Nonparametric estimation of a conditional quantile for α-mixing processes

被引：54

作者：

Honda, T ^{[1
]}

机构：

[1] Univ Tsukuba, Inst Social Sci, Tsukuba, Ibaraki 3058571, Japan

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2000年 / 52卷 / 03期

关键词：

conditional quantile; local polynomial fitting; alpha-mixing process; exponential inequality; Bahadur representation; uniform convergence;

D O I：

10.1023/A:1004113201457

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let (X'(i),Y-i)' be a set of observations form a stationary alpha-mixing process and theta(x) be the conditional alpha-th quantile of Y give X = x. Several authors considered nonparametric estimation of theta(x) in the i.i.d. setting. Assuming the smoothIless of theta(x), we estimate it by local polynomial fitting and prove the asymptotic normality and the uniform convergence.

引用

页码：459 / 470

页数：12

共 18 条

[1] STRONG REPRESENTATIONS FOR LAD ESTIMATORS IN LINEAR-MODELS [J].

BABU, GJ .

PROBABILITY THEORY AND RELATED FIELDS, 1989, 83 (04) :547-558

[2] KERNEL AND NEAREST-NEIGHBOR ESTIMATION OF A CONDITIONAL QUANTILE [J].

BHATTACHARYA, PK ;

GANGOPADHYAY, AK .

ANNALS OF STATISTICS, 1990, 18 (03) :1400-1415

[3] NONPARAMETRIC ESTIMATES OF REGRESSION QUANTILES AND THEIR LOCAL BAHADUR REPRESENTATION [J].

CHAUDHURI, P .

ANNALS OF STATISTICS, 1991, 19 (02) :760-777

[4] GLOBAL NONPARAMETRIC-ESTIMATION OF CONDITIONAL QUANTILE FUNCTIONS AND THEIR DERIVATIVES [J].

CHAUDHURI, P .

JOURNAL OF MULTIVARIATE ANALYSIS, 1991, 39 (02) :246-269

[5]

Chaudhuri P, 1997, ANN STAT, V25, P715

[6]

Fan J., 1996, Local Polynomial Modelling and Its Applications: Monographs on Statistics and Applied Probability

[7]

FAN JQ, 1994, SCAND J STAT, V21, P433

[8]

HALL P, 1980, MARTINGALE LIMIT THE

[9] MEAN SQUARED ERROR PROPERTIES OF KERNEL ESTIMATES OF REGRESSION QUANTILES [J].

JONES, MC ;

HALL, P .

STATISTICS & PROBABILITY LETTERS, 1990, 10 (04) :283-289

[10] Strong convergence of sums of alpha-mixing random variables with applications to density estimation [J].

Liebscher, E .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1996, 65 (01) :69-80

← 1 2 →