Optimal tuning parameter estimation in maximum penalized likelihood method

2008 ◽  
Vol 62 (3) ◽  
pp. 413-438 ◽  
Author(s):  
Masao Ueki ◽  
Kaoru Fueda
Keyword(s):  
Parameter Estimation ◽  
Penalized Likelihood ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Optimal Tuning ◽  
Maximum Penalized Likelihood

Local influence for elliptical partially varying-coefficient model

2017 ◽  
Vol 18 (2) ◽  
pp. 149-174
Author(s):  
Germán Ibacache-Pulgar ◽  
Sebastián Reyes
Keyword(s):  
Penalized Likelihood ◽  
Smoothing Splines ◽  
Local Influence ◽  
Likelihood Method ◽  
Varying Coefficient Models ◽  
Varying Coefficient Model ◽  
Real Dataset ◽  
Varying Coefficient ◽  
Maximum Penalized Likelihood ◽  
Heavy Tailed

In this article, we extend varying-coefficient models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. This class of models includes all symmetric continuous distributions, such as Student-t, Pearson VII, power exponential and logistic, among others. Estimation is performed by maximum penalized likelihood method and by using smoothing splines. In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data, the local influence curvatures are derived and some diagnostic graphics are proposed. A real dataset previously analysed by using varying-coefficient models with normal errors is reanalysed under varying-coefficient models with heavy-tailed errors.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

The Shark Attack Problem Revisited: MCMC with the Metropolis Algorithm

2019 ◽  
pp. 193-211
Author(s):  
Therese M. Donovan ◽  
Ruth M. Mickey
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Markov Chain ◽  
Posterior Distribution ◽  
Metropolis Algorithm ◽  
Tuning Parameter ◽  
The Mean ◽  
Shark Attacks ◽  
Mcmc Approach

In this chapter, the “Shark Attack Problem” (Chapter 11) is revisited. Markov Chain Monte Carlo (MCMC) is introduced as another way to determine a posterior distribution of λ‎, the mean number of shark attacks per year. The MCMC approach is so versatile that it can be used to solve almost any kind of parameter estimation problem. The chapter highlights the Metropolis algorithm in detail and illustrates its application, step by step, for the “Shark Attack Problem.” The posterior distribution generated in Chapter 11 using the gamma-Poisson conjugate is compared with the MCMC posterior distribution to show how successful the MCMC method can be. By the end of the chapter, the reader should also understand the following concepts: tuning parameter, MCMC inference, traceplot, and moment matching.

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