The problem of estimation of change-points in a sequence of Poisson random variables is approached by allowing the change-point to range over the continuous time interval (0; T). A maximum-likelihood point estimator is derived, along with a Bayesian-based interval estimator. Simulation studies connrm that the true coverage probability is close to the nominal one for several locations of the cha...

We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of Hölder-regularity (any Hurst parameter)...

Approximate Bayesian Computation (ABC) may be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Considering the first step as an explicit approximation of the likelihood allows, also, maximum-likelihood (or maximum-aposteriori) inference to be conducted, approximately, using essentially the same techniques. Such an approach is developed...

We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of Holder-regularity (any Hurst parameter...

The least weighted squares estimator is a well known technique in robust regression. Its likelihood analogy in logistic regression is the maximum weighted likelihood estimator, proposed in Vandev and Neykov (1998) and Mueller and Neykov (2003). This article mentions already proved properties, shows its inconsistency and compare it to the other estimators by an extensive simulation. Introduction...

The efficiency of the MLE is demonstrated indirectly by using the following theorem. Theorem [7, p. ZSS]: If an estimator exists such that equality is satisfied in the Cramer-Rao inequality, it can be determined as a solution of the maximum likelihood equation. We will show that such an estimator exists. This implies that the covariance matrix of the MLE is given by the inverse of the Fisher in...

We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we presen...

For 1 dimension reduction in l1, the method of Cauchy random projections multiplies the original data matrix A ∈ R with a random matrix R ∈ R (k ≪ min(n,D)) whose entries are i.i.d. samples of the standard Cauchy C(0, 1). Because of the impossibility results, one can not hope to recover the pairwise l1 distances in A from B = AR ∈ R, using linear estimators without incurring large errors. Howev...

The paper addresses the problem of determining the Cramer–Rao lower bounds (CRLBs) for noise and change-point parameters, for steplike signals corrupted by multiplicative and/or additive white noise. Closed-form expressions for the signal and noise CRLBs are 5rst derived for an ideal step with a known change point. For an unknown change-point, the noise-free signal is modeled by a sigmoidal fun...

Change point estimation is as an effective method for identifying the time of a change in production and service processes. In most of the statistical quality control literature, it is usually assumed that the quality characteristic of interest is independently and identically distributed over time. It is obvious that this assumption could be easily violated in practice. In this paper, we use m...