In this paper, we present an interpretation of the Maximum Likelihood Estimator (MLE) and the Delogne-Kåsa Estimator (DKE) for circle-parameter estimation via convolution. Under a certain model for theoretical images, this convolution is an exact description of the MLE. We use our convolution based MLE approach to find good starting estimates for the parameters of a circle, that is, the centre ...

This paper develops a simple and computationally efficient parametric approach to the estimation of general hidden Markov models (HMMs). For non-Gaussian HMMs, computation maximum likelihood estimator (MLE) involves high-dimensional integral that has no analytical solution can be difficult accurately. We develop new alternative method based on theory estimating functions deconvolution strategy....

In some statistical process control applications, the combination of both variable and attribute quality characteristics which are correlated represents the quality of the product or the process. In such processes, identification the time of manifesting the out-of-control states can help the quality engineers to eliminate the assignable causes through proper corrective actions. In this paper, f...

As you learned in previous courses, if we have a statistical model we can often estimate unknown “parameters” by the maximum likelihood principle. Suppose we have independent, but not necessarily identically distributed, data. Namely, we model the data {Yi}i=1 as independent random variables with densities (with respect to a common dominating measure) given by pi(·; θ), where θ is an unknown “p...

We study optimal and suboptimal decentralized estimators in wireless sensor networks over orthogonal multipleaccess fading channels in this paper. Considering multiple-bit quantization for digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case o...

Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hen...

let be a random sample from a normal distribution with unknown mean and known variance the usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. in many practical situations, is known in advance to lie in an interval, say for some in this case, the maximum likelihood estimator changes and d...

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...

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0, d, 0) model is well known to be asymptotically N(0, 6/π). This paper develops a second order asymptotic expansion to the distribution of this statistic. The correction term for the density is shown to be independent of d, so that the MLE is second order pivotal for d. This feature of the MLE ...

The Pareto distribution is often used in many areas of economics to model the right tail of heavytailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution– the maximum likelihood estimator (MLE) – is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years...