This paper presents a systematic overview
of the genome-wide association study. We mainly focus on the
statistical methods. Some problems and challenges are also
provided.

This article considers the compound Poisson
insurance risk model perturbed by diffusion with investment and
constant dividend barrier. Integro-differential equations for the
high order moments of the discounted dividend payments prior to ruin
are derived. Closed form solutions are formulated when the
individual claim amount distribution is exponential. Some satisfying
results about the distribution of the aggregate dividend are
obtained, even for general claim size distributions. We also
investigate the number and the amount of the dividend streams. Both
the time of ruin and the deficit at ruin are considered in some
special cases. Confluent hypergeometric functions play a key role in
this paper.

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.

The $\chi^{2}$ conditional test for
multivariate normality is suggested. The transformed sample
$\mathbf{Y}_{d}=R\mathbf{V}_{d}$ from a $d$-variate normal
distribution has a symmetric multivariate Pearson type II
distribution, the result that $R^{2}$ has a beta distribution is
proved, the asymptotic Chi squared distribution of the statistic
$\chi^{2}$ based on beta distribution and sphere uniform
distribution is obtained. The Monte Carlo power study for
multivariate normality suggests that our test is a powerful
competitor to existing tests. The goodness-of-fit for multivariate
normality of iris data is analyzed.

This paper discusses the pricing of total
return swap which is one of the credit derivatives. As the total
return swap contracts are exposed to both interest rate risk and
default risk, this paper characterizes the interest rate risk
through HJM model. Intensity model and hybrid model are used to
characterize the default risk and to derive the corresponding
pricing formula for two cases when the default time and interest
rate are independent or correlated, respectively. Monte Carlo
simulation method is used here to derive the numerical solution of
the pricing problem.

This paper improves the convergence
of two variance parameters in He and Sun (2000) by applying the
ancillarity-sufficiency interweaving strategy (ASIS in Yu and Meng
(2011)) algorithm to the Gibbs sampling steps. The performance of
the ASIS algorithm is compared with the regular Gibbs sampling by
the potential scale reduction factor, trace plots and posterior
estimates. The convergence of one parameter improves greatly, but
the other one does not have a very significant improvement. However,
the overall sampling performance has improved greatly since it needs
much fewer iterations than using regular Gibbs sampling to achieve
convergence.

The probability of success in a Binomial
model is often viewed as a continuous random variable when
 needs to be considered. In this note, we study the
mixed Binomial model with the probability of success having the
Kumaraswamy distribution. Stochastic orders and dependence in this
model are discussed; Further, the new models are employed to fit
some real data sets, and the numerical results reveal that KB models
perform better than Beta-Binomial model in some occasions.

An optimal control problem motivated by a
portfolio and consumption choice problem in the financial market
where the expected utility of the investor is assumed to be the
Constant Relative Risk Aversion (CRRA) case is discussed. A local
stochastic maximum principle is obtained in the jump-diffusion
setting using classical variational method. The result is applied to
make optimal portfolio and consumption choice strategy for the
problem and the explicit optimal solution in the state feedback form
is given.

This paper considers the state space representation
for the ARFIMA-GARCH model, which combines both the long memory time
series and the conditional heteroscedastic processes. Although this
state space representation is infinite dimensional, an exact maximum
likelihood (ML) estimator based on this kind of representation can
be computed in a finite number of iterations. Quasi ML estimators
based on the autoregressive approximation for the likelihood
function are proposed. Due to the facility of the state space
representation, these estimation approaches can be easily applied to
the missing data case. Simulation results of both the non-missing
data case and the missing data case are reported. A real data
example from stock market illustrates the proposed method.

The conditional mean, variance and higher-conditional
moment functions are often of special interest in regression. In
this paper,we generalize central mean subspace and focus especial
attention on the k th-conditional moment function. For this, we
first borrow the new concept --- the central k th-conditional
moment subspace, and study its basic properties. To avoid computing
the inverse of the covariance of predictors with large
dimensionality and highly collinearity, we develop a method called
the $k$th-moment weighted partial least squares to handle with the
estimation of the central k th-conditional moment subspace.
Finally, we obtain strong consistency

Semiparametric Archimedean copulas, which have a fexible
dependence structure because of the special way constructed by using
the existing archimedean generator, can describe the dependence
structure between the financial data auto-adaptively. The empirical
results on the exchange rate market suggest that the semiparametric
Archimedean copula is more flexible than the other three copulas,
and is suggestive when selecting copulas.

Methods for interval estimation and hypothesis
testing about the ratio of expected lifetimes of two independently
distributed two-parameter exponential distribution based on the
concept of generalized variable approach are proposed. As assessed
by simulation, the coverage probabilities of the proposed approach
are found to be very close to the nominal level even for small
samples. The proposed new approaches are conceptually simple and are
easy to use. Similar procedures are developed for constructing
confidence intervals and hypothesis testing about the difference
between means of two independent two-parameter exponential
distribution.

The varying-coefficient single-index
models (VCSIM) have been applied in many fields since they combine
the advantages of single-index models and varying-coefficient
models. In this paper, their estimation method is proposed based on
B-spline approximation technique and two calculation methods can be
used. The first one is to directly calculate the parametric and
nonparametric parts simultaneously by Newton-Raphson iteration
algorithm. The second one is to calculate the two parts by profile
method individually. We suggest that the second method is for our
preference when the large amount of parameters are involved,
otherwise the first method will be more convenient. Two simulated
examples are given to illustrate the performances of the proposed
estimation methodologies and calculation procedures.

This paper extends Hull-White interest
rate model to cover cross-currency case. In the extended model we
discuss valuation of cross-currency Bermudan swaptions. Since the
closed-form pricing formula is hard to obtain, we apply the Least
Squared Monte-Carlo approach to find the optimal exercising time.
Some numerical results with different parameters are presented.

The bi-directional long short-term memory neural network model is widely used in natural language processing, but hyperparameter tuning of the model is difficult in practice. In this paper, we take the semantic role recognition task as an example, consider four candidate features (word, part of speech, target word and position) and two hyperparameters (the number of layers of the network and whether CRF classifier is used) as factors in robust design, and select the optimal combination of features and hyperparameters by setting levels of each factor and performing experiments. In particular, we perform 32 cross validation on a small datasets to select the optimal configuration combination of the model based on the SNR of robust design. Then, we analyze the influence of each factor on the performance of the model by quantitatively analyze so that the model has a certain degree of interpretability. Moreover, in order to verify the superiority of our tuning method, we use the standard segmentation of natural language processing on a big dataset, adopt the traditional greedy strategy to select the optimal configuration combination, and compare with our method on the test set. The results show that our method is better than the traditional tuning method.

In this paper, we consider two linear models with
missing data, where the covariates are not missing, but response variables are missing
at random(MAR). The inverse probability weighted imputation is used to impute the missing
data of response variables, we can obtain the 'complete' data for two linear regression models.
Then we can construct the empirical log-likelihood ratios of quantile differences of response
variables. And the difference is that the asymptotic distributions for the empirical
log-likelihood ratios of quantile differences of response variables are standard  comparing with the results of previous studies. The empirical likelihood confidence
intervals for quantile difference of response variables is more accurate because the errors
caused right of the coefficient estimates is reduced.

The empirical likelihood method has been
extensively applied to many models of statistical inference. This
paper is based on empirical likelihood for partial linear models for
statistical diagnosis. First, the estimating equations of the model
are given and the maximum empirical likelihood estimates of the
parameters are obtained; then, based on empirical likelihood method,
the three different measures of influence curvatures are studied;
last, stochastic simulation and data analysis are given to
illustrate the validity of statistical diagnostic measures

Under the hypothesis of normal distribution,
the change-point problems have four cases according to mean and
variance changing. In this paper, we look upon the threshold
nonlinearity test of TAR models as a change-point problem, which has
a change-mean and constant-variance. We adopt reversible-jump Markov
chain Monte Carlo (RJMCMC) methods to calculate the posterior
probabilities of two competitive models, namely AR and TAR models.
Posterior evidence favoring the TAR model indicates threshold
nonlinearity. Simulation experiments demonstrate that our method
works very well in distinguishing AR and TAR models.

In the paper, a global solution is guaranteed
under local Lipschitz condition and some additional conditions
without linear growth condition. Later, the convergence in
probability of approximate solutions is investigated on the neutral
stochastic differential delay equations with Poisson jumps and
Markovian switching, instead of $L^{2}$. Some known results are
generalized and improved.

Based on adaptive type-II progressive
hybrid censored data statistical analysis for constant-stress
accelerated life test (CS-ALT) with products' lifetime following
two-parameter generalized exponential (GE) distribution is
investigated. The estimates of the unknown parameters and the
reliability function are obtained through a new method combining the
EM algorithm and the least square method. The observed Fisher
information matrix is achieved with missing information principle,
and the asymptotic unbiased estimate (AUE) of the scale parameter is
also obtained. Confidence intervals (CIs) for the parameters are
derived using asymptotic normality of the estimators and the
percentile bootstrap (Boot-p) method. Finally, Monte Carlo
simulation study is carried out to investigate the precision of the
point estimates and interval estimates, respectively. It is shown
that the AUE of the scale parameter is better than the corresponding
two-step estimation, and the Boot-p CIs are more accurate than the
corresponding asymptotic CIs.