On the Singularities of the Information Matrix and Multipath Change-Point Problems

Asgharian, Masoud

doi:10.1137/s0040585x97986783

Cited by 10 publications

(5 citation statements)

References 50 publications

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“…Under some regularity conditions, Murphy & van der Vaart () proved that for any random sequence

ξ_{n} \to ξ_{0}

in probability,

\begin{matrix} right p ℓ_{n} (ξ_{n}) & center = & left p ℓ_{n} (ξ_{0}) + {(ξ_{n} - ξ_{0})}^{⊤} \sum_{i = 1}^{n} ℓ_{0} {(Y_{i 1}, Δ_{i 1}, X_{i 1}), \dots, (Y_{italiciK}, Δ_{italiciK}, X_{italiciK})} \\ right & center & left - \frac{1}{2} n {(ξ_{n} - ξ_{0})}^{⊤} I_{0} (ξ_{0}) (ξ_{n} - ξ_{0}) + o_{p} {(\sqrt{n} | | ξ_{n} - ξ_{0} | | + 1)}^{2}, \end{matrix}

where

ℓ_{0}

is the efficient score function for

ξ_{0}

, the ordinary score function minus its orthogonal projection onto the closed linear span of the score functions for the nuisance parameter, and

I_{0} false(ξ_{0} false)

is the covariance matrix, the efficient Fisher information matrix .

I_{0} false(ξ_{0} false)

is nonsingular according to Theorem 4 in Asgharian () assuming the boundness of

Λ_{k} false(τ false)

. The nonsingularity of

I_{0} false(ξ_{0} false)

can also be shown in a similar way in Theorem 2 and Proposition A.2 of Zeng & Lin ().…”

Section: Methodsmentioning

confidence: 70%

Variable selection for frailty transformation models with application to diabetic complications

et al. 2016

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This article focuses on variable selection in the context of gamma frailty transformation models for multivariate survival times. We propose a method based on a nonconcave penalty function to select relevant regression predictors and simultaneously estimate model parameters and nonparametric functions. Our procedure performs as well as the oracle one in which the true model is assumed to be known. We conduct simulation studies to demonstrate the performance of the proposed methodology. We apply our method to a case study based on the Hong Kong Diabetes Registry, and obtain new insights on the risk factors of cardiovascular–renal complications for type 2 diabetic patients. The Canadian Journal of Statistics 44: 375–394; 2016 © 2016 Statistical Society of Canada

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“…Under some regularity conditions, Murphy & van der Vaart () proved that for any random sequence

ξ_{n} \to ξ_{0}

in probability,

\begin{matrix} right p ℓ_{n} (ξ_{n}) & center = & left p ℓ_{n} (ξ_{0}) + {(ξ_{n} - ξ_{0})}^{⊤} \sum_{i = 1}^{n} ℓ_{0} {(Y_{i 1}, Δ_{i 1}, X_{i 1}), \dots, (Y_{italiciK}, Δ_{italiciK}, X_{italiciK})} \\ right & center & left - \frac{1}{2} n {(ξ_{n} - ξ_{0})}^{⊤} I_{0} (ξ_{0}) (ξ_{n} - ξ_{0}) + o_{p} {(\sqrt{n} | | ξ_{n} - ξ_{0} | | + 1)}^{2}, \end{matrix}

where

ℓ_{0}

is the efficient score function for

ξ_{0}

, the ordinary score function minus its orthogonal projection onto the closed linear span of the score functions for the nuisance parameter, and

I_{0} false(ξ_{0} false)

is the covariance matrix, the efficient Fisher information matrix .

I_{0} false(ξ_{0} false)

is nonsingular according to Theorem 4 in Asgharian () assuming the boundness of

Λ_{k} false(τ false)

. The nonsingularity of

I_{0} false(ξ_{0} false)

can also be shown in a similar way in Theorem 2 and Proposition A.2 of Zeng & Lin ().…”

Section: Methodsmentioning

confidence: 70%

Variable selection for frailty transformation models with application to diabetic complications

et al. 2016

View full text Add to dashboard Cite

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“…Verifying such condition in practice for specific choices of the parametric baseline hazard is complicated. However, it has been shown that certain smoothness and identifiability conditions, which are easier to verify in practice, guarantee the non-singularity of this matrix (see Asgharian 30 ). Similar asymptotic results have also been obtained for parametric copula survival models for clustered data in Prenen et al, 29 where parametric models were found to perform better than their semiparametric counterparts.…”

Section: Likelihood Function and Parameter Estimationmentioning

confidence: 99%

MEGH: A parametric class of general hazard models for clustered survival data

Rubio

Drikvandi

2022

Stat Methods Med Res

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In many applications of survival data analysis, the individuals are treated in different medical centres or belong to different clusters defined by geographical or administrative regions. The analysis of such data requires accounting for between-cluster variability. Ignoring such variability would impose unrealistic assumptions in the analysis and could affect the inference on the statistical models. We develop a novel parametric mixed-effects general hazard (MEGH) model that is particularly suitable for the analysis of clustered survival data. The proposed structure generalises the mixed-effects proportional hazards and mixed-effects accelerated failure time structures, among other structures, which are obtained as special cases of the MEGH structure. We develop a likelihood-based algorithm for parameter estimation in general subclasses of the MEGH model, which is implemented in our R package MEGH. We propose diagnostic tools for assessing the random effects and their distributional assumption in the proposed MEGH model. We investigate the performance of the MEGH model using theoretical and simulation studies, as well as a real data application on leukaemia.

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“…Assumption B4(i) is essentially identifiability (see Wang, 1989;Andersen, 1970), while B4(ii) is essentially positive-definiteness of the information matrix. The latter condition rarely fails to hold provided that identifiability and some smoothness conditions hold (see Theorem 3 in Asgharian, 2014). The kernel function K and the bandwidth b n satisfy the conditions Assumptions K1, K2: ] d𝜉(y, 1|x)…”

Section: Appendix Notationsmentioning

confidence: 99%

A semiparametric regression model under biased sampling and random censoring: A local pseudo‐likelihood approach

Rabhi

Asgharian

2020

Can J Statistics

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Methodologies developed for left‐truncated right‐censored failure time data can mostly be categorized according to the assumption imposed on the truncation distribution, i.e., being completely unknown or completely known. While the former approach enjoys robustness, the latter is more efficient when the assumed form of the truncation distribution can be supported by the data. Motivated by data from an HIV/AIDS study, we consider the middle ground and develop methodologies for estimation of a regression function in a semiparametric setting where the truncation distribution is parametrically specified while the failure time, censoring and covariate distribution are left completely unknown. We devise an estimator for the regression function based on a local pseudo‐likelihood approach that properly accounts for the bias induced on the response variable and covariate(s) by the sampling design. One important spin‐off from these results is that they yield the adjustment for length‐biased sampling and right‐censoring; the so‐called stationary case. We study the small and large sample behaviour of our estimators. The proposed method is then applied to analyze a set of HIV/AIDS data.

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On the Singularities of the Information Matrix and Multipath Change-Point Problems

Cited by 10 publications

References 50 publications

Variable selection for frailty transformation models with application to diabetic complications

Variable selection for frailty transformation models with application to diabetic complications

MEGH: A parametric class of general hazard models for clustered survival data

A semiparametric regression model under biased sampling and random censoring: A local pseudo‐likelihood approach

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