Non-Gaussian bifurcating models and quasi-likelihood estimation

2004 ◽  
Vol 41 (A) ◽  
pp. 55-64 ◽  
Author(s):  
I. V. Basawa ◽  
J. Zhou
Keyword(s):  
General Class ◽  
Cell Lineage ◽  
Likelihood Estimation ◽  
Random Coefficient ◽  
Model Parameters ◽  
Large Sample ◽  
Poisson Models ◽  
Bivariate Exponential ◽  
Non Gaussian ◽  
Quasi Likelihood Estimation

A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasi-likelihood estimation for the model parameters and large-sample properties of the estimates are discussed.

Non-Gaussian bifurcating models and quasi-likelihood estimation

2004 ◽  
Vol 41 (A) ◽  
pp. 55-64 ◽  
Author(s):  
I. V. Basawa ◽  
J. Zhou
Keyword(s):  
General Class ◽  
Cell Lineage ◽  
Likelihood Estimation ◽  
Random Coefficient ◽  
Model Parameters ◽  
Large Sample ◽  
Poisson Models ◽  
Bivariate Exponential ◽  
Non Gaussian ◽  
Quasi Likelihood Estimation

A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasi-likelihood estimation for the model parameters and large-sample properties of the estimates are discussed.

scholarly journals Maximum approximate likelihood estimation of general continuous-time state-space models

2022 ◽  
pp. 1471082X2110657
Author(s):  
Sina Mews ◽  
Roland Langrock ◽  
Marius Ötting ◽  
Houda Yaqine ◽  
Jost Reinecke
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Likelihood Estimation ◽  
The State ◽  
State Space Models ◽  
State Transitions ◽  
Model Parameters ◽  
State Process ◽  
Approximate Likelihood ◽  
Non Gaussian

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

scholarly journals Maximum Likelihood Estimation of the VAR(1) Model Parameters with Missing Observations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Helena Mouriño ◽  
Maria Isabel Barão
Keyword(s):  
Stochastic Process ◽  
Missing Data ◽  
Maximum Likelihood ◽  
Moving Average ◽  
Practical Importance ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Missing Observations ◽  
Data Set ◽  
The Impact

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.

scholarly journals Agricultural drought periods analysis by using nonhomogeneous poisson models and regionalization of appropriate model parameters

2021 ◽  
Vol 73 (1) ◽  
pp. 1-15
Author(s):  
Asad Ellahi ◽  
Ijaz Hussain ◽  
Muhammad Zaffar Hashmi ◽  
Mohammed Mohammed Ahmed Almazah ◽  
Fuad S. Al-Duais
Keyword(s):  
Agricultural Drought ◽  
Model Parameters ◽  
Poisson Models
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