Sequential Maximum Likelihood Estimation for the Parameter of the Linear Drift Term of the Rayleigh Diffusion Process

2015 ◽  
Vol 16 (1) ◽  
pp. 35-41
Author(s):  
Nenghui Kuang ◽  
Chunli Li ◽  
Huantian Xie
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Diffusion Process ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Linear Drift ◽  
Drift Term ◽  
Strongly Consistent ◽  
Drift Parameter

AbstractIn this paper, we investigate the properties of a sequential maximum likelihood estimator of the unknown linear drift parameter for the Rayleigh diffusion process. The estimator is shown to be closed, unbiased, normally distributed and strongly consistent. Finally a simulation study is presented to illustrate the efficiency of the estimator.

scholarly journals On the Maximum Likelihood Estimation of Extreme Value Index Based on k-Record Values

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Abderrahim Louzaoui ◽  
Mohamed El Arrouchi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimation ◽  
Record Values ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Likelihood Estimator ◽  
Consistent Solution ◽  
Strongly Consistent

In this paper, we study the existence and consistency of the maximum likelihood estimator of the extreme value index based on k-record values. Following the method used by Drees et al. (2004) and Zhou (2009), we prove that the likelihood equations, in terms of k-record values, eventually admit a strongly consistent solution without any restriction on the extreme value index, which is not the case in the aforementioned studies.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Maximum likelihood estimation of the Latent Class Model through model boundary decomposition

2019 ◽  
Vol 10 (1) ◽  
pp. 51-84 ◽  
Author(s):  
Elizabeth Allman ◽  
Hector Banos Cervantes ◽  
Serkan Hosten ◽  
Kaie Kubjas ◽  
Daniel Lemke ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Maximum Likelihood Estimator ◽  
Latent Class ◽  
Latent Class Model ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Class Model ◽  
Small Models

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.

scholarly journals Maximum likelihood estimation for cooperative sequential adsorption

2009 ◽  
Vol 41 (04) ◽  
pp. 978-1001 ◽  
Author(s):  
Mathew D. Penrose ◽  
Vadim Shcherbakov
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Thermodynamic Limit ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Current Configuration ◽  
Sequential Adsorption ◽  
Spatial Locations

We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝ d , and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function β k of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters β k (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.

scholarly journals Maximum likelihood estimation of the geometric niche preemption model

2021 ◽  
Author(s):  
Jan Graffelman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Ecological Model ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Likelihood Estimator ◽  
Two Samples ◽  
Multinomial Sampling ◽  
Geometric Decay

AbstractThe geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May’s equation. This article proposes a maximum likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.

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