Double One-sided Cross-validation of Local Linear Hazards

Gámiz, María Luz; Mammen, Enno; Miranda, María Dolores Martínez; Nielsen, Jens Perch

doi:10.1111/rssb.12133

Cited by 10 publications

(31 citation statements)

References 42 publications

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“…The asymptotic behavior of bandwidths from cross-validation (see Rudemo (1982), Bowman (1984) and Hall (1983)) and double one-sided cross-validation (DO-validation, see Hart and Yi (1998), Martínez-Miranda et al (2009)) for the counting process estimatorf h,C is given in Hiabu et al (2016) where the estimator is applied on data with a data-driven bandwidth. Cross-validation and DO-validation for the hazard estimatorα h,R that is used for the computation off h,H and full asymptotics of the resulting 405 bandwidths are given in Gámiz et al (2016). However, data-driven bandwidth selection for the structured histogram approach and for the bias corrected versions of the counting process density and hazard estimators are not covered yet in literature.…”

Section: Simulation Studymentioning

confidence: 99%

“…This approach describes a sieves estimator since we get less aggregated histograms as pre-estimators with decreasing bandwidth δ but the choice δ = 0 is not possible. See Martínez-Miranda et al (2013) for a review 305 of other sieves methods for two-dimensional multiplicative in-sample forecasting and Gámiz et al (2016) for a pre-binned local linear hazard estimator.…”

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confidence: 99%

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A comparison of in-sample forecasting methods

Bischofberger

Hiabu

Mammen

et al. 2019

Computational Statistics & Data Analysis

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In-sample forecasting is a recent continuous modification of well-known forecasting methods based on aggregated data. These aggregated methods are known as age-cohort methods in demography, economics, epidemiology and sociology and as chain ladder in non-life insurance. Data is organized in a two-way table with age and cohort as indices, but without measures of exposure. It has recently been established that such structured forecasting methods based on aggregated data can be interpreted as structured histogram estimators. Continuous in-sample forecasting transfers these classical forecasting models into a modern statistical world including smoothing methodology that is more efficient than smoothing via histograms. All in-sample forecasting estimators are collected and their performance is compared via a finite sample simulation study.All methods are extended via multiplicative bias correction. Asymptotic theory is being developed for the histogram-type method of sieves and for the multiplicatively corrected estimators. The multiplicative bias corrected estimators improve all other known in-sample forecasters in the simulation study. The density projection approach seems to have the best performance with forecasting based on survival densities being the runner-up. not reported) claims is often solved via model (2): For each past claim, one considers the date (cohort i) when the accident had happened and the delay (age k) there was until the claim was reported to the insurer.Hence, cohort and age satisfy i + k − 1 ≤ today; given a certain year-wise aggregation. This information is then used to estimate the number of future claims µ ik , i + k − 1 > today, for accidents in the past, i ≤ today.Under model (2), the parameters α i and β k for each cohort i and age k can be estimated from past data. 50Assuming a maximum delay (usually 7 to 10 years in practice, depending on the business line), the estimates of the parameters can be used to forecast the number of future claims with i + k − 1 > today. More details of this age-cohort-reserving example are given in the recent contribution Harnau and Nielsen (2018) and are also included in the highly-cited overview paper of actuarial reserving (England and Verrall, 2002).Other examples where no significant period effect has been found include among many others cancer stud-55 ies (Leung et al., 2002;Remontet et al., 2003), returns due to education (Duraisamy, 2002), unemployment numbers (Wilke, 2017), mesothelioma mortality (Peto et al., 1995;Martínez-Miranda et al., 2014).Given the importance of age-period-cohort models and age-cohort models, it is surprising that continuous versions have not been considered much in the literature. Continuous modeling avoids inefficient pre-smoothing and is in line with recent trends around big data and the drive of modeling and understanding 60 every individual separately. Modeling every individual separately, possibly with additional covariates, results in the estimation of a large number of parameters. An increase of dimension means that ...

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Section: Simulation Studymentioning

confidence: 99%

mentioning

confidence: 99%

A comparison of in-sample forecasting methods

Bischofberger

Hiabu

Mammen

et al. 2019

Computational Statistics & Data Analysis

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“…On the basis of studies of bootstrap estimators in similar tail estimation problems, such as Hall (), Hall and Weissman () and Gámiz et al . (), we conjecture that estimator is asymptotically consistent.…”

Section: Data‐driven Methods To Select the Censoring Proportionmentioning

confidence: 71%

“…This serves as an empirical assessment of the bootstrap procedure, and we shall address the asymptotic properties of this bootstrap estimation in future work. On the basis of studies of bootstrap estimators in similar tail estimation problems, such as Hall (1990), Hall and Weissman (1997) and Gámiz et al (2016), we conjecture that estimator (4) is asymptotically consistent.…”

Section: Amount Of Censoring Selection Via the Bootstrapmentioning

confidence: 87%

Using Artificial Censoring to Improve Extreme Tail Quantile Estimates

Liu

Salibián‐Barrera

Zamar

et al. 2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Under certain regularity conditions, maximum‐likelihood‐based inference enjoys several optimality properties, including high asymptotic efficiency. However, if the distribution of the data deviates slightly from the model proposed, the statistical properties of inference methods based on maximum likelihood can quickly deteriorate. We focus on the situation when the interest lies in one of the tails of the distribution, e.g. when we are estimating a high or low quantile. In this case, it may be natural, if slightly unorthodox, to consider models that fit well the corresponding tail of the sample, rather than its whole range. For example, if we are interested in estimating the fifth percentile, we can pretend that all observations above the 10th percentile have been censored and fit a parametric censored model to the lower tail of the sample. Such an approach, which we call ‘artificial censoring’, has been studied in the engineering literature. We study a data‐dependent method to select the amount of artificial censoring and show that it compares favourably with the optimally chosen (‘oracle’) method, which is generally unavailable in practice. We also show that the artificial censoring approach can be applied to estimate tail dependence parameters in copula models, and that it performs well both in simulation and in real data studies.

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“…Mean integrated squared error ISE Integrated squared error SSB Smoothed stationary bootstrap SMBB Smoothed moving blocks bootstrap iid Independent and identically distributed h DO DO-validation bandwidth selector for hazard rate estimation (see [10]) h * GCM González-Manteiga, Cao, Marron bandwidth selector for hazard rate estimation (see [11]) h PI Plug-in bandwidth selector for bandwidth selection with dependent data (see [12]) h CV l Leave-(2l + 1)-out cross-validation for density estimation (see [13]) h SMCV Modified cross validation for density estimation with dependent data (see [8]) h PCV Penalized cross validation for density estimation with dependent data (see [8]) h CV Cross validation bandwidth selector for hazard rate estimation (see [14]) h MISE Bandwidth selector which minimizes the theoretical MISE(h)…”

Section: Misementioning

confidence: 99%

Computationally Efficient Bootstrap Expressions for Bandwidth Selection in Nonparametric Curve Estimation

Barbeito

Cao

2018

XoveTIC Congress 2018

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Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data (smoothed stationary bootstrap and smoothed moving blocks bootstrap), and (2) nonparametric kernel hazard rate estimation (smoothed bootstrap). In these contexts, four new bandwidth parameter selectors are proposed based on closed bootstrap expressions of the MISE of the kernel density estimator (case 1) and two approximations of the kernel hazard rate estimation (case 2). These expressions turn out to be very useful since Monte Carlo approximation is no longer needed. Finally, these smoothing parameter selectors are empirically compared with the already existing ones via a simulation study.

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Double One-sided Cross-validation of Local Linear Hazards

Cited by 10 publications

References 42 publications

A comparison of in-sample forecasting methods

A comparison of in-sample forecasting methods

Using Artificial Censoring to Improve Extreme Tail Quantile Estimates

Computationally Efficient Bootstrap Expressions for Bandwidth Selection in Nonparametric Curve Estimation

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