Parameter estimation of mixed generalized
exponential distribution model under grouped and right-censored data
is considered by using EM algorithm in this paper. The estimation
formulae are obtained and some simulations are presented to
illustrate the proposed method. Finally, a set of medicine data is
analyzed.

In this paper, we proposed the preliminary
test two-parameter estimators based on the Wald (W), the Likelihood
Ration (LR) and the Lagrangian Multiplier (LM) tests, when it is
suspected that the regression parameter may be restricted to a
subspace. The bias and the mean square error (MSE) of the proposed
estimators are derived and compared. The conditions of superiority
of the proposed estimators are obtained.

When the hyperparameters of prior
distribution are partly known in linear model, the simultaneous
parametric empirical Bayes estimators (PEBE) of the regression
coefficients and error variance are constructed. The superiority of
PEBE over the least squares estimator (LSE) of regression
coefficients is investigated in terms of the the mean square error
matrix (MSEM) criterion, and the superiority of PEBE over LSE of the
error variance is discussed under the the mean square error (MSE)
criterion. Finally, when all hyperparameters are unknown, the PEBE
of regression coefficients and error variance are reconstructed and
the superiority of them over LSE under the MSE criterion are studied
by simulation methods.

Suppose that the cause-effect relationships
between variables can be described by a causal network. To identify
the causal effect of a stochastic intervention, an augmented causal
network for stochastic intervention is proposed in this paper. Then,
we obtain two graphical criteria for identifying the causal effects
of stochastic interventions from passive observations on observed
variables only. When either of the two criteria is satisfied, a
simple closed-form expression is provided for the causal effect of a
stochastic intervention, which enables researchers to assess the
causal effect with little effort.

Partially linear model is a class of commonly
used semiparametric models, this paper focus on variable selection
and parameter estimation for partially linear models via adaptive
LASSO method. Firstly, based on profile least squares and adaptive
LASSO method, the adaptive LASSO estimator for partially linear
models are constructed, and the selections of penalty parameter and
bandwidth are discussed. Under some regular conditions, the
consistency and asymptotic normality for the estimator are
investigated, and it is proved that the adaptive LASSO estimator has
the oracle properties. The proposed method can be easily
implemented. Finally a Monte Carlo simulation study is conducted to
assess the finite sample performance of the proposed variable
selection procedure, results show the adaptive LASSO estimator
behaves well.

Least squares method based on Euclidean
distance and Lebesgue distance between fuzzy data is used to study
parameter estimation of fuzzy linear regression model based on case
deletion respectively. And the parameter estimations on two kinds of
distance are compared. The input of the above model is real data and
output is fuzzy data. The statistical diagnosis --- estimation
standard error of regression equations is constructed to test highly
influential point or outlier in observation data. At last through
identifying highly influential point or outlier in actual data, it
shows that the statistic constructed in this paper is effective.

A new nonlinear covariance based on
-expectation, -covariance, is introduced and some properties
of -covariance including commutativity, homogeneity, additivity
are studied. According to these results, the sufficient and
necessary condition of -covariance satisfied homogeneity and
additivity is obtained. That is , a linear function of .
Correlation coefficient based on -expectation does not rang from
-1 to 1 and it does not reflect the linear relationship between
two random variables, either.

In this paper, absolute ruin problems
for a kind of renewal risk model with constant interest force are
studied. For certain situations of the claim distribution with heavy
tail, consider the surplus of the arrival time, and discrete the
surplus process, then use the method of renewal function and
convolution, we present the asymptotic properties of absolute ruin
probability when the initial surplus tends to infinity.

The class of reduced form models is
a very important class of credit risk models, and the modelling of
the default dependence structure is essential in the reduced form
models. This paper models dependent defaults under a
thinning-dependent structure in the reduced form framework. In our
tractable model, the joint survival probability for correlated
defaults can be derived, and hence the CDS premium rates (with or
without counterparty risk) are given in closed form. The numerical
result shows that the thinning-dependent structure is effective to
model the default dependence.

In this paper, various concepts of
recurrence and transience are introduced into the research field
of Markov chains in random environments, and the concepts and
properties of invariant function for Markov chains in random
environments are investigated. By using those properties, we obtain
a criterion for the state to be recurrent or transient.