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The Bayesian model is established in this paper, and the risk
parameters of claim amounts in Pareto distribution are estimated. The maximum likelihood
estimation, Bayesian estimation and credibility estimation are derived and the strong
consistency of these estimates are proved. We also compared their mean square error both
in theory and in numerical simulation. The results show that Bayesian estimation is better
than other estimates in sense of mean square error. Finally, the structural parameters in
Bayes estimation and credibility estimation are estimated and the corresponding empirical
Bayes estimates are proved asymptotically optimal.
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Let be a non-parametric kernel density estimator based
on a kernel function and a sequence of independent and identically distributed
random variables taking values in . The goal of this article is to extend
the large deviations results in He and Gao (2008), i.e., to prove large deviations for
the statistic .
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This paper studies the ergodicity of a GARCH-M type model considered
by Christensen et al.(2012). By adopting certain restrictions on mean function and parameters
in GARCH equation, geometric ergodicity of the model is proved. The obtained results can be
applied to usual conditional mean functions of the GARCH-M models.
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In this paper, we derive the Bayes estimator of the location
parameter in double-exponential family under the LINEX loss function, and then construct
the corresponding empirical Bayes estimator. It is shown that the empirical Bayes
estimator is asymptotically optimal with convergence rate being ,
, where 1/2<r<1-1/(2s), while
is a given integer.
Finally, an example is demonstrated.
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In this paper Bayesian statistical analysis of masked data is
considered based on the Pareto distribution. The likelihood function is simplified by
introducing auxiliary variables, which describe the causes of failure. Three Bayesian
approaches (Bayes using subjective priors, hierarchical Bayes and empirical Bayes) are
utilized to estimate the parameters, and we compare these methods by analyzing a real
data. Finally we discuss the method of avoiding the choice of the hyperparameters in
the prior distributions.
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In this paper, the differentiability and asymptotic properties of
Gerber-Shiu expected discounted penalty function (Gerber-Shiu function for short) associated
with the absolute ruin time are investigated, where the risk model is given by classical risk
model with additional random premium incomes. The additional random premium income process is
specified by a compound Poisson process. A couple of integro-differential equations satisfied
by Gerber-Shiu function are derived, several sufficient conditions which guarantee the
second-order or third-order differentiability of Gerber-Shiu function are provided. Based
on the differentiability results, when the individual claim and premium income are both
exponential distribution, the previous integro-differential equations can be deduced into
a third-order constant ordinary differential equation (ODE for short). With the standard
techniques on ODE, we find the asymptotic behavior of absolute ruin probability when the
initial surplus tends to infinity.
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In this paper, we investigate the RBNS reserving problem in a discrete
time model. The individual RBNS reserving is evaluated with the unknown quantities in the RBNS
reserve replaced by their estimates. The parameters related to the settlement delay are
estimated using the method of maximum likelihood and the weak convergence of the estimates are
studied. The conditional means in the RBNS reserve are estimated by the Watson-Nadaraya
estimate. Moreover, the weak convergence of the aggregate RBNS reserving computed by the chain
ladder algorithm are also studied. Simulation studies in finite sample case show that the
individual method has smaller MSE compared to the the aggregate method.
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In this paper, we use neural network to classify schizophrenia
patients and healthy control subjects. Based on 4005 high dimensions feature space consist
of functional connectivity about 63 schizophrenic patients and 57 healthy control as the
original data, attempting to try different dimensionality reduction methods, different
neural network model to find the optimal classification model. The results show that using
the Mann-Whitney U test to select the more discrimination features as input and using
Elman neural network model for classification to get the best results, can reach a highest
accuracy of 94.17%, with the sensitivity being 92.06% and the specificity being 96.49%.
For the best classification neural network model, we identified 34 consensus functional
connectivities that exhibit high discriminative power in classification, which includes 26
brain regions, particularly in the thalamus regions corresponding to the maximum number of
functional connectivity edges, followed by the cingulate gyrus and frontal region.
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The fractional factorial designs are widely used in various
experiments. The optimality theories and construction methods of the fractional factorial
designs are the core of the investigation on experimental designs. Many researchers have
investigated this issue since 1980. This paper gives a summary on the optimality theories
and construction methods of the regular fractional factorial designs.
