1,522 research outputs found
Liu-type Negative Binomial Regression: A Comparison of Recent Estimators and Applications
This paper introduces a new biased estimator for the negative binomial
regression model that is a generalization of Liu-type estimator proposed for
the linear model in [12]. Since the variance of the maximum likelihood
estimator (MLE) is inflated when there is multicollinearity between the
explanatory variables, a new biased estimator is proposed to solve the problem
and decrease the variance of MLE in order to make stable inferences. Moreover,
we obtain some theoretical comparisons between the new estimator and some
others via matrix mean squared error (MMSE) criterion. Furthermore, a Monte
Carlo simulation study is designed to evaluate performances of the estimators
in the sense of mean squared error. Finally, a real data application is used to
illustrate the benefits of new estimator
Bayesian analysis of Turkish Income and Living Conditions data, using clustered longitudinal ordinal modelling with Bridge distributed random-effects
This paper is motivated by the panel surveys, called Statistics on Income and
Living Conditions (SILC), conducted annually on (randomly selected)
country-representative households to monitor EU 2020 aims on poverty reduction.
We particularly consider the surveys conducted in Turkey, within the scope of
integration to the EU, between 2010 and 2013. Our main interests are on health
aspects of economic and living conditions. The outcome is {\it self-reported
health} that is clustered longitudinal ordinal, since repeated measures of it
are nested within individuals and individuals are nested within families.
Economic and living conditions were measured through a number of individual-
and family-level explanatory variables. The questions of interest are on the
marginal relationships between the outcome and covariates that are addressed
using a polytomous logistic regression with Bridge distributed random-effects.
This choice of distribution allows one to {\it directly} obtain marginal
inferences in the presence of random-effects. Widely used Normal distribution
is also considered as the random-effects distribution. Samples from the joint
posterior density of parameters and random-effects are drawn using Markov Chain
Monte Carlo. Interesting findings from public health point of view are that
differences were found between sub-groups of employment status, income level
and panel year in terms of odds of reporting better health
Marginally specified models for analyzing multivariate longitudinal binary data
Marginally specified models have recently become a popular tool for discrete
longitudinal data analysis. Nonetheless, they introduce complex constraint
equations and model fitting algorithms. Moreover, there is a lack of available
software to fit these models. In this paper, we propose a three-level
marginally specified model for analysis of multivariate longitudinal binary
response data. The implicit function theorem is introduced to approximately
solve the marginal constraint equations explicitly. Furthermore, the use of
\textit{probit} link enables direct solutions to the convolution equations. We
propose an R package \textbf{pnmtrem} to fit the model. A simulation study is
conducted to examine the properties of the estimator. We illustrate the model
on the Iowa Youth and Families Project data set
Efficiency of the principal component Liu-type estimator in logistic regression model
In this paper we propose a principal component Liu-type logistic estimator by
combining the principal component logistic regression estimator and Liu-type
logistic estimator to overcome the multicollinearity problem. The superiority
of the new estimator over some related estimators are studied under the
asymptotic mean squared error matrix. A Monte Carlo simulation experiment is
designed to compare the performances of the estimators using mean squared error
criterion. Finally, a conclusion section is presented.Comment: 16 pages, 4 table
On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression
In order to overcome multicollinearity, we propose a stochastic restricted
Liu-type max- imum likelihood estimator by incorporating Liu-type maximum
likelihood estimator (Inan and Erdo- gan, 2013) to the logistic regression
model when the linear restrictions are stochastic. We also discuss the
properties of the new estimator. Moreover, we give a method to choose the
biasing parameter in the new estimator. Finally, a simulation study is given to
show the performance of the new estimator.Comment: 8 pages, 2 table
Flexible multivariate marginal models for analyzing multivariate longitudinal data, with applications in R
Most of the available multivariate statistical models dictate on fitting
different parameters for the covariate effects on each multiple responses. This
might be unnecessary and inefficient for some cases. In this article, we
propose a modeling framework for multivariate marginal models to analyze
multivariate longitudinal data which provides flexible model building
strategies. We show that the model handles several response families such as
binomial, count and continuous. We illustrate the model on the Mother's Stress
and Children's Morbidity data set. A simulation study is conducted to examine
the parameter estimates. An R package mmm2 is proposed to fit the model
Liu-type Shrinkage Estimations in Linear Models
In this study, we present the preliminary test, Stein-type and positive part
Liu estimators in the linear models when the parameter vector
is partitioned into two parts, namely, the main effects
and the nuisance effects such
that . We consider the case that a priori known or suspected set of the
explanatory variables do not contribute to predict the response so that a
sub-model may be enough for this purpose. Thus, the main interest is to
estimate when is close to zero.
Therefore, we conduct a Monte Carlo simulation study to evaluate the relative
efficiency of the suggested estimators, where we demonstrate the superiority of
the proposed estimators
On the restricted almost unbiased Liu estimator in the Logistic regression model
It is known that when the multicollinearity exists in the logistic regression
model, variance of maximum likelihood estimator is unstable. As a remedy, in
the context of biased shrinkage ridge estimation, Chang (2015) introduced an
almost unbiased Liu estimator in the logistic regression model. Making use of
his approach, when some prior knowledge in the form of linear restrictions are
also available, we introduce a restricted almost unbiased Liu estimator in the
logistic regression model. Statistical properties of this newly defined
estimator are derived and some comparison result are also provided in the form
of theorems. A Monte Carlo simulation study along with a real data example are
given to investigate the performance of this estimator.Comment: 15 pages, 1 Figure, 9 Table
Stancu type generalization of the q-Favard-Szasz operators
In this paper, we introduce a Stancu type generalization of the
q-Favard-Szasz operators, estimate the rates of statistical convergence and
study the local approximation properties of these operators
Pretest and Stein-Type Estimations in Quantile Regression Model
In this study, we consider preliminary test and shrinkage estimation
strategies for quantile regression models. In classical Least Squares
Estimation (LSE) method, the relationship between the explanatory and explained
variables in the coordinate plane is estimated with a mean regression line. In
order to use LSE, there are three main assumptions on the error terms showing
white noise process of the regression model, also known as Gauss-Markov
Assumptions, must be met: (1) The error terms have zero mean, (2) The variance
of the error terms is constant and (3) The covariance between the errors is
zero i.e., there is no autocorrelation. However, data in many areas, including
econometrics, survival analysis and ecology, etc. does not provide these
assumptions. First introduced by Koenker, quantile regression has been used to
complement this deficiency of classical regression analysis and to improve the
least square estimation. The aim of this study is to improve the performance of
quantile regression estimators by using pre-test and shrinkage strategies. A
Monte Carlo simulation study including a comparison with quantile --type
estimators such as Lasso, Ridge and Elastic Net are designed to evaluate the
performances of the estimators. Two real data examples are given for
illustrative purposes. Finally, we obtain the asymptotic results of suggested
estimatorsComment: arXiv admin note: text overlap with arXiv:1707.0105
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