Single Functional Index Quantile Regression for Functional Data with Missing Data at Random

• Authors: Nadia Kadiri , Sanaà Dounya Mekki , Abbes Rabhi

Title variants

PL

Właściwości asymptotyczne estymatorów półparametrycznych dla kwantyla warunkowego pojedynczego wskaźnika funkcjonalnego z losowymi brakami danych

Abstracts

PL

Głównym celem przedstawionych w artykule badań jest oszacowanie kwantyla rozkładu warunkowego przy użyciu podejścia półparametrycznego w obecności losowo brakujących danych, gdzie zmienna predykcyjna należy do przestrzeni semimetrycznej. Założono strukturę pojedynczego indeksu, aby połączyć zmienną objaśniającą i zmienną odpowiedzi. Wstępnie zaproponowano estymator jądra dla funkcji rozkładu warunkowego, zakładając, że dane są losowo wybierane z procesu stacjonarnego z brakującymi danymi (MAR). Nakładając pewne ogólne warunki, ustalono jednolitą, prawie całkowitą zgodność modelu ze współczynnikami konwergencji.

EN

The primary goal of this research was to estimate the quantile of a conditional distribution using a semi-parametric approach in the presence of randomly missing data, where the predictor variable belongs to a semi-metric space. The authors assumed a single index structure to link the explanatory and response variable. First, a kernel estimator was proposed for the conditional distribution function, assuming that the data were selected from a stationary process with missing data at random (MAR). By imposing certain general conditions, the study established the model’s uniform almost complete consistencies with convergence rates.

Keywords

EN

functional data analysis; functional single index process; kernel estimator; missing at random; nonparametric estimation; small ball probability

PL

funkcjonalna analiza danych; funkcjonalny proces pojedynczego indeksu; estymator jądra; losowe braki; estymacja nieparametryczna; prawdopodobieństwo małej kuli

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Econometrics. Ekonometria. Advances in Applied Data Analytics
• Year: 2023
• Volume: 27
• Issue: 3
• Pages: 1-19

Dates

published

2023

Contributors

author

Nadia Kadiri

• University Djillali Liabes of Sidi Bel Abbes, Algeria

author

Sanaà Dounya Mekki

• University Center Salhi Ahmed of Naâama, Algeria

author

Abbes Rabhi

• University Djillali Liabes of Sidi Bel Abbes, Algeria

References

• Aït-Saidi, A., Ferraty, F., Kassa, R., and Vieu, P. (2008). Cross-Validated Estimation in the Single Functional Index Model. Statistics, (42), 475-494.
• Akkal, F., Rabhi, A., and Keddani, L. (2021). Some Asymptotic Properties of Conditional Density Function for Functional Dataunder Random Censorship. Applications and Applied Mathematics: An International Journal (AAM), 16(1), 12-42.
• Attaoui, S., and Boudiaf, M. (2014). On the Nonparametric Conditional Density and Mode Estimates in the Single Functional Index Model with Strongly Mixing Data. Sankhyã Indian J. Stat., 76(2), 356-378.
• Attaoui, S., and Ling, N. (2016). Asymptotic Results of a Nonparametric Conditional Cumulative Distribution Estimator in theSingle Functional Index Modeling for Time Series Data with Applications. Metrika: International Journal for Theoretical and Applied Statistics, 79(5), 485-511.
• Bosq, D., and Lecoutre, J. P. (1987). Théorie de l'estimation fonctionnelle. ECONOMICA, Paris.
• Chaudhuri, P., Doksum, K., and Samarov, A. (1997). On Average Derivative Quantile Regression. Ann. Statist., (25), 715-744.
• Cheng, P.E. (1994). Nonparametric Estimation of Mean Functional with Data Missing at Random. Journal of the American Statistical Association, 89(425), 81-87.
• Ezzahrioui, M., and Ould-Saïd, E. (2008). Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series. Comm. Statist. Theory and Methods, 37(16-17), 2735-2759.
• Ferraty, F., Rabhi, A. and Vieu, P. (2005). Conditional Quantiles for Functional Dependant Data with Application to the Climatic El Niño Phenomenon. Sankhyã, 67, 378-398.
• Ferraty, F., Sued, F., and Vieu, P. (2013). Mean Estimation with Data Missing at Random for Functional Covariables. Statistics, 47(4), 688-706.
• Hamri, M. M., Mekki, S. D., Rabhi, A., and Kadiri, N. (2022). Single Functional Index Quantile Regression for Independent Functional Data Under Right-Censoring. Econometrics, 26(1), 31-62. https://doi.org/10.15611/ eada.2022.1.03 Kadiri, N., Rabhi, A., and Bouchentouf, A. A. (2018). Strong Uniform Consistency Rates of Conditional Quantile Estimation in the Single Functional Index Model under Random Censorship. Journal Dependence Modeling, 6(1), 197-227.
• Lemdani, M., Ould-Saïd, E., and Poulin, N. (2009). Asymptotic Properties of a Conditional Quantile Estimator with Randomly Truncated Data. Journal of Multivariate Analysis, 100(3), 546-559.
• Liang, H., and de Uña-Alvarez, J. (2010). Asymptotic Normality for Estimator of Conditional Mode under Left-Truncated and Dependent Observations. Metrika, 72(1), 1-19.
• Ling, N., Liang, L. and Vieu, P. (2015). Nonparametric Regression Estimation for Functional Stationary Ergodic Data with Missing at Random. Journal of Statistical Planning and Inference, 162, 75-87.
• Ling, N., Liu, Y., and Vieu, P. (2016). Conditional Mode Estimation for Functional Stationary Ergodic Data with Responses Missing at Random. Statistics, 50(5), 991-1013.
• Ould-Saïd, E., and Cai, Z. (2005). Strong Uniform Consistency of Nonparametric Estimation of the Censored Conditional Mode Function. Journal of Nonparametric Statistics, 17(7), 797-806.
• Ould-Saïd, E., and Djabrane, Y. (2011). Asymptotic Normality of a Kernel Conditional Quantile Estimator under Strong Mixing Hypothesis and Left-Truncation. Communications in Statistics. Theory and Methods, 40(14), 2605-2627.
• Ould-Saïd, E., and Tatachak, A. (2011). A Nonparametric Conditional Mode Estimate under RLT Model and Strong Mixing Condition. International Journal of Statistics and Economics, (6), 76-92.
• Rabhi, A., Kadiri, N., and Akkal, F. (2021). On the Central Limit Theorem for Conditional Density Estimator in the Single Functional Index Model. Applications and Applied Mathematics: An International Journal (AAM), 16(2), 844-866.
• Rabhi, A., Kadiri, N., and Mekki, S. D. (2021). Asymptotic Properties of the Semi-Parametric Estimators of the Conditional Density for Functional Data in the Single Index Model with Missing Data at Random. Statistica, 81(4), 399-422.

Identifiers

DOI

10.15611/eada.2023.3.01

Biblioteka Nauki

21375671