On the Choice of the Optimal Tuning Parameter in Robust One-Shot Device Testing Analysis

Castilla, Elena; Chocano, Pedro J.

doi:10.1007/978-3-031-04137-2_16

Cited by 3 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…\end{align}$$In practical applications, this tuning parameter is typically chosen from a grid of potential values ranging between 0 and 1, since it is uncommon to work with a tuning parameter

\lambda

greater than 1. This aligns with 25 , which employed different loss functions relating empirical and theoretical model probabilities to choose the optimal tuning parameter inside the family of minimum DPD estimators in this context.…”

Section: Minimum Phi‐divergence Estimatorsmentioning

confidence: 64%

A new estimation approach based on phi‐divergence measures for one‐shot device accelerated life testing

Castilla

2024

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

One‐shot device testing data are used only once and they get destroyed when tested. As these products usually have large mean times to failure under normal operating conditions, accelerated life tests are commonly used to infer their lifetime distribution. While much work has been done to determine the maximum likelihood estimates (MLEs) of model parameters for one‐shot device accelerated life testing, the efficiency of these methods may not be guaranteed for small to moderate sample sizes. In this paper, we develop new estimators and confidence intervals based on phi‐divergences, we show that they outperform the conventional MLE under different lifetime distributions and present an example to illustrate all the inferential methods developed here.

show abstract

“…\end{align}$$In practical applications, this tuning parameter is typically chosen from a grid of potential values ranging between 0 and 1, since it is uncommon to work with a tuning parameter

\lambda

Section: Minimum Phi‐divergence Estimatorsmentioning

confidence: 64%

A new estimation approach based on phi‐divergence measures for one‐shot device accelerated life testing

Castilla

2024

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…The proof of Proposition 99 works analogously to the proof of Proposition 72, by replacing Theorem 22(a) with (196). Proposition 101: In the above set-up, one has…”

Section: A Naive Estimators Of Min and Argmin -Base-divergence-method...mentioning

confidence: 95%

“…is the random vector constructed from (i) an auxiliary deterministic probability vector P aux ∈ S K >0 inducing index blocks I 125) respectively ( 126)). From (196), we obtain for large m the minimal-empirical-risk approximation (cf. ( 147))…”

Section: A Naive Estimators Of Min and Argmin -Base-divergence-method...mentioning

confidence: 99%

See 1 more Smart Citation

A Precise Bare Simulation Approach to the Minimization of Some Distances. I. Foundations

Broniatowski¹,

Stummer

2023

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition. In our previous paper "A precise bare simulation approach to the minimization of some distances. I. Foundations", we obtained such kind of constrained optima by a new dimension-free precise bare (pure) simulation method, provided basically that (i) the underlying directed distance is of f −divergence type, and that (ii) this can be connected to a light-tailed probability distribution in a certain manner. In the present paper, we extend this approach such that constrained optimization problems of a very huge amount of directed distances and generalized entropies -and beyond -can be tackled by a newly developed dimension-free extended bare simulation method, for obtaining both optima as well as optimizers. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). For instance, we cover constrained optimizations of arbitrary f −divergences, Bregman distances, scaled Bregman distances and weighted ℓr−distances. The potential for wide-spread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences in various different research fields (which may also serve as an interdisciplinary interface).

show abstract

Robust estimation based on one-shot device test data under log-normal lifetimes

Castilla

2023

Statistics

View full text Add to dashboard Cite

On the Choice of the Optimal Tuning Parameter in Robust One-Shot Device Testing Analysis

Cited by 3 publications

References 15 publications

A new estimation approach based on phi‐divergence measures for one‐shot device accelerated life testing

A new estimation approach based on phi‐divergence measures for one‐shot device accelerated life testing

A Precise Bare Simulation Approach to the Minimization of Some Distances. I. Foundations

Robust estimation based on one-shot device test data under log-normal lifetimes

Contact Info

Product

Resources

About