JournalTOCs

Japanese Journal of Statistics and Data Science
Number of Followers: 0

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2520-8756 - ISSN (Online) 2520-8764
Published by Springer-Verlag

[2468 journals]

Applications of Population Sampling to Insurance Ratemaking and Reserving
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  Abstract: Abstract This paper explores the underutilized application of population sampling in the realm of actuarial science, a field where these statistical methodologies have been traditionally overlooked. Focusing on two distinct applications within insurance ratemaking and reserving, we unveil innovative approaches to address challenges in actuarial contexts and provide valuable insights into advancing methodologies in the field. The first application introduces population sampling as a solution to the computational complexities inherent in credibility premium calculation, particularly under Bayesian regression models. By combining population sampling with surrogate modeling, we present a method to manage computation challenges effectively. The second application delves into incurred but not reported reserves, challenging the conventional Chain–Ladder method and individual reserving models by incorporating population sampling. Proposing a reserve estimator based on inverse probability weighting techniques, we demonstrate a statistically robust, distribution-free method for IBNR reserving, emphasizing the integration of granular policyholder information
  PubDate: 2024-08-07
  DOI: 10.1007/s42081-024-00260-3
q-Generalization of Nakagami distribution with applications
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  Abstract: Abstract The standard Nakagami (NK) distribution is a two-parameter distribution applicable in various disciplines, such as, communication engineering, hydrology, medical imaging etc. We present NK distribution as maximum entropy probability distribution (MEPD) satisfying two moment constraints. The main objective of this article is q-generalization of NK distribution which is more useful for heavy tail datasets. We define q-NK distribution and discuss some of its statistical properties. We use the q-NK density function to obtain cumulative distribution function (cdf), moments and survival function. Datasets from four different domains are used to demonstrate the applicability of q-NK distribution. Finally, we compare the results with mixture and slash NK distribution.
  PubDate: 2024-07-29
  DOI: 10.1007/s42081-024-00265-y
Parametric estimation of stochastic differential equations via online
gradient descent
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  Abstract: Abstract We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the estimators over a family of stochastic differential equations. Theoretical guarantees for the estimation of stochastic differential equations with discrete observations by online gradient descent are novel to our best knowledge.
  PubDate: 2024-07-27
  DOI: 10.1007/s42081-024-00266-x
Reduced-bias estimator of the ruin probability in infinite time for
heavy-tailed distributions with index in the upper half of the unit
interval
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  Abstract: Abstract In insurance companies, the ruin probability is considered as the one of the main risk measures developed in risk theory, and the problems of its calculation and approximation have attracted a lot of attention. Statistical estimation have been investigated on the ruin probability in infinite time for heavy-tailed insurance loses. However, these estimation suffer heavily from under-coverage or have a bias problem. We therefore need another method for estimating the probability of ruin in infinite time for heavy-tailed losses. This is why, in this paper, we propose a reduced-bias estimator for the ruin probability in infinite time for heavy-tailed distributions with an index in the upper half of the unit interval. Our approach is based on a reduced-bias estimator for this specific index in the context of heavy-tailed distributions. Additionally, we demonstrate the behavior of the proposed estimator and compare it to the classical estimator in terms of bias and mean squared error. The simulation results clearly show that our bias reduction methodology performs well.
  PubDate: 2024-07-18
  DOI: 10.1007/s42081-024-00259-w
Estimation and backtesting of risk measures with emphasis on distortion
risk measures
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  Abstract: Abstract Statistical methodology has an important role to play in risk measurement. In this paper, we will review and discuss some statistical issues on risk measures. Examples we consider are value-at-risk, expected shortfall, expectiles, and distortion risk measures. Several methods of estimating these risk measures based on time series data have been proposed, and we will try to explain in some detail. Another main issue we would like to address is a problem of backtesting: the evaluation of risk measurement procedures using historical data, by comparing ex ante estimates of loss distributions or risk measures with the ex post realized losses. There have been several suggestions concerning backtestability of risk measures, which will be discuss in detail. We also examine and suggest backtesting procedures for predictive distributions, expected shortfall and distortion risk measures.
  PubDate: 2024-07-10
  DOI: 10.1007/s42081-024-00264-z
Bayesian and minimax estimators of loss
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  Abstract: Abstract We study the problem of loss estimation that involves for an observable \(X \sim f_{\theta }\) the choice of a first-stage estimator \(\hat{\gamma }\) of \(\gamma (\theta )\) , incurred loss \(L=L(\theta , \hat{\gamma })\) , and the choice of a second-stage estimator \(\hat{L}\) of L. We consider both: (i) a sequential version where the first-stage estimate and loss are fixed and optimization is performed at the second-stage level, and (ii) a simultaneous version with a Rukhin-type loss function designed for the evaluation of \((\hat{\gamma }, \hat{L})\) as an estimator of \((\gamma , L)\) . We explore various Bayesian solutions and provide minimax estimators for both situations (i) and (ii). The analysis is carried out for several probability models, including multivariate normal models \(N_d(\theta , \sigma ^2 I_d)\) with both known and unknown \(\sigma ^2\) , Gamma, univariate and multivariate Poisson, and negative binomial models, and relates to different choices of the first-stage and second-stage losses. The minimax findings are achieved by identifying a least favourable sequence of priors and depend critically on particular Bayesian solution properties, namely situations where the second-stage estimator \(\hat{L}(x)\) is constant as a function of x.
  PubDate: 2024-07-02
  DOI: 10.1007/s42081-024-00261-2
Dynamic factor models for claim reserving
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  Abstract: Abstract This study presents a new approach to claim reserving in the insurance industry using dynamic factor models (DFMs). Traditional methods often struggle to adapt to temporal variations in loss development, a gap that DFMs can effectively address. By employing DFMs on a multivariate time series of loss development factors (LDFs), we offer a more sensitive adaptation and understanding of loss development over time. Our methodology not only facilitates adjustment to trends in loss development but also provides clear explanations for the underlying reasons behind these trends. This aspect is crucial for actuaries, whose responsibilities include offering transparent and understandable reserve estimates. We apply the proposed DFMs to datasets from two different lines of business, demonstrating their ability to capture the temporal evolution of factors influencing loss development. The results indicate that our approach enhances fitting ability and provides deep insights into the dynamics of claim reserving. Furthermore, we assess the uncertainty in the ultimate loss amounts required for risk management to ensure financial stability and compliance with insurance regulatory requirements. This study contributes to the field of actuarial science by highlighting the potential of DFMs in enhancing the accuracy and reliability of claim reserving processes.
  PubDate: 2024-06-29
  DOI: 10.1007/s42081-024-00257-y
On the cost of risk misspecification in insurance pricing
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  Abstract: Abstract In the non-life insurance industry, pricing is often done relative to individual criteria of policyholders. Various classification algorithms are in use to categorize policyholders into risk classes defined by the insurer, but classification errors may result from this process. In the light of recent automatic classification practices, it becomes important to assess the risks caused by such errors. In this paper we examine the impact of risk class misspecifications for a simple situation with two risk types. We provide a mean-variance framework for quantitatively studying the insurer’s optimization problem of specifying premiums and we analyze the tradeoff of costs and benefits when classification error probabilities are known.
  PubDate: 2024-06-25
  DOI: 10.1007/s42081-024-00256-z
Bayesian projection of cohort healthy life expectancies with long-term
care insurance data
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  Abstract: Abstract Over the past few decades, life expectancy has increased across the world. However, such a rise in longevity appears to be accompanied by a decline in health at advanced ages. This paper investigates future changes in longevity and health status at advanced ages and their interdependence by constructing a multinomial logit model using Japan’s public long-term care insurance data. Given that the decline in mortality at older ages continues, healthy life expectancy has attracted attention as an indicator of good health and well-being instead of life expectancy. We project cohort healthy life expectancies at advanced ages using the smultinomial logit model. We adopt a Bayesian approach to take prediction error into account.
  PubDate: 2024-06-11
  DOI: 10.1007/s42081-024-00253-2
Likelihood-based instrumental variable methods for Cox proportional
hazards model
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  Abstract: Abstract The Cox proportional hazards model is widely used for analyzing time-to-event outcomes while adjusting for covariates. However, obtaining a consistent estimator can be challenging if certain covariates remain unobserved. Instrumental variable (IV) methods are frequently employed to address unmeasured covariates; however, standard IV methods cannot be applied to time-to-event outcomes without modification. In this study, we propose extending IV methods capable of handling binary, multivalue, or continuous treatments, as well as non-binary and multiple IVs, which has not been achieved by previous methods. Our approach leverages the frailty model to directly capture the variability of unmeasured covariates and allows for flexible treatment models. The proposed method outperforms previous approaches, as demonstrated by theoretical considerations and numerical experiments. Furthermore, we performed a real data analysis using health insurance claims data from Hiroshima Prefecture, Japan. The proposed method is expected to address the issue of unmeasured covariates in time-to-event outcomes across a wider range of scenarios. Additionally, it can serve as a type of sensitivity analysis to assess the influence of unmeasured covariates.
  PubDate: 2024-06-06
  DOI: 10.1007/s42081-024-00254-1
Test for high-dimensional outliers with principal component analysis
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  Abstract: Abstract We herein consider a test of outlier detection for high-dimensional, low-sample-size (HDLSS) data. Although outlier detection is a fundamental problem, it has not been extensively studied in the HDLSS setting. We derive asymptotic properties of the first principal component scores with outliers. We consider high-dimensional outlier detection by applying the asymptotic properties to the Grubbs test, a well-known method for testing outliers. Our results indicate that the test statistic provides preferable performance for both the size and power. Using this test procedure, we propose an algorithm to identify multiple outliers. We present an investigation of the theoretical properties of a sure independent screening and it can achieve complete identification of the outliers with high accuracy. Finally, we investigate the performance for both numerical studies and real data analyses as compared to available outlier detection methods in HDLSS settings. The proposed method exhibits superiority in terms of not only correctly detecting outliers, but also identifying a number of false identifications.
  PubDate: 2024-06-04
  DOI: 10.1007/s42081-024-00255-0
Semiparametric regression analysis of doubly censored recurrent event data
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  Abstract: Abstract Recurrent event data are common in survival and reliability studies, where a subject experiences the same type of event repeatedly. There are situations, in which the event of interest can be observed only if they belong to a window of observational range, leading to double censoring of recurrent event times. In this paper, we study recurrent event data subject to double censoring. We propose a proportional mean model for the analysis of doubly censored recurrent event data based on the mean function of the underlying recurrent event process. The estimators of the regression parameters and the baseline mean function are derived and their asymptotic properties are studied. A Monte Carlo simulation study is conducted to assess the finite sample behavior of the proposed estimators. Finally, the procedures are illustrated using two real-life data sets, one from a bladder cancer study and the other from a study on chronic granulomatous disease.
  PubDate: 2024-06-01
  DOI: 10.1007/s42081-023-00234-x
Non-minimaxity of debiased shrinkage estimators
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  Abstract: Abstract We consider the estimation of the p-variate normal mean of \(X\sim \mathcal {N}_p(\theta ,I)\) under the quadratic loss function. We investigate the decision theoretic properties of debiased shrinkage estimator, the estimator which shrinks towards the origin for smaller \(\Vert x\Vert ^2\) and which is exactly equal to the unbiased estimator X for larger \(\Vert x\Vert ^2\) . Such debiased shrinkage estimator seems superior to the unbiased estimator X, which implies minimaxity. However, we show that it is not minimax under mild conditions.
  PubDate: 2024-06-01
  DOI: 10.1007/s42081-023-00218-x
Shrinkage estimation with logarithmic penalties
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  Abstract: Abstract In this paper, we have developed a novel approach for deriving shrinkage estimators of means without assuming normality. Our method is based on the equation of the first-order condition with a logarithmic penalty, and it introduces both one-step and two-step shrinkage estimators. The one-step estimator closely resembles the James–Stein estimator, while the differentiable two-step estimator exhibits similar performance to the positive-part Stein estimator. Although the latter does not satisfy Baranchik’s conditions, both estimators can be demonstrated to be minimax under normality assumptions. Furthermore, we have extended this method to handle cases involving an unknown scale. We have successfully applied this approach to the simultaneous estimation of Poisson means.
  PubDate: 2024-06-01
  DOI: 10.1007/s42081-023-00225-y
Bivariate dynamic weighted cumulative residual entropy
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  Abstract: Abstract As a way to measure uncertainty, the cumulative residual entropy (CRE) was initially developed. Later came the dynamic version of CRE, called dynamic cumulative residual entropy (DCRE). The bivariate dynamic cumulative residual entropy (BDCRE), a more sophisticated version of this measure, was also presented. In this study, we introduce and investigate the features of a weighted version of BDCRE.
  PubDate: 2024-06-01
  DOI: 10.1007/s42081-023-00232-z
An adaptive singular value shrinkage for estimation problem of low-rank
matrix mean with unknown covariance matrix
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  Abstract: Abstract Matrix models which are constructed from a deterministic signal plus noise are used in variety of fields. In particular, it commonly happens that a signal matrix is of low-rank, however, the rank itself is unknown. In this paper, it is assumed that the noises are distributed as real normal or complex normal distributions, across columns are independently and identically distributed, and across rows of noise matrix are correlated. But the covariance matrix is unknown. For the problem of estimating a low-rank matrix, estimators with soft-thresholding singular values are considered and a formula to choose a threshold is proposed based on the celebrated SURE method and eigenvalue-calculus due to Stein (Proceedings of the Prague symposium on asymptotic statistics, vol II. Charles University, Prague, pp 345–381, 1973) who employed these methods for matrix estimation problem. Very few results are obtained here. However, the procedures proposed are expected to be useful for situations to occur in practice.
  PubDate: 2024-06-01
  DOI: 10.1007/s42081-023-00223-0
Machine learning and the James–Stein estimator
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  Abstract: Abstract It is now 62 years since the publication of James and Stein’s seminal article on the estimation of a multivariate normal mean vector. The paper made a spectacular first impression on the statistical community through its demonstration of inadmissability of the maximum likelihood estimator. It continues to be influential, but not for the initial reasons. Empirical Bayes shrinkage estimation, now a major topic, found its early justification in the James–Stein formula. Less obvious downstream topics include Tweedie’s formula and Benjamini and Hochberg’s false discovery rate algorithm. This is a short and mainly non-technical review of the James–Stein rule and its effects on the machine learning era of statistical innovation.
  PubDate: 2024-06-01
  DOI: 10.1007/s42081-023-00209-y
Special feature: Stein estimation and statistical shrinkage methods
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  PubDate: 2024-05-11
  DOI: 10.1007/s42081-024-00250-5
Outlier-robust parameter estimation for unnormalized statistical models
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  Abstract: Abstract Unnormalized statistical models are ubiquitous in modern statistical data analysis. Recent methods take a classification approach to estimate unnormalized models. However, the classification problem is often solved based on the maximum-likelihood estimation, which can be seriously hampered by the contamination of outliers. In this paper, we propose two outlier-robust methods for estimation of unnormalized statistical models. The proposed methods are developed by combining robust divergences with the classification approach, and their robustness is theoretically investigated based on influence function. Interestingly, our theoretical analysis reveals a counter-intuitive robustness of the proposed methods, and shows the importance of not only employing robust divergences but also taking the classification approach for outlier-robust estimation. Finally, we experimentally demonstrate that the proposed methods are robust against outliers.
  PubDate: 2024-02-06
  DOI: 10.1007/s42081-023-00237-8
Stein’s identities and the related topics: an instructive explanation on
shrinkage, characterization, normal approximation and goodness-of-fit
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  Abstract: Abstract The Stein-type identities are widely recognized for their substantial utility and potency in deriving shrinkage estimators improving on crude estimators in normal, gamma, Poisson, and negative binomial distributions. Additionally, these identities serve to characterize these distributions themselves. The Stein identities are also used to demonstrate normal approximation. Moreover, they are instrumental in constructing statistical tests to assess the goodness-of-fit for normality, exponentiality, and Poissonity of distributions. This article offers an instructive and comprehensive explanation of the applications of Stein-type identities in the aforementioned contexts.
  PubDate: 2024-01-31
  DOI: 10.1007/s42081-023-00239-6

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