Identifiability of Asymmetric Circular and Cylindrical Distributions

Miyata, Yoichi; Shiohama, Takayuki

doi:10.1007/s13171-022-00294-3

Cited by 4 publications

(6 citation statements)

References 16 publications

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“…The fact that simpler models represent an alternative to avoid problematic inferential cases points to the need for developing formal model selection tools in the context of the GH model (see Rossell & Rubio, 2023 for a general overview on model and variable selection in survival models). Finally, other areas in statistics where flat likelihoods appear, such as inference in circular models (Johnson, 2022; Miyata et al., 2022), may also benefit from linking inferential problems in those models with the concepts of NR and PNI.…”

Section: Discussionmentioning

confidence: 99%

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

Rubio

Espíndola²,

Montoya³

2023

Biometrical J

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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.

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Section: Discussionmentioning

confidence: 99%

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

Rubio

Espíndola²,

Montoya³

2023

Biometrical J

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“…As can be seen from [12], the skewing function of the sine-skewed wrapped Cauchy distribution, which is the marginal distribution of the circular component Θ, is given by the distribution function of a uniform random variable. To extend the WeiSSVM distribution, we replace the skewing function with the distribution function of a density function on the interval [−1, 1] proposed in [13]:…”

Section: A New Model For Linear-circular Datamentioning

confidence: 99%

“…Figure 1 depicts plots of the functions g m (x) and G m (x) for different orders m ∈ {0, 1, 4}. As shown in Section 3.1 of [13], the greater the slope of the function G m near 0, the stronger the influence of the skewness parameter λ on the marginal density of Θ. Figure 2 shows contour plots of the density (1) with µ = 0, κ = 1, α = 2 and β = 1.…”

Section: A New Model For Linear-circular Datamentioning

confidence: 99%

“…For non-zero location µ, the sth cosine and sine moments of Θ are given by α s,µ = E{cos(sΘ)} = cos(sµ)α s − sin(sµ)β s and β s,µ = E{sin(sΘ)} = cos(sµ)β s + sin(sµ)α s , respectively. These equations are derived in [13], and thus details are omitted here.…”

Section: Moment Expressionsmentioning

confidence: 99%

“…The rest of this paper is organized as follows. In Section 2, we introduce a class of cylindrical model whose marginal distribution of Θ is the extended sine-skewed (ESS) wrapped Cauchy distribution, as proposed in [11]. In addition, the proposed class of cylindrical distribution has the Weibull distribution as the conditional distribution of the linear random variable X given Θ.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

Miyata,

Shiohama,

Abe

2024

Symmetry

Self Cite

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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.

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Complex-Valued Time Series Models and Their Relations to Directional Statistics

Shiohama

2023

Research Papers in Statistical Inference for Time Series and Related Models

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Identifiability of Asymmetric Circular and Cylindrical Distributions

Cited by 4 publications

References 16 publications

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

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

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

Complex-Valued Time Series Models and Their Relations to Directional Statistics

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