20,048 research outputs found
Probabilistic performance estimators for computational chemistry methods: the empirical cumulative distribution function of absolute errors
Benchmarking studies in computational chemistry use reference datasets to
assess the accuracy of a method through error statistics. The commonly used
error statistics, such as the mean signed and mean unsigned errors, do not
inform end-users on the expected amplitude of prediction errors attached to
these methods. We show that, the distributions of model errors being neither
normal nor zero-centered, these error statistics cannot be used to infer
prediction error probabilities. To overcome this limitation, we advocate for
the use of more informative statistics, based on the empirical cumulative
distribution function of unsigned errors, namely (1) the probability for a new
calculation to have an absolute error below a chosen threshold, and (2) the
maximal amplitude of errors one can expect with a chosen high confidence level.
Those statistics are also shown to be well suited for benchmarking and ranking
studies. Moreover, the standard error on all benchmarking statistics depends on
the size of the reference dataset. Systematic publication of these standard
errors would be very helpful to assess the statistical reliability of
benchmarking conclusions.Comment: Supplementary material: https://github.com/ppernot/ECDF
Reliability analysis of structural ceramic components using a three-parameter Weibull distribution
Described here are nonlinear regression estimators for the three-Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data
When, where and how to perform efficiency estimation
In this paper we compare two flexible estimators of technical efficiency in a cross-sectional setting: the nonparametric kernel SFA estimator of Fan, Li and Weersink (1996) to the nonparametric bias corrected DEA estimator of Kneip, Simar andWilson (2008). We assess the finite sample performance of each estimator via Monte Carlo simulations and empirical examples. We find that the reliability of efficiency scores critically hinges upon the ratio of the variation in efficiency to the variation in noise. These results should be a valuable resource to both academic researchers and practitioners.Bootstrap; Nonparametric kernel; Technical efficiency
When, Where and How to Perform Efficiency Estimation
In this paper we compare two flexible estimators of technical efficiency in a cross-sectional setting: the nonparametric kernel SFA estimator of Fan, Li and Weersink (1996) to the nonparametric bias corrected DEA estimator of Kneip, Simar and Wilson (2008). We assess the finite sample performance of each estimator via Monte Carlo simulations and empirical examples. We find that the reliability of efficiency scores critically hinges upon the ratio of the variation in efficiency to the variation in noise. These results should be a valuable resource to both academic researchers and practitioners.nonparametric kernel, technical efficiency, bootstrap
When, where and how to perform efficiency estimation
In this paper we compare two flexible estimators of technical efficiency in a cross-sectional setting: the nonparametric kernel SFA estimator of Fan, Li and Weersink (1996) to the nonparametric bias corrected DEA estimator of Kneip, Simar and Wilson (2008). We assess the finite sample performance of each estimator via Monte Carlo simulations and empirical examples. We find that the reliability of efficiency scores critically hinges upon the ratio of the variation in efficiency to the variation in noise. These results should be a valuable resource to both academic researchers and practitioners.Bootstrap, Nonparametric Kernel, Technical Efficiency
Change-Point Testing and Estimation for Risk Measures in Time Series
We investigate methods of change-point testing and confidence interval
construction for nonparametric estimators of expected shortfall and related
risk measures in weakly dependent time series. A key aspect of our work is the
ability to detect general multiple structural changes in the tails of time
series marginal distributions. Unlike extant approaches for detecting tail
structural changes using quantities such as tail index, our approach does not
require parametric modeling of the tail and detects more general changes in the
tail. Additionally, our methods are based on the recently introduced
self-normalization technique for time series, allowing for statistical analysis
without the issues of consistent standard error estimation. The theoretical
foundation for our methods are functional central limit theorems, which we
develop under weak assumptions. An empirical study of S&P 500 returns and US
30-Year Treasury bonds illustrates the practical use of our methods in
detecting and quantifying market instability via the tails of financial time
series during times of financial crisis
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