The dependence on the sum of bivariate random vectors with
Farlie-Gumbel-Morgenstern copulas is studied in the paper. Firstly, the Kendall's
 and the Spearman's  on two independent random vectors' sum with the
copulas are deduced, and the specific equation with exponential marginal distribution
is shown. Then, the proposition is proved that there exists no tail-dependence under
some conditions on marginal distribution. Finally, we calculate some numerical
instances for different marginal distributions by using Monte Carlo method. The
conclusions and methods in this paper have theoretical significance for the dependence
between two random indices of the combination of enterprise, and lay foundations for
the further study.

Most distribution-free control charts in the literature are
used to monitor process location parameters, such as mean or median, rather than process
dispersion parameters. This paper develops a new distribution-free control chart by
integrating a two-sample nonparametric test into the effective change-point model.
Our proposed chart is easy in computation, convenient to use, and very powerful in
detecting process dispersion shifts. As it avoids the need for a lengthy data-gathering
step before charting and it does not require knowledge of the underlying distribution,
the proposed chart is particularly useful in start-up or short-run situations.

In this note, we prove the Borel-Cantelli lemma for capacity
without pairwise independent assumption. The best lower bound about union for capacity
is obtained. Classical Borel-Cantelli lemma is extended to the case of capacity.

Nonparametric regression estimation has been studied intensively
for the censored data. However, in some practical applications, some censoring indicators
may be missing because of various reasons. In this paper, we propose two kernel estimators
for the regression function when the censoring indicator is missing at random. The strong
uniform convergence rates and the asymptotic normality of the estimators are established.
Some simulations are carried out to assess the finite sample performances of the proposed
methods.

In this paper, we give the discrete form of the definition
of bifurcating Markov chains indexed by a binary tree, and then study the equivalent
properties of it. Finally, we prove that tree-indexed Markov chains are bifurcating
Markov chains indexed by a binary tree in certain situation.

A jump-diffusion Omega model is studied in this paper. In this
model, the surplus process is a perturbation of a compound Poisson process by a Brown
motion. For exponential claim size and constant bankruptcy rate function, several
explicit formulae on bankruptcy probability for the model are derived. The relationship
between bankruptcy probability and occupation time in the red is also discussed. Then
numerical examples are given to show some comparisons for the model with the Omega model
of Albrecher and Lautscham (2013).

This paper studies the price of extension of the European
exchange option (including generalized exchange option; compound exchange option;
barrier exchange option; traffic-light option) with the geometric Brownian motion.
Firstly, the reflection principle and property of the Browian motion with drift
are given; Secondly, the definitions and properties of the Esscher transform of
multidimensional processes with stationary and independent increments and
two-dimensional Browian motion with drift are given by borrowing from the idea of
Gerber and Shiu (1994); Finally, using related theory of Esscher transform, pricing
formulas of extension of several European exchange options are obtained when the
price of the underlying asset follows the geometric Brownian motion.

Empirical (Euclidean) likelihood is a very popular nonparametric
statistical method in recent years. In view of the convex hull restrictions and complex
calculation of empirical (Euclidean) likelihood, the balanced augmented empirical Euclidean
likelihood (BAEEL) is proposed by using the idea of Emerson and Owen (2009). Then the BAEEL
method is investigated from two aspects of theory and simulation. In theory, the connection
between BAEEL method and the empirical Euclidean likelihood method is deduced. That is,
with fixed sample size and the continuous varied location of augmented points, the test
can be varied from the simple mean augmented empirical Euclidean likelihood to empirical
Euclidean likelihood test. Simulation results show that the distribution of the BAEEL
converges its limit distribution more rapidly than that of the (adjusted) empirical
Euclidean likelihood in most cases.

Quantile varying coefficient model is one of the robust
nonparametric modeling method. When one uses varying coefficient model to analyze data,
a natural question is how to simultaneously select the relevant variables and separate
the nonzero constant effect variables from nonzero varying effect variables. In this
paper, we address the problem of both robustness and efficiency of estimation and variable
selection procedure based on quantile regression. By combining the idea of the local
kernel modeling and adaptive group Lasso method, we obtain penalized estimation through
imposing double penalties on the quantile check function. With appropriate selection of
tuning parameters by BIC criterion, the theoretical properties of the new variable
selection procedure can be established. The finite sample performance of the new method
is investigated through simulation studies and the analysis of body fat data. Numerical
studies show that the new method can simultaneously identify unimportant variables and
separate non-varying coefficient variables among important variables without any prior
information about variables and irrespective of model error distribution.