Related papers: Bootstrap Consistency for the Mack Bootstrap
We revisit the famous Mack's model which gives an estimate for the conditional mean squared error of prediction of the chain-ladder claims reserves. We introduce a stochastic differential equation driven by a Brownian motion to model the…
The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…
Background and Objective: Uncertainty in non-linear mixed effect models is often assessed using the Fisher information matrix to derive the standard errors of estimation. The bootstrap is an alternative to the asymptotic method, with…
Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited…
The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss…
An insurance company is required to prepare a certain amount of money, called reserve, as a mean to pay its policy holders claims in the future. There are several types of reserve, one of them is IBNR reserve, for which the payments are…
The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and…
Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…
For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap…
This paper studies a fixed-design residual bootstrap method for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Expected Shortfall. For a general class of volatility models the bootstrap is shown to be…
It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations.…
The partially linear binary choice model can be used for estimating structural equations where nonlinearity may appear due to diminishing marginal returns, different life cycle regimes, or hectic physical phenomena. The inference procedure…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
The bootstrap variance estimate is widely used in semiparametric inferences. However, its theoretical validity is a well known open problem. In this paper, we provide a {\em first} theoretical study on the bootstrap moment estimates in…