Discrete triangular associated kernel and bandwidth choices in semiparametric estimation for count data

Kiessé, Tristan Senga; Cuny, Henri E.

doi:10.1080/00949655.2013.768995

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…The equivalence between ( 24) and ( 25) is achieved by taking a triangular kernel, defined as [60] and is illustrated in Figure 2. [60,61], stating that it corresponds to a discrete pdf, while it is exposed as continuous in [62], Chapter 13. This question depends on the conditions of the definition of the variable domain and its support.…”

Section: Discrete and Continuous Variables Case Equivalencementioning

confidence: 99%

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Revisiting Probabilistic Latent Semantic Analysis: Extensions, Challenges and Insights

Figuera,

García Bringas

2024

Technologies

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This manuscript provides a comprehensive exploration of Probabilistic latent semantic analysis (PLSA), highlighting its strengths, drawbacks, and challenges. The PLSA, originally a tool for information retrieval, provides a probabilistic sense for a table of co-occurrences as a mixture of multinomial distributions spanned over a latent class variable and adjusted with the expectation–maximization algorithm. The distributional assumptions and the iterative nature lead to a rigid model, dividing enthusiasts and detractors. Those drawbacks have led to several reformulations: the extension of the method to normal data distributions and a non-parametric formulation obtained with the help of Non-negative matrix factorization (NMF) techniques. Furthermore, the combination of theoretical studies and programming techniques alleviates the computational problem, thus making the potential of the method explicit: its relation with the Singular value decomposition (SVD), which means that PLSA can be used to satisfactorily support other techniques, such as the construction of Fisher kernels, the probabilistic interpretation of Principal component analysis (PCA), Transfer learning (TL), and the training of neural networks, among others. We also present open questions as a practical and theoretical research window.

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Section: Discrete and Continuous Variables Case Equivalencementioning

confidence: 99%

“…Interpreting probabilities as coordinates, Klingenberg has introduced simplicial cones Γ [19] Γ = y j s.t. y = ∑ j α j h j with α j ≥ 0 and h j ∈ [H] kj (61) which is a convex region in the positive orthant. Figure 4 illustrates this transformation.…”

Section: Principal Component Analysismentioning

confidence: 99%

Revisiting Probabilistic Latent Semantic Analysis: Extensions, Challenges and Insights

Figuera,

García Bringas

2024

Technologies

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“…See also Harfouche et al (2018) and Senga Kiessé (2017) for other properties. Notice that one can use them to estimate, instead of the pmf, discrete regression or weighted functions; see, e.g., Kokonendji and Somé (2021), Senga Kiessé and Cuny (2014) and, Senga Kiessé and Ventura (2016).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of the normalized discrete associated-kernel estimator for probability mass function

Esstafa¹,

Kokonendji²,

Somé³

2022

Preprint

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Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalized discrete associated-kernel estimator of a probability mass function. We show, under some regularity and nonrestrictive assumptions on the associated-kernel, that the normalizing random variable converges in mean square to 1. We then derive the consistency and the asymptotic normality of the proposed estimator. Various families of discrete kernels already exhibited satisfy the conditions, including the refined CoM-Poisson which is underdispersed and of second-order. Finally, the first-order binomial kernel is discussed and, surprisingly, its normalized estimator has a suitable asymptotic behaviour through simulations.

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Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

2015

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This work takes advantage of semiparametric modelling which improves significantly in many situations the estimation accuracy of the purely nonparametric approach. Herein for semiparametric estimations of probability mass function (pmf) of count data, and an unknown count regression function (crf), the kernel used is a binomial one and the bandiwdth selection is investigated by developing Bayesian approaches. About the latter, Bayes local and global bandwidth approaches are used to establish data-driven selection procedures in semiparametric framework. From conjugate beta prior distributions of the smoothing parameter and under the squared errors loss function, Bayes estimate for pmf is obtained in closed form. This is not available for the crf which is computed by the Markov Chain Monte Carlo technique. Simulation studies demonstrate that both proposed methods perform better than the classical cross-validation procedures, in particular the smoothing quality and execution times are optimized. All applications are made on real data sets. B Nabil Zougab

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Discrete triangular associated kernel and bandwidth choices in semiparametric estimation for count data

Cited by 6 publications

References 16 publications

Revisiting Probabilistic Latent Semantic Analysis: Extensions, Challenges and Insights

Revisiting Probabilistic Latent Semantic Analysis: Extensions, Challenges and Insights

Asymptotic properties of the normalized discrete associated-kernel estimator for probability mass function

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

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