Flexible Models for Complex Data with Applications

Ley, Christophe; Babić, Slađana; Craens, Domien

doi:10.1146/annurev-statistics-040720-025210

Cited by 11 publications

(6 citation statements)

References 86 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this subsection, we present some correlations and a linear-circular squared correlation of X and vector (cos Θ, sin Θ). By Equations ( 8), (10), ( 12) and ( 13), the covariance of X and cos Θ with µ = 0, that of X and sin Θ, and that of cos Θ and sin Θ are expressed as…”

Section: Linear-circular Correlationmentioning

confidence: 99%

“…The WeiSSVM density has a simple normalizing constant and is amenable to calculations. This characteristic is referred to as tractability, which is one of the desirable properties of a class of flexible distributions in [10]. The WeiSSVM distribution also provides explicit expressions for the higher-order moments for X and Θ.…”

Section: Introductionmentioning

confidence: 99%

“…) − sinh(κ) cos θ} ν+1 dθ.Therefore, the result holds from the same argument.Appendix A.1. Derivation of the Moment in the Case of m = 1We use the following elementary properties to derive the moment(10):sin 3 θ = 3 sin θ − sin 3θ 4 and sin A sin B = cos(A − B) − cos(A + B)Let s ∈ {0, 1, 2, . .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

Miyata,

Shiohama,

Abe

2024

Symmetry

View full text Add to dashboard Cite

A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed distributions is shown to have simple normalizing constants, easy random number generation methods, explicit moment expressions, and identifiability in parameters. In particular, the marginal distribution of the circular random variable, and its conditional distribution given a linear random variable give relatively stronger skewness than those of existing cylindrical models. Some Monte Carlo simulations and real data analysis are performed to investigate the feasibility and tractability of the proposed models.

show abstract

Section: Linear-circular Correlationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

Miyata,

Shiohama,

Abe

2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…We also refer the reader to Ley et al. (2021) for a general discussion on basic desiderata in the use of flexible parametric models. Indeed, nonidentifiability, along with NR and PNI, makes parametric models fail one of their key requirements, namely, “Straightforward parameter estimation.”…”

Section: Parametric General Hazard Regression Modelsmentioning

confidence: 99%

On near‐redundancy and identifiability of parametric hazard regression models under censoring

Rubio

Espíndola²,

Montoya³

2023

Biometrical J

View full text Add to dashboard Cite

We study parametric inference on a rich class of hazard regression models in the presence of right‐censoring. Previous literature has reported some inferential challenges, such as multimodal or flat likelihood surfaces, in this class of models for some particular data sets. We formalize the study of these inferential problems by linking them to the concepts of near‐redundancy and practical nonidentifiability of parameters. We show that the maximum likelihood estimators of the parameters in this class of models are consistent and asymptotically normal. Thus, the inferential problems in this class of models are related to the finite‐sample scenario, where it is difficult to distinguish between the fitted model and a nested nonidentifiable (i.e., parameter‐redundant) model. We propose a method for detecting near‐redundancy, based on distances between probability distributions. We also employ methods used in other areas for detecting practical nonidentifiability and near‐redundancy, including the inspection of the profile likelihood function and the Hessian method. For cases where inferential problems are detected, we discuss alternatives such as using model selection tools to identify simpler models that do not exhibit these inferential problems, increasing the sample size, or extending the follow‐up time. We illustrate the performance of the proposed methods through a simulation study. Our simulation study reveals a link between the presence of near‐redundancy and practical nonidentifiability. Two illustrative applications using real data, with and without inferential problems, are presented.

show abstract

“…Understanding the links between probability laws and grouping them into classes with similar properties has become particularly important nowadays, given the plethora of new distributions. We refer the interested reader to the review papers Jones (2015) and Babić et al (2019) for further information about classifying flexible distributions for univariate respectively multivariate data, and to Ley et al (2021) for an overview and discussion of advantages and limitations of flexible models.…”

Section: Final Remarksmentioning

confidence: 99%

From Pareto to Weibull – A Constructive Review of Distributions on ℝ⁺

Sinner

Dominicy

Trufin

et al. 2022

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

Power laws and power laws with exponential cut-off are two distinct families of size distributions. In the present paper, we propose a unified treatment of both families by building a family of distributions that interpolates between them, hence the name Interpolating Family (IF) of distributions. Our original construction, which relies on techniques from statistical physics, provides a connection for hitherto unrelated distributions like the Pareto and Weibull distributions, and sheds new light on them. The IF also contains several distributions that are neither of power law nor of power law with exponential cut-off type. We calculate quantilebased properties, moments and modes for the IF. This allows us to review known properties of famous size distributions and to provide in a single sweep these characteristics for various less known (and new) special cases of our Interpolating Family.

show abstract

Flexible Models for Complex Data with Applications

Cited by 11 publications

References 86 publications

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

On near‐redundancy and identifiability of parametric hazard regression models under censoring

From Pareto to Weibull – A Constructive Review of Distributions on ℝ⁺

Contact Info

Product

Resources

About

Flexible Models for Complex Data with Applications

Cited by 11 publications

References 86 publications

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

On near‐redundancy and identifiability of parametric hazard regression models under censoring

From Pareto to Weibull – A Constructive Review of Distributions on ℝ+

Contact Info

Product

Resources

About

From Pareto to Weibull – A Constructive Review of Distributions on ℝ⁺