STRONG UNIFORM CONSISTENCY RATES OF CONDITIONAL DENSITY ESTIMATION IN THE SINGLE FUNCTIONAL INDEX MODEL FOR FUNCTIONAL DATA UNDER RANDOM CENSORSHIP

被引：0

作者：

Kadiri, Nadia ^{[1
]}

Meghnafi, Mustapha ^{[2
]}

Rabhi, Abbes ^{[3
]}

机构：

[1] Univ Djillali LIABES Sidi Bel Abbes, Sidi Bel Abbes, Algeria

[2] Univ Bechar, Fac Exact Sci, Dept Math, Bechar, Algeria

[3] Univ Djillali Liabes Sidi Bel Abbes, Lab Math, Sidi Bel Abbes, Algeria

来源：

REVSTAT-STATISTICAL JOURNAL | 2022年 / 20卷 / 02期

关键词：

conditional density; functional single-index process; functional random variable; nonparametric estimation; small ball probability; NONPARAMETRIC-ESTIMATION; ASYMPTOTIC NORMALITY; LAWS;

D O I：

暂无

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：

The main objective of this paper is to investigate the estimation of conditional density function based on the single-index model in the censorship model when the sample is considered as an inde-pendent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated when the observations are linked with a single-index structure. The pointwise almost com-plete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. As an application the conditional mode in functional single-index model is presented. Finally, a simulation study is carried out to evaluate the performance of this estimate.

引用

页码：221 / 249

页数：29

共 50 条

[21] Consistency rates and asymptotic normality of the high risk conditional for functional data [J].

Rabhi, Abbes ;

Keddani, Latifa ;

Hammon, Yassine .

ACTA UNIVERSITATIS SAPIENTIAE-MATHEMATICA, 2016, 8 (01) :127-149

[22] Consistency rates and asymptotic normality of the high risk conditional for functional data [J].

Rabhi, Abbes ;

Keddani, Latifa ;

Hammou, Yassine .

ACTA UNIVERSITATIS SAPIENTIAE-MATHEMATICA, 2015, 7 (02) :220-242

[23] Semi-recursive kernel conditional density estimators under random censorship and dependent data [J].

Laksaci, Ali ;

Khardani, Salah ;

Semmar, Sihem .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2022, 51 (07) :2116-2138

[24] ASYMPTOTIC NORMALITY OF THE LOCAL LINEAR ESTIMATION OF THE CONDITIONAL DENSITY FOR FUNCTIONAL DEPENDENT AND CENSORED DATA [J].

Benkhaled, Abdelkader ;

Madani, Fethi ;

Khardani, Salah .

SOUTH AFRICAN STATISTICAL JOURNAL, 2020, 54 (02) :131-151

[25] ASYMPTOTIC NORMALITY SINGLE FUNCTIONAL INDEX QUANTILE REGRESSION UNDER RANDOMLY CENSORED DATA [J].

Dib, Abdessamad ;

Hamri, Mohamed Mehdi ;

Rabhi, Abbes .

JOURNAL OF SCIENCE AND ARTS, 2022, (04) :845-864

[26] Conditional mode estimation for functional stationary ergodic data with responses missing at random [J].

Ling, Nengxiang ;

Liu, Yang ;

Vieu, Philippe .

STATISTICS, 2016, 50 (05) :991-1013

[27] FDA: strong consistency of the kNN local linear estimation of the functional conditional density and mode [J].

Chikr-Elmezouar, Zouaoui ;

Almanjahie, Ibrahim M. ;

Laksaci, Ali ;

Rachdi, Mustapha .

JOURNAL OF NONPARAMETRIC STATISTICS, 2019, 31 (01) :175-195

[28] Non Parametric Regression Quantile Estimation for Dependent Functional Data under Random Censorship: Asymptotic Normality [J].

Horrigue, Walid ;

Said, Elias Ould .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2015, 44 (20) :4307-4332

[29] Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors [J].

Horrigue, Walid ;

Said, Elias Ould .

RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2011, 19 (02) :131-156

[30] The conditional cumulative distribution function in single functional index model [J].

Saidi, Ahmed Ait ;

Kheira, Mecheri .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2016, 45 (16) :4896-4911

← 1 2 3 4 5 →