scholarly journals Bayes Estimation of Two-Phase Linear Regression Model

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Mayuri Pandya ◽  
Krishnam Bhatt ◽  
Paresh Andharia
Keyword(s):  
Regression Model ◽  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Random Errors ◽  
Two Phase ◽  
Inference Problem ◽  
Bayes Estimates ◽  
Linex Loss

Let the regression model be Yi=β1Xi+εi, where εi are i. i. d. N (0,σ2) random errors with variance σ2>0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in slope, regression parameter β2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β1,β2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

scholarly journals Bayes Estimation of Change Point in Discrete Maxwell Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Mayuri Pandya ◽  
Hardik Pandya
Keyword(s):  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Maxwell Distribution ◽  
Bayes Estimators ◽  
Asymmetric Loss ◽  
Bayes Estimates

A sequence of independent lifetimes X1,…,Xm,Xm+1,…,Xn was observed from Maxwell distribution with reliability r1(t) at time t but later, it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in reliability r2(t) at time t. The Bayes estimators of m, θ1, θ2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

Empirical Bayes Estimation of Parameter of Burr-Type X Model under LINEX and Squared Error Loss Functions

2011 ◽  
Vol 403-408 ◽  
pp. 5273-5277
Author(s):  
Hai Ying Lan
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimate ◽  
Squared Error Loss ◽  
Bayes Estimates ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimate

The Empirical Bayes estimate of the parameter of Burr-type X distribution is contained .The estimate is obtained under squared error loss and Varian’s linear-exponential (LINEX) loss functions, and is compared with corresponding maximum likelihood and Bayes estimates. Finally, a Monte Carlo numerical example is given to illustrate our results.

scholarly journals Bayes Estimation of a Two-Parameter Geometric Distribution under Multiply Type II Censoring

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
J. B. Shah ◽  
M. N. Patel
Keyword(s):  
Geometric Distribution ◽  
Correct Choice ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Type Ii ◽  
Expected Loss ◽  
Bayes Estimators ◽  
Linex Loss ◽  
Type Ii Censored Data ◽  
Two Parameter

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

Detecting a Change in School Performance: A Bayesian Analysis for a Multilevel Join Point Problem

2001 ◽  
Vol 26 (4) ◽  
pp. 443-468 ◽  
Author(s):  
Yeow Meng Thum ◽  
Suman K. Bhattacharya
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Test Scores ◽  
Evaluation Studies ◽  
Regression Function ◽  
Hierarchical Bayes ◽  
Bayes Estimation ◽  
Point Problem ◽  
Two Phase ◽  
Multilevel Linear Regression

A substantial literature on switches in linear regression functions considers situations in which the regression function is discontinuous at an unknown value of the regressor, Xk , where k is the so-called unknown “change point.” The regression model is thus a two-phase composite of yi ∼ N(β01 + β11xi, σ12), i=1, 2,..., k and yi ∼ N(β02 + β12xi, σ22), i= k + 1, k + 2,..., n. Solutions to this single series problem are considerably more complex when we consider a wrinkle frequently encountered in evaluation studies of system interventions, in that a system typically comprises multiple members (j = 1, 2, . . . , m ) and that members of the system cannot all be expected to change synchronously. For example, schools differ not only in whether a program, implemented system-wide, improves their students’ test scores, but depending on the resources already in place, schools may also differ in when they start to show effects of the program. If ignored, heterogeneity among schools in when the program takes initial effect undermines any program evaluation that assumes that change points are known and that they are the same for all schools. To describe individual behavior within a system better, and using a sample of longitudinal test scores from a large urban school system, we consider hierarchical Bayes estimation of a multilevel linear regression model in which each individual regression slope of test score on time switches at some unknown point in time, kj. We further explore additional results employing models that accommodate case weights and shorter time series.

scholarly journals WEIGHTED CROSS VALIDATION IN THE SELECTION OF ROBUST REGRESSION MODEL WITH CHANGE-POINT FOR TELEVISION RATING FORECAST

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Carlos Alberto Huaira Contreras ◽  
Carlos Cristiano Hasenclever Borges ◽  
Camila Borelli Zeller ◽  
Amanda Romanelli
Keyword(s):  
Regression Model ◽  
Change Point ◽  
Regression Models ◽  
Cross Validation ◽  
Robust Regression ◽  
Model Parameters ◽  
Random Errors ◽  
Type Algorithm ◽  
T Distribution ◽  
Selection Of

The paper proposes a weighted cross-validation (WCV) algorithm  to select a linear regression model with change-point under a scale mixtures of normal (SMN) distribution that yields the best prediction results. SMN distributions are used to construct robust regression models to the influence of outliers on the parameter estimation process. Thus, we relaxed the usual assumption of normality of the regression models and considered that the random errors follow a SMN distribution, specifically the Student-t distribution. In addition, we consider the fact that the parameters of the regression model can change from a specific and unknown point, called change-point. In this context, the estimations of the model parameters, which include the change-point, are obtained via the EM-type algorithm (Expectation-Maximization). The WCV method is used in the selection of the model that presents greater robustness and that offers a smaller prediction error, considering that the weighting values come from step E of the EM-type algorithm. Finally, numerical examples considering simulated and real data (data from television audiences) are presented to illustrate the proposed methodology.

scholarly journals ON THE BAYESIAN ANALYSIS OF EXTENDED WEIBULL-GEOMETRIC DISTRIBUTION

2019 ◽  
pp. 115-137
Author(s):  
Azeem Ali ◽  
Sajid Ali ◽  
Shama Khaliq
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Geometric Distribution ◽  
Real Life ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Bayes Estimates

The paper deals with the Bayes estimation of Extended Weibull-Geometric (EWG) distribution. In particular, we discuss Bayes estimators and their posterior risks using the noninformative and informative priors under different loss functions. Since the posterior summaries cannot be obtained analytically, we adopt Markov Chain Monte Carlo (MCMC) technique to assess the performance of Bayes estimates for different sample sizes. A real life example is also part of this study.  

scholarly journals Bayesian Estimation for Nadarajah-Haghighi Distribution Based on Upper Record Values

2019 ◽  
pp. 217-230
Author(s):  
MS Sana ◽  
M. Faizan
Keyword(s):  
Prior Information ◽  
Record Values ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Jeffreys Prior ◽  
Unknown Parameters ◽  
R Software ◽  
Squared Error ◽  
Upper Record Values ◽  
Upper Record

This paper discusses maximum likelihood and Bayes estimation of the two unknown parameters of Nadarajah and Haghighi distribution based on record values. Different Bayes estimates are derived under squared error, balanced squared error and general entropy loss functions by using Jeffreys' prior information and extension of Jeffreys' prior information. It is observed that the associated posterior distribution appears in an intractable form. So, we have used Tierney and Kadane approximation method to compute these estimates. Finally, numerical computations are presented based on generated record values using R software.

Wavelet shrinkage generalized Bayes estimation for elliptical distribution parameter’s under LINEX loss

2019 ◽  
Vol 17 (03) ◽  
pp. 1950009 ◽  
Author(s):  
Hamid Karamikabir ◽  
Mahmoud Afshari
Keyword(s):  
Wavelet Transformation ◽  
Test Validity ◽  
Bayes Estimator ◽  
Bayes Estimation ◽  
Multivariate Normal ◽  
Elliptical Distribution ◽  
Wavelet Shrinkage ◽  
Linex Loss ◽  
Generalized Bayes ◽  
Generalized Bayes Estimator

In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.

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