The problem of parameter estimation is considered for the twostate telegraph process, observed in white Gaussian observation noise. An online one-step Maximum Likelihood Estimator (MLE) process is constructed, using a preliminary Method of Moments (MM) estimator. The obtained estimation procedure is shown to be asymptotically normal and efficient in the large sample regime. MSC 2000 Classificat...

In this study, I investigate the necessary condition for the consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of pa...

We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to compute the exact likelihood using the Kalm...

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 classic statistical method for modelling the rates and proportions is beta regression model (BRM). standard maximum likelihood estimator (MLE) used to estimate coefficients of BRM. However, this MLE very sensitive when regressors are linearly correlated. Therefore, study introduces a new ridge (BRR) as remedy problem instability MLE. We mean squared error properties BRR analytically then ba...

A Hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. Based on hybrid censored samples, this paper deals with the inference on R = P (X > Y ), when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape parameter. The maximum likelihood estimator (MLE), and the approximate MLE (AMLE) of R are obtained. The asymptotic ...

The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in interval (0, 1), such as rates, proportions, percentages fractions. Generally, parameters of BRM are estimated by method maximum likelihood estimation (MLE). However, MLE does not offer accurate reliable estimates explanatory variables correlated. To solve this problem, ridge Liu est...

We provide in this paper asymptotic theory for the multivariate GARCH(p, q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a stationary and ergodic solution to the multivariate GARCH(p, q) process. We prove asymptotic norma...

3.1 Maximum likelihood estimates — in exponential families. Let (X, B) be a measurable space and {P θ , θ ∈ Θ} a measurable family of laws on (X, B), dominated by a σ-finite measure v. Let f (θ, x) be a jointly measurable version of the density (dP θ /dv)(x) by Theorem 1.3.3. For each x ∈ X, a maximum likelihood estimate (MLE) of θ is any θ ˆ = θ ˆ (x) such that f (ˆ θ, x) = sup{f (φ, x) : φ ∈ ...

When a change occurs in a process, one expects to receive a signal from a control chart as quickly as possible. Upon the receipt of signal from the control chart a search for identifying the source of disturbance begins. However, searching for assignable cause around the signal time, due to the fact that the disturbance may have manifested itself into the rocess sometimes back, may not always l...