Using the likelihood depth, new consistent and robust tests for the parameters of the Weibull distribution are developed. Uncensored as well as type-I right-censored data are considered. Tests are given for the shape parameter and also the scale parameter of the Weibull distribution, where in...

Denecke and Müller (CSDA 55:2724–2738, <CitationRef CitationID="CR2">2011</CitationRef>) presented an estimator for the correlation coefficient based on likelihood depth for Gaussian copula and Denecke and Müller (J Stat Planning Inference 142: 2501–2517, <CitationRef CitationID="CR3">2012</CitationRef>) proved a theorem about the consistency of general estimators based on...</citationref></citationref>

This article investigates the application of depth estimators to crack growth models in construction engineering. Many crack growth models are based on the Paris–Erdogan equation which describes crack growth by a deterministic differential equation. By introducing a stochastic error term,...

Data depth provides a natural means to rank multivariate vectors with respect to an underlying multivariate distribution. Most existing depth functions emphasize a centre-outward ordering of data points, which may not provide a useful geometric representation of certain distributional features,...

In this paper, a novel projection-based depth based on the Rayleigh quotient, Rayleigh projection depth (RPD), is proposed. Although, the traditional projection depth (PD) has many good properties, it is indeed not practical due to its difficult computation, especially for the high-dimensional...

In the M-estimation theory developed by Huber (1964, Ann. Math. Statist.43, 1449-1458), the parameter under estimation is the value of [theta] which minimizes the expectation of what is called a discrepancy measure (DM) [delta](X, [theta]) which is a function of [theta] and the underlying...