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Arxiv.org
by Amir T. Payandeh Najafabadi; Saeed MohammadPour
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This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model's parameters. Then, such new model along with a Pareto mixture model have been employed to design an optimal rate--making system. Namely, this article employs number/size of reported claims of Iranian third party insurance dataset. Then, it employs the k-Inflated...
Topics: Statistics, Methodology
Source: http://arxiv.org/abs/1701.05452
Arxiv.org
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This article, in a first step, considers two Bayes estimators for the relativity premium of a given Bonus--Malus system. It then develops a linear relativity premium that closes, in the sense of weighted mean square error loss, to such Bayes estimators. In a second step, it supposes that the claim size distribution for a given Bonus--Malus system can be formulated as a finite mixture distribution. It then evaluates the base premium under a Bayesian framework for such a finite mixture...
Topics: Statistics, Methodology
Source: http://arxiv.org/abs/1701.05441
Arxiv.org
by Amir T. Payandeh Najafabadi; Ghobad Barmalzan; Shahla Aghaei
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This article provides a weighted model confidence set, whenever underling model has been misspecified and some part of support of random variable $X$ conveys some important information about underling true model. Application of such weighted model confidence set for local and mixture model confidence sets have been given. Two simulation studies have been conducted to show practical application of our findings.
Topics: Statistics, Applications
Source: http://arxiv.org/abs/1701.05455
Arxiv.org
by Amir T. Payandeh Najafabadi; Ali Panahi Bazaz
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A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy $f(\cdot).$ In the first step, it cuts...
Topics: Statistics, Risk Management, Methodology, Quantitative Finance
Source: http://arxiv.org/abs/1701.05447
Arxiv.org
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A reinsurance contract should address the conflicting interests of the insurer and reinsurer. Most of existing optimal reinsurance contracts only considers the interests of one party. This article combines the proportional and stop-loss reinsurance contracts and introduces a new reinsurance contract called proportional-stop-loss reinsurance. Using the balanced loss function, unknown parameters of the proportional-stop-loss reinsurance have been estimated such that the expected surplus for both...
Topics: Statistics, Risk Management, Methodology, Quantitative Finance
Source: http://arxiv.org/abs/1701.05450
Arxiv.org
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Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-specific variables that are related to both the treatment assignment and the outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity...
Topics: Statistics, Methodology
Source: http://arxiv.org/abs/1703.06086
Arxiv.org
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Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores close to zero or one, and therefore both theoretical and practical researchers suggest dropping units with extreme estimated propensity scores. We advance the literature in three directions. First, we clarify a conceptual issue of sample trimming by defining...
Topics: Statistics, Methodology
Source: http://arxiv.org/abs/1704.00666
Arxiv.org
by Shu Yang; Jae Kwang Kim
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Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation, the conventional bootstrap inference for matching estimators with fixed matches has been shown to be invalid due to the nonsmoothess nature of the matching estimator. We propose asymptotically valid replication variance estimation. The key strategy is to...
Topics: Statistics, Methodology
Source: http://arxiv.org/abs/1703.10256
Arxiv.org
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We consider causal inference from observational studies when confounders have missing values. When the confounders are missing not at random, causal effects are generally not identifiable. In this article, we propose a novel framework for nonparametric identification of causal effects with confounders missing not at random, but subject to instrumental missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounder values. We...
Topics: Statistics, Methodology
Source: http://arxiv.org/abs/1702.03951