Distance Mean and Variance Functions and Sphere Fitting

Statistics ◽  
1994 ◽  
Vol 25 (3) ◽  
pp. 251-266 ◽  
Author(s):  
J. Gates
Keyword(s):  
Variance Functions ◽  
Mean And Variance ◽  
Sphere Fitting

scholarly journals EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR

2018 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
S. UTAMI ◽  
I W. MANGKU ◽  
I G. P. PURNABA
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Observation Interval ◽  
Compound Poisson Process ◽  
Intensity Function ◽  
Significance Level ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean ◽  
Strongly Consistent

<em>Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be </em>𝑒𝑥𝑝(𝛼+𝛽𝑠) <em>with </em>0&lt;𝛽&lt;<em>∞</em>, <em>where </em>𝛽 <em>is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to </em>1−𝛼 <em>of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level </em>𝛼<em>, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to </em>1−𝛼<em>.</em>

scholarly journals Semiparametric Smoothing Spline in Joint Mean and Dispersion Models with Responses from the Biparametric Exponential Family: A Bayesian Perspective

2021 ◽  
Vol 9 (2) ◽  
pp. 351-367
Author(s):  
Héctor Zárate ◽  
Edilberto Cepeda
Keyword(s):  
Exponential Family ◽  
Parametric Models ◽  
Efficient Estimation ◽  
Smoothing Methods ◽  
Markov Chain Sampling ◽  
Variance Functions ◽  
Natural Connection ◽  
Mean And Variance ◽  
The Mean ◽  
Two Parameter

This article extends the fusion among various statistical methods to estimate the mean and variance functions in heteroscedastic semiparametric models when the response variable comes from a two-parameter exponential family distribution. We rely on the natural connection among smoothing methods that use basis functions with penalization, mixed models and a Bayesian Markov Chain sampling simulation methodology. The significance and implications of our strategy lies in its potential to contribute to a simple and unified computational methodology that takes into account the factors that affect the variability in the responses, which in turn is important for an efficient estimation and correct inference of mean parameters without the requirement of fully parametric models. An extensive simulation study investigates the performance of the estimates. Finally, an application using the Light Detection and Ranging technique, LIDAR, data highlights the merits of our approach.

scholarly journals Variational Bayesian Learning and Semiparametric Models on the Double Exponential Family

2021 ◽  
Author(s):  
Hector Zarate-Solano ◽  
Edilberto Cepeda-Cuervo
Keyword(s):  
Bayesian Learning ◽  
Linear Models ◽  
Computation Time ◽  
Semiparametric Regression ◽  
Optimization Methods ◽  
Data Models ◽  
Accurate Estimation ◽  
Variational Bayesian ◽  
Variance Functions ◽  
Mean And Variance

In this paper, we focus on variational Bayesian learning deterministic optimization methods for inference in biparametric exponential models where the parameters follow semiparametric regression structures. This combination of data models and algorithms contributes to solving real-world problems and reduces the computation time. This allows both the rapid exploration of many data models and the accurate estimation of the mean and variance functions through the connection between generalized linear models and graph theory. A simulation study was carried out to assess the performance of the deterministic approximation. Finally, herein, we present an application using macroeconomic data to emphasize the benefits of the proposed approach.

First-order stochastic chemical reactions and oscillations in the variance

1980 ◽  
Vol 17 (04) ◽  
pp. 1087-1093 ◽  
Author(s):  
Richard C. Hertzberg ◽  
Vincent F. Gallucci
Keyword(s):  
General Solution ◽  
Markov Model ◽  
Random Processes ◽  
Numerical Examples ◽  
First Order ◽  
Variance Functions ◽  
First Order Kinetics ◽  
Component Systems ◽  
Mean And Variance ◽  
The Mean

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

Sign in / Sign up

Export Citation Format

Share Document