摘要: We show that weighted averaged regression α-quantile in the linear model, with regressor components as weights, is monotone \(\alpha\in(0,1),\) and asymptotically equivalent to of location model. This relation remains true under local heteroscedasticity model errors. As such, quantile provides various scale statistics, used for studentization standardization an estimate density based on data. The properties are numerically illustrated.
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sci-hub.st 参考文章(32)
Hira L. Koul, Weighted Empirical Processes in Dynamic Nonlinear Models ,(2002)
Hira L. Koul, A. K. Md. E. Saleh, Autoregression Quantiles and Related Rank-Scores Processes Annals of Statistics. ,vol. 23, pp. 670- 689 ,(1995) , 10.1214/AOS/1176324541
Michael Falk, On the estimation of the quantile density function Statistics & Probability Letters. ,vol. 4, pp. 69- 73 ,(1986) , 10.1016/0167-7152(86)90020-9
Jana Jureckov�, Jan Picek, Pranab Kumar Sen, Goodness-of-fit test with nuisance regression and scale Metrika. ,vol. 58, pp. 235- 258 ,(2003) , 10.1007/S001840300262
Xiaojing Xiang, Estimation of conditional quantile density function Journal of Nonparametric Statistics. ,vol. 4, pp. 309- 316 ,(1995) , 10.1080/10485259508832621
Emanuel Parzen, Quantile Probability and Statistical Data Modeling Statistical Science. ,vol. 19, pp. 652- 662 ,(2004) , 10.1214/088342304000000387
Daniel Zelterman, Smooth nonparametric estimation of the quantile function Journal of Statistical Planning and Inference. ,vol. 26, pp. 339- 352 ,(1990) , 10.1016/0378-3758(90)90136-I
Y. S. Chow, Herbert Robbins, ON THE ASYMPTOTIC THEORY OF FIXED-WIDTH SEQUENTIAL CONFIDENCE INTERVALS FOR THE MEAN. Annals of Mathematical Statistics. ,vol. 36, pp. 457- 462 ,(1965) , 10.1007/978-1-4612-5110-1_19
Eve Bofingeb, ESTIMATION OF A DENSITY FUNCTION USING ORDER STATISTICS1 Australian & New Zealand Journal of Statistics. ,vol. 17, pp. 1- 7 ,(1975) , 10.1111/J.1467-842X.1975.TB01366.X
Daniel A. Bloch, Joseph L. Gastwirth, On a Simple Estimate of the Reciprocal of the Density Function Annals of Mathematical Statistics. ,vol. 39, pp. 1083- 1085 ,(1968) , 10.1214/AOMS/1177698342