arXiv subjects

Aliou Diop

Publications and source records attributed to Aliou Diop.

5 recordsLinked to original sources

arXiv2021

Nonparametric kernel estimation of Weibull-tail coefficient in presence of the right random censoring

In this paper, nonparametric estimation of the conditional Weibull-tail coefficient when the variable of interest is right random censored is addressed. A Weissman-type estimator of conditional extreme quantile is also proposed. In addition, a simulation study is conducted to assess the finite-sample behavior of the proposed estimators and a comparison with alternative strategies is provided. Finally, the practical applicability of the methodology is presented using a real datasets of men suffering from a larynx cancer.

stat.ME↗

arXiv2021

Zero-inflated generalized extreme value regression model for binary data and application in health study

Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable $Y$ and a set of potential predictors $\mathbf X$. The binary response may represent, for example, the occurrence of some outcome of interest ($Y=1$ if the outcome occurred and $Y=0$ otherwise). When the dependent variable $Y$ represents a rare event, the logistic regression model shows relevant drawbacks. In order to overcome these drawbacks we propose the Generalized Extreme Value (GEV) regression model. In particular, we suggest the quantile function of the GEV distribution as link function, so our attention is focused on the tail of the response curve for values close to one. A sample of observations is said to contain a cure fraction when a proportion of the study subjects (the so-called cured individuals, as opposed to the susceptibles) cannot experience the outcome of interest. One problem arising then is that it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In these settings, a logistic regression analysis of the relationship between $\mathbf X$ and $Y$ among the susceptibles is no more straightforward. We develop a maximum likelihood estimation procedure for this problem, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model. Then, we conduct a simulation study to investigate its finite-sample behavior, and application to real data.

stat.ME↗

arXiv2015

Classification approach based on association rules mining for unbalanced data

This paper deals with the binary classification task when the target class has the lower probability of occurrence. In such situation, it is not possible to build a powerful classifier by using standard methods such as logistic regression, classification tree, discriminant analysis, etc. To overcome this short-coming of these methods which yield classifiers with low sensibility, we tackled the classification problem here through an approach based on the association rules learning. This approach has the advantage of allowing the identification of the patterns that are well correlated with the target class. Association rules learning is a well known method in the area of data-mining. It is used when dealing with large database for unsupervised discovery of local patterns that expresses hidden relationships between input variables. In considering association rules from a supervised learning point of view, a relevant set of weak classifiers is obtained from which one derives a classifier that performs well.

stat.ML↗

arXiv2012

Estimation for seasonal fractional ARIMA with stable innovations via the empirical characteristic function method

Maximum likelihood methods, while widely used, may be non-robust due to disagreement between the assumptions upon which the models are based and the true density probability distribution of observed data. Because the Empirical Characteristic Function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for stable seasonal fractional ARIMA processes. Under some assumptions, we show that the resulting estimators are consistent and asymptotically normally distributed. For comparison purpose, we consider also the MCMC Whittle method developed by Ndongo et al. (2010). The performance of the two methods is discussed using a Monte Carlo simulation.

math.ST↗

arXiv2011

On the Generalized Hill Process for Small Parameters and Applications

Let $X_{1},X_{2},...$ be a sequence of independent copies (s.i.c) of a real random variable (r.v.) $X\geq 1$, with distribution function $df$ $F(x)=\mathbb{P}% (X\leq x)$ and let $X_{1,n}\leq X_{2,n} \leq ... \leq X_{n,n}$ be the order statistics based on the $n\geq 1$ first of these observations. The following continuous generalized Hill process {equation*} T_{n}(τ)=k^{-τ}\sum_{j=1}^{j=k}j^τ(\log X_{n-j+1,n}-\log X_{n-j,n}), \label{dl02} {equation*} $τ>0$, $1\leq k \leq n$, has been introduced as a continuous family of estimators of the extreme value index, and largely studied for statistical purposes with asymptotic normality results restricted to $τ> 1/2$. We extend those results to $0 < τ\leq 1/2$ and show that asymptotic normality is still valid for $τ=1/2$. For $0 < τ<1/2$, we get non Gaussian asymptotic laws which are closely related to the Riemann function $% ζ(s)=\sum_{n=1}^{\infty} n^{-s},s>1$

stat.ME↗