Construction Of Bootstrap Confidence Intervals Research Articles

Mean regression model for the zero-truncated Poisson distribution and its generalization

Zero-truncated count data (e.g., days of staying in hospital; survival weeks of female patients with breast cancer) often arise in various fields such as medical studies. To model such data, the zero-truncated Poisson (ZTP) distribution is commonly utilized to investigate the relationship between the response counts and a set of covariates. For existing ZTP regression models, it is very hard to explain the regression coefficients β or it is quite difficult to perform a constrained optimization to calculate the maximum likelihood estimates (MLEs) of β. This paper aims to introduce a new mean regression model for the ZTP distribution with a clear interpretation about the regression coefficients. Because of a challenge that the original Poisson mean parameter λi cannot be expressed explicitly by the ZTP mean parameter μi, an embedded Newton–Raphson algorithm is developed to calculate the MLEs of regression coefficients. The construction of bootstrap confidence intervals is presented and three hypothesis tests (i.e., the likelihood ratio test, the Wald test and the score test) are considered. Furthermore, the ZTP mean regression model is generalized to the mean regression model for the k-truncated Poisson distribution. Simulation studies are conducted and two real data are analyzed to illustrate the proposed model and methods.

On the Construction of Bootstrap Confidence Intervals for Estimating the Correlation Between Two Time Series Not Sampled on Identical Time Points

Two important issues characterize the design of bootstrap methods to construct confidence intervals for the correlation between two time series sampled (unevenly or evenly spaced) on different time points: (i) ordinary block bootstrap methods that produce bootstrap samples have been designed for time series that are coeval (i.e., sampled on identical time points) and must be adapted; (ii) the sample Pearson correlation coefficient cannot be readily applied, and the construction of the bootstrap confidence intervals must rely on alternative estimators that unfortunately do not have the same asymptotic properties. In this paper it is argued that existing proposals provide an unsatisfactory solution to issue (i) and ignore issue (ii). This results in procedures with poor coverage whose limitations and potential applications are not well understood. As a first step to address these issues, a modification of the bootstrap procedure underlying existing methods is proposed, and the asymptotic properties of the estimator of the correlation are investigated. It is established that the estimator converges to a weighted average of the cross-correlation function in a neighborhood of zero. This implies a change in perspective when interpreting the results of the confidence intervals based on this estimator. Specifically, it is argued that with the proposed modification of the bootstrap, the existing methods have the potential to provide a useful lower bound for the absolute correlation in the non-coeval case and, in some special cases, confidence intervals with approximately the correct coverage. The limitations and implications of the results presented are demonstrated with a simulation study. The extension of the proposed methodology to the problem of estimating the cross-correlation function is straightforward and is illustrated with a real data example. Related applications include the estimation of the autocorrelation function and the periodogram of a time series.

Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion

Sensitivity analysis aims at quantifying influence of input parameters dispersion on the output dispersion of a numerical model. When the model evaluation is time consuming, the computation of Sobol' indices based on Monte Carlo method is not applicable and a surrogate model has to be used. Among all approximation methods, polynomial chaos expansion is one of the most efficient to calculate variance-based sensitivity indices. Indeed, their computation is analytically derived from the expansion coefficients but without error estimators of the meta-model approximation. In order to evaluate the reliability of these indices, we propose to build confidence intervals by bootstrap re-sampling on the experimental design used to estimate the polynomial chaos approximation. Since the evaluation of the sensitivity indices is obtained with confidence intervals, it is possible to find a design of experiments allowing the computation of sensitivity indices with a given accuracy.

ICONE19-43254 TOWARDS A BETTER UNDERSTANDING OF CLOGGED STEAM GENERATORS : A SENSITIVITY ANALYSIS OF DYNAMIC THERMOHYDRAULIC MODEL OUTPUT

Tube support plate clogging of steam generators affects their operating and requires frequent maintenance operations. A diagnosis method based on dynamic behaviour analysis is under development at EDF to provide means of optimisation of maintenance strategies. Previous work showed that the dynamic response to a power transient of the wide range level measurement contains informations about the clogging state of steam generators. The diagnosis method consists of comparisons of the measured dynamic response with simulations on a mono-dimensional dynamic steam generator model for various input clogging configurations. In order to assess the potential of this method, a sensitivity analysis has been conducted through a quasi-Monte Carlo scheme to compute sensitivity indices for each half tube support plate’s clogging ratio. Sensitivity indices are usually defined for scalar model outputs. Principal component analysis has been used to determine a small subset of variables that condense the information about the shape of the response curves. Finally, estimation variability was assessed by construction of bootstrap confidence intervals. The results showed that half of the preselected input variables have negligible influence and allowed to rank the most important ones. Interactions of input variables have been estimated to exert only a small influence on the output. The effects of clogging on the steam generator dynamics has been characterised qualitatively and quantitatively.

Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment

Motivated by applications in call center management, we propose a framework based on empirical process techniques for inference about waiting time and patience distributions in multiserver queues with abandonment. The framework rigorises heuristics based on survival analysis of independent and identically distributed observations by allowing correlated waiting times. Assuming a regenerative structure of offered waiting times, we establish asymptotic properties of estimators of limiting distribution functions and derived functionals. We discuss construction of bootstrap confidence intervals and statistical tests, including a simple bootstrap two-sample test for comparing patience distributions. A small simulation study and a real data example are presented.

A robust process capability index

The existing process capability indices (PCI's) assume that the distribution of the process being investigated is normal. For non-normal distributions, PCI's become unreliable in that PCI's may indicate the process is capable when in fact it is not. In this paper, we propose a new index which can be applied to any distribution. The proposed indexCf:, is directly related to the probability of non-conformance of the process. For a given random sample, the estimation of Cf boils down to estimating non-parametrically the tail probabilities of an unknown distribution. The approach discussed in this paper is based on the works by Pickands (1975) and Smith (1987). We also discuss the construction of bootstrap confidence intervals of Cf: based on the so-called accelerated bias correction method (BC a:). Several simulations are carried out to demonstrate the flexibility and applicability of Cf:. Two real life data sets are analyzed using the proposed index.

Analytical approximations for iterated bootstrap confidence intervals

Standard algorithms for the construction of iterated bootstrap confidence intervals are computationally very demanding, requiring nested levels of bootstrap resampling. We propose an alternative approach to constructing double bootstrap confidence intervals that involves replacing the inner level of resampling by an analytical approximation. This approximation is based on saddlepoint methods and a tail probability approximation of DiCiccio and Martin (1991). Our technique significantly reduces the computational expense of iterated bootstrap calculations. A formal algorithm for the construction of our approximate iterated bootstrap confidence intervals is presented, and some crucial practical issues arising in its implementation are discussed. Our procedure is illustrated in the case of constructing confidence intervals for ratios of means using both real and simulated data. We repeat an experiment of Schenker (1985) involving the construction of bootstrap confidence intervals for a variance and demonstrate that our technique makes feasible the construction of accurate bootstrap confidence intervals in that context. Finally, we investigate the use of our technique in a more complex setting, that of constructing confidence intervals for a correlation coefficient.