing, 3, 135– 146. doi: 10.1007/BF00147776
   Web of Science ®Google Scholar
• Jones M.C., Linton O., and Nielsen J.P. ( 1995), ‘A Simple Bias Reduction Method for Density Estimation’, Biometrika, 82, 327–338. doi: 10.1093/biomet/82.2.327
   Web of Science ®Google Scholar
• Karunamuni R.J., and Alberts T. ( 2005), ‘A Generalized Reflection Method of Boundary Correction in Kernel Density Estimation’, Canadian Journal of Statistics, 33, 497–509. doi: 10.1002/cjs.5550330403
   Web of Science ®Google Scholar
• Kuruwita C.N., Kulasekera K.B., and Padgett W.J. ( 2010), ‘Density Estimation Using Asymmetric Kernels and Bayes Bandwidths with Censored Data’, Journal of Statistical Planning and Inference, 140, 1765–1774. doi: 10.1016/j.jspi.2010.01.001
   Web of Science ®Google Scholar
• Malec P., and Schienle M. ( 2014), ‘Nonparametric Kernel Density Estimation Near the Boundary’, Computational Statistics & Data Analysis, 72, 57–76. doi: 10.1016/j.csda.2013.10.023
   Web of Science ®Google Scholar
• Nakagami M. (1943), ‘Some Statistical Characters of Short-Wave Fading’ [in Japanese], Journal of the Institute of Electrical Communication Engineers of Japan, 27, 145–150.
   Google Scholar
• Nakagami M. (1960), ‘The m-Distribution – A General Formula of Intensity Distribution of Rapid Fading’, in Statistical Methods in Radio Wave Propagation: Proceedings of a Symposium Held at the University of California, Los Angeles, June 18–20, 1958, ed. W.C. Hoffman, New York: Pergamon Press, pp. 3–36.
   Google Scholar
• Scaillet O. (2004), ‘Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels’, Journal of Nonparametric Statistics, 16, 217–226. doi: 10.1080/10485250310001624819
   Web of Science ®Google Scholar
• Sheather S.J., and Jones M.C. ( 1991), ‘A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation’, Journal of the Royal Statistical Society, Series B, 53, 683–690.
   Google Scholar
• Silverman B.W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman & Hall.
   Google Scholar
• Stacy E.W. (1962), ‘A Generalization of the Gamma Distribution’, Annals of Mathematical Statistics, 33, 1187–1192. doi: 10.1214/aoms/1177704481
   Google Scholar
• Stone C.J. (1980), ‘Optimal Rates of Convergence for Nonparametric Estimators’, Annals of Statistics, 8, 1348–1360. doi: 10.1214/aos/1176345206
   Web of Science ®Google Scholar
• Terrell G.R., and Scott D.W. ( 1980), ‘On Improving Convergence Rates for Nonnegative Kernel Density Estimators’, Annals of Statistics, 8, 1160–1163. doi: 10.1214/aos/1176345153
   Web of Science ®Google Scholar
• Wand M.P., Marron J.S., and Ruppert D. ( 1991), ‘ Transformations in Density Estimation’, Journal of the American Statistical Association, 86, 343– 353. doi: 10.1080/01621459.1991.10475041
   Web of Science ®Google Scholar