Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelatio...

We derive two convergence results for a sequential alternating maximization procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator by Andresen and Spokoiny (2013), that means a finite sample Wilks and Fisher theorem. Further ...

We analyze the relationship between a Minimum Description Length (MDL) estimator (posterior mode) and a Bayes estimator for exponential families. We show the following results concerning these estimators: a) Both the Bayes estimator with Jeffreys prior and the MDL estimator with the uniform prior with respect to the expectation parameter are nearly equivalent to a bias-corrected maximum-likelih...

The Maximum Likelihood Estimator (MLE) has commonly been used to estimate the unknown parameters in the finite mixture of distributions via the expectationmaximization (EM) algorithm. However, the MLE can be very sensitive to outliers in the data. Various approaches that have incorporated robustness in fitting mixtures and clustering are discussed. Special attention is given to the Weighted Tri...

This paper presents an optimum plan for simple (two stresses) time-step-stress accelerated life tests under the log-logistic model considered appropriate for insulating materials. A log-logistic life distribution with a median that is a log-linear function of stress, and a cumulative exposure model are assumed. The optimum test plan is obtained by minimizing the asymptotic variance of the maxim...

We present an improved version of random projections that takes advantage of marginal norms. Using a maximum likelihood estimator (MLE), marginconstrained random projections can improve estimation accuracy considerably. Theoretical properties of this estimator are analyzed in detail.

In this paper we obtain robust estimators for copula parameters through the minimization of weighted goodness of ̄t statistics. Di®erent weight functions emphasize di®erent regions on the unit square and are able to handle di®erent locations of model violation. The resultingWMDE estimators are compared to the classical maximum likelihood estimatorsMLE, and to their weighted version WMLE, an est...

A hazard rate λ(t) is assumed to be of the shape of the “first” part of a “bathtub” model, i.e., λ(t) is non-increasing for t < τ and is constant for t ≥ τ . The isotonic maximum likelihood estimator of the hazard rate is obtained and its asymptotic distribution is investigated. This leads to the maximum likelihood estimator and a confidence interval for a new version of the change point parame...

An exponentiated Pareto distribution is defined. We then consider maximum likelihood estimator (MLE) of the threshold parameter β with known parameters α and c for the exponentiated Pareto distribution in (2.1) and then obtain the MLE of the tail-probability of the exponentiated Pareto distribution. Finally, we consider MLE of reliability in two independent exponentiated Pareto distributions.

A recent short communication [1] showed that an orthogonal subspace projection (OSP) classifier developed for hyperspectral image classification in [2] was equivalent to a maximum likelihood estimator (MLE) resulting from a standard method of linear unmixing. It further concluded that the MLE subsumed the OSP classifier in spite of a constant difference in their magnitudes. Coincidentally, the ...