Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics

Bouanani, Oussama; Laksaci, Ali; Rachdi, Mustapha; Rahmani, Saâdia

doi:10.1007/s41237-018-0057-9

Cited by 8 publications

(6 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof of Lemma 1. We use the same decomposition idea as in the proof of Theorem 3.1 in Bouanani et al [9], we obtain : where To show 1, it suffices applying the Slutsky's theorem and we deduced the following claim : Claim 1 :…”

Section: Appendixmentioning

confidence: 99%

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

Bouanani¹,

Guendouzi²,

Chemikh³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In this work, we treat a prediction problem via the conditional hazard function of a scalar response variable Y given a functional random variable X by using the local linear technique. The main purpose of this paper is to investigate the asymptotic normality of the nonparametric estimator of the conditional hazard function, under some general conditions. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our method than the standard kernel method

show abstract

Section: Appendixmentioning

confidence: 99%

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

Bouanani¹,

Guendouzi²,

Chemikh³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…To find the local likelihood estimators at x fixed, we numerically solve the equation (9). Note that the system of equations ( 9) is convex, then it can be solved by the Newton-Raphson algorithm.…”

Section: Estimation Of the Likelihoodmentioning

confidence: 99%

“…We can mention, without being exhaustive, James and Hastie [1] applying the linear discriminant analysis of Fisher in case of functional variables. In 2002, James [2] offered the functional generalized linear model with a solution based on the EM algorithm (Expectation-Maximization) and Ferraty and Vieu [3] also offer non-parametric estimation methods of conditional probabilities based on kernel methods (see also [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] and [20] and references therein). Müller and Stadtmüller [21] propose the functional quasi-likelihood model.…”

Section: Introductionmentioning

confidence: 99%

Curves Classification by Using a Local Likelihood Function and Its Practical Usefulness for Real Data

Rachdi¹,

Laksaci²,

Hamié³

et al. 2020

Fuzzy Systems and Data Mining VI

Self Cite

View full text Add to dashboard Cite

We extend the classical approach in supervised classification based on the local likelihood estimation to the functional covariates case. The estimation procedure of the functional parameter (slope parameter) in the linear model when the covariate is of functional kind is investigated. We show, on simulated as well on real data, that classification error rates estimated using test samples, and the estimation procedure by local likelihood seem to lead to better estimators than the classical kernel estimation. In addition, this approach is no longer assuming that the linear predictors have a specific parametric form. However, this approach also has two drawbacks. Indeed, it was more expensive and slower than the kernel regression. Thus, as mentioned earlier, kernels other than the Gaussian kernel can lead to a divergence of the Newton-Raphson algorithm. In contrast, using a Gaussian kernel, 4 to 6 iterations are then sufficient to achieve convergence.

show abstract

“…In addition, in this issue, one special feature were included "Functional data analysis and its applications" (Araki and Kawaguchi 2019;Misumi et al 2019;Takagishi and Yadohisa 2019;Bouanani et al 2019) which was edited by Gil González-Rodríguez and Hidetoshi Matsui.…”

mentioning

confidence: 99%

Introduction to the Vol.46, No.1, 2019

Ueno

2019

Behaviormetrika

View full text Add to dashboard Cite

In this issue, we are happy to publish the following nine original papers and one invited paper.The first paper is "A generalized procedure for estimating the multinomial proportions in randomized response sampling using scrambling variables" by Housila P. Singh and Swarangi M. Gorey (2019). The authors have suggested a generalized randomized response procedure, for estimating the multinomial proportions of potentially sensitive attributes in survey sampling, using higher order moments of scrambling variables at the estimation stage to produce unbiased estimators. This study derived expressions for variance and covariance of the generalized estimator with its development and showed that the developed estimator is more efficient than the previous estimators.The second paper is "Bayesian analysis of happiness with individual heterogeneity" by Lei Shi and Hikaru Hasegawa (2019). This study applies a new Bayesian univariate ordered probit model to happiness data on Australia, Canada, and the United States, with immigration status and religion status reflecting individual heterogeneity in the threshold model. The empirical results show that the models including individual heterogeneity perform better than those without individual heterogeneity do. Furthermore, the effects of heterogeneity vary between the three countries. Having a religious affiliation affects the thresholds in the United States, but shows no evident effects in Canada or Australia. In addition, parents' immigration status can affect the thresholds in Australia, but shows no effects in the United States or Canada.The third paper is "Logistic regression and Ising networks: prediction and estimation when violating lasso assumptions" by Lourens J. Waldorp, Maarten Marsman and Gunter Maris (2019). Recently, the Ising model was applied in psychology to model cooccurrences of mental disorders. It has been shown that the connections between the variables (nodes) in the Ising network can be estimated with a series of logistic regressions. This study demonstrates how well such a model predicts new observations and how well parameters of the Ising model can be estimated using logistic regressions from simulation experiments.

show abstract

Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics

Cited by 8 publications

References 24 publications

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

Limit Law of the Local Linear Estimate of the Conditional Hazard Function for Functional Data

Curves Classification by Using a Local Likelihood Function and Its Practical Usefulness for Real Data

Introduction to the Vol.46, No.1, 2019

Contact Info

Product

Resources

About