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Tchilabalo Abozou Kpanzou

Publications and source records attributed to Tchilabalo Abozou Kpanzou.

13 recordsLinked to original sources
arXiv2026

Long-Memory Estimation and Fractionally Integrated Modeling of White Maize Prices in Togo

Agricultural commodity prices often exhibit strong temporal persistence, which may limit the performance of conventional time series models. This study investigates long memory in logarithmic monthly white maize prices from six major markets in Togo between January 2001 and June 2022. Long memory is examined using the Geweke--Porter--Hudak, Local Whittle, Exact Local Whittle, and wavelet log-regression estimators. SARIMA, ARFIMA, and SARFIMA models are subsequently compared using the Bayesian Information Criterion and residual diagnostics. Long-range dependence is found across all markets. Fractionally integrated models provide the best fit for most markets, although SARIMA remains preferable for some. The results demonstrate that evidence of long memory does not necessarily imply that a fractionally integrated model provides the best empirical fit, emphasizing the importance of data-driven model selection.

stat.AP↗
arXiv2026

Asymptotic distribution of a robust wavelet-based NKK periodogram

This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time series, we analyze the probabilistic structure of the resulting periodogram under long-range dependence. It is shown that, under suitable regularity conditions, the NKK periodogram converges in distribution to a nonstandard limit characterized as a quadratic form in a Gaussian random vector, whose covariance structure depends on the memory properties of the process and on the chosen wavelet filters. This result establishes a rigorous theoretical foundation for the use of robust wavelet-based periodograms in the spectral analysis of long-memory time series with heavy-tailed inovations.

stat.ME↗
arXiv2025

General asymptotic representations of indexes based on the functional empirical process and the residual functional empirical process and applications

The objective of this paper is to establish a general asymptotic representation (\textit{GAR}) for a wide range of statistics, employing two fundamental processes: the functional empirical process (\textit{fep}) and the residual functional empirical process introduced by Lo and Sall (2010a, 2010b), denoted as \textit{lrfep}. The functional empirical process (\textit{fep}) is defined as follows: $$ \mathbb{G}_n(h)=\frac{1}{\sqrt{n}} \sum_{j=1}^{n} \{h(X_j)-\mathbb{E}h(X_j)\}, $$ \Bin [where $X$, $X_1$, $\cdots$, $X_n$ is a sample from a random $d$-vectors $X$ of size $(n+1)$ with $n\geq 1$ and $h$ is a measurable function defined on $\mathbb{R}^d$ such that $\mathbb{E}h(X)^2<+\infty$]. It is a powerful tool for deriving asymptotic laws. An earlier and simpler version of this paper focused on the application of the (\textit{fep}) to statistics $J_n$ that can be turned into an asymptotic algebraic expression of empirical functions of the form $$ J_n=\mathbb{E}h(X) + n^{-1/2} \mathbb{G}_n(h) + o_{\mathbb{P}}(n^{-1/2}). \ \ \ \textit{SGAR} $$ \Bin However, not all statistics, in particular welfare indexes, conform to this form. In many scenarios, functions of the order statistics $X_{1,n}\leq$, $\cdots$, $\leq X_{n,n}$ are involved, resulting in $L$-statistics. In such cases, the (\textit{fep}) can still be utilized, but in combination with the related residual functional empirical process introduced by Lo and Sall (2010a, 2010b). This combination leads to general asymptotic representations (GAR) for a wide range of statistical indexes $$ J_n=\mathbb{E}h(X) + n^{-1/2} \biggr(\mathbb{G}_n(h) + \int_{0}^{1} \mathbb{G}_n(\tilde{f}_s) \ell(s) \ ds + o_{\mathbb{P}}(1)\biggr), \ \ \textit{FGAR} $$

math.ST↗
arXiv2025

Comparative analysis and practical applications of cubic transmutations for the Pareto distribution

Transmutation is a technique for extending classical probability distributions in order to give them more flexibility. In this paper, we are interested in cubic transmutations of the Pareto distribution. We establish a general formula that unifies existing cubic transmutations of the Pareto distribution and facilitates the derivation of new cubic transmutations that have not yet been explored in the literature. We also derive general formulas for the related mathematical properties. Finally, we perform a comparative analysis of the six transmutations existing in the literature using real-world data. The results obtained confirm the flexibility and effectiveness of cubic transmutations in modeling various types of data.

stat.ME↗
arXiv2025

Wavelet-based estimation of long-memory parameter in stochastic volatility models using a robust log-periodogram

In this paper, we propose a novel method for estimating the long-memory parameter in time series. By combining the multi-resolution framework of wavelets with the robustness of the Least Absolute Deviations (LAD) criterion, we introduce a periodogram providing a robust alternative to classical methods in the presence of non-Gaussian noise. Incorporating this periodogram into a log-periodogram regression, we develop a new estimator. Simulation studies demonstrate that our estimator outperforms the Geweke and Porter-Hudak (GPH) and Wavelet-Based Log-Periodogram (WBLP) estimators, particularly in terms of mean squared error, across various sample sizes and parameter configurations.

stat.ME↗
arXiv2025

Theoretical analysis and improvements in cubic transmutations of probability distributions

In statistics, processed data are becoming increasingly complex, and classical probability distributions are limited in their ability to model them. This is why, to better model data, extensive work has been conducted on extending classical probability distributions. Generally, this extension is achieved by transforming the cumulative distribution function of a baseline distribution through the addition of one or more parameters to enhance its flexibility. Cubic transmutation (CT) is one of the most popular methods for such extensions. However, CT does not have a unique definition because different approaches for CT have been proposed in the literature but are yet to be compared. The main goal of this paper is to compare these different approaches from both theoretical and empirical viewpoints. We study the relationships between the different approaches and we propose modified versions based on the extension of parameter ranges. The results are illustrated using Pareto distribution as baseline distribution.

stat.ME↗
arXiv2022

Extensions of two classical Poisson limit laws to non-stationary independent data

In earlier stages in the introduction to asymptotic methods in probability theory, the weak convergence of sequences $(X_n)_{n\geq 1}$ of Binomial of random variables (\textit{rv}'s) to a Poisson law is classical and easy-to prove. A version of such a result concerning sequences $(Y_n)_{n\geq 1}$ of negative binomial \textit{rv}'s also exists. In both cases, $X_n$ and $Y_n-n$ are by-row sums $S_n[X]$ and $S_n[Y]$ of arrays of Bernoulli \textit{rv}'s and corrected geometric \textit{rv}'s respectively. When considered in the general frame of asymptotic theorems of by-row sums of \textit{rv}'s of arrays, these two simple results in the independent and identically distributed scheme can be generalized to non-stationary data and beyond to non-stationary and dependent data. Further generalizations give interesting results that would not be found by direct methods. In this paper, we focus on generalizations to the non-stationary independent data. Extensions to dependent data will addressed later.

math.PR↗
arXiv2019

Statistical tests for the Pseudo-Lindley distribution and applications

The pseudo-Lindley distribution was introduced as a useful generalization of the Lindley distribution in Zeghdoudi and Nedjar (2016) who showed interesting properties of their new laws and efficiencies in modeling data in Reliability and Survival Analysis. In this paper we study the estimators of the pair of parameters and determine their asymptotic law from which a chi-square law is derived. From both asymptotic laws, statistical tests are built. Simulation studies on the tests conclude to their efficiency for data sizes generally used in Reliability. R codes related to statistical analysis on that law are given in an appropriate archive repository code paper in Arxiv.

math.ST↗
arXiv2018

On the influence function for the Theil-like class of inequality measures

On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in Mergane and Lo (2013). On the other hand, the influence function of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analysed in various aspects for a large number of statistics. We proceed to a unifying study of the IF of all the members of the so-called Theil-like family and regroup those IF's in one formula. Comparative studies become easier.

stat.ME↗
arXiv2018

A Theil-like Class of Inequality Measures, its Asymptotic Normality Theory and Applications

In this paper, we consider a coherent theory about the asymptotic representations for a family of inequality indices called Theil-Like Inequality Measures (TLIM), within a Gaussian field. The theory uses the functional empirical process approach. We provide the finite-distribution and uniform asymptotic normality of the elements of the TLIM class in a unified approach rather than in a case by case one. The results are then applied to some UEMOA countries databases.

stat.ME↗
arXiv2017

Measuring inequality: application of semi-parametric methods to real life data

A number of methods have been introduced in order to measure the inequality in various situations such as income and expenditure. In order to curry out statistical inference, one often needs to estimate the available measures of inequality. Many estimators are available in the literature, the most used ones being the non parametric estimators. kpanzou(2011) has developed semi-parametric estimators for measures of inequality and showed that these are very appropriate especially for heavy tailed distributions. In this paper we apply such semi-parametric methods to a practical data set and show how they compare to the non parametric estimators. A guidance is also given on the choice of parametric distributions to fit in the tails of the data

stat.ME↗
arXiv2017

On the joint distribution of variations of the Gini index and Welfare indices

The aim of this paper is to establish the asymptotic behavior of the mutual influence of the Gini index and the poverty measures by using the Gaussian fields described in Mergane and Lo(2013). The results are given as representation theorems using the Gaussian fields of the unidimensional or the bidimensional functional Brownian bridges. Such representations, when combined with those already available, lead to joint asymptotic distributions with other statistics of interest like growth, welfare and inequality indices and then, unveil interesting results related to the mutual influence between them. The results are also appropriate for studying whether a growth is fair or not, depending on the variation of the inequality measure. Datadriven applications are also available. Although the variances may seem complicated at a first sight, their computations which are needed to get confidence intervals of the indices, are possible with the help of R codes we provide. Beyond the current results, the provided representations are useful in connection with different ones of other statistics.

stat.ME↗