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In this paper, we will prove another Borel-Cantelli lemma for capacities induced by sublinear expectations.
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A cured model is a useful approach for analysing failure
time data in which some subjects could eventually experience and others never
experience the event of interest. All subjects in the test belong to one of the
two groups: the susceptible group and the non-susceptible group. There has been
considerable progress in the development of semi-parametric models for regression
analysis of time-to-event data. However, most of the current work focuses on
right-censored data, especially when the population contains a non-ignorable
cured subgroup. In this paper, we propose a semi-parametric cure model for current
status data. In general, treatments are developed to both increase the patients'
chances of being cured and prolong the survival time among non-cured patients. A
logistic regression model is proposed for whether the subject is in the susceptible
group. An accelerated failure time regression model is proposed for the event
time when the subject is in the non-susceptible group. An EM algorithm is used
to maximize the log-likelihood of the observed data. Simulation results show that
the proposed method can get efficient estimations.
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The paper is concerned with the two-sample mean
testing problem in high-dimension settings. We propose a composite Hotelling's
T-square test, establish its asymptotical normality and study its local power.
The finite-sample priority of the proposed test over existing high-dimensional
tests is shown by simulations and illustrated by a real data-set analysis.
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As a new reliability test plan, generalized progressive
hybrid censoring can improve test efficiency by allowing experimenters to observe
a pre-specified number of failure samples before the final termination point.
Based on a class of widely used life distribution in life data analysis ---
generalized exponential distribution, this paper discusses its parameters
inference issue under generalized progressive hybrid censoring scheme. EM
Algorithm is used to estimate parameters of the considered model. Simulation
studies and a real-data analysis are carried out to illustrate the performance
of finite sample for the proposed procedure.
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Credit valuation adjustment is the price adjustment
of financial contract considering possible default of counterparty and it
is an important way to measure counterparty risk. It is the key to establish
a reasonable default dependence structure model. We introduce an economic
state variable and shot noise processes in a Markov copula model and establish
a regime switching Markov copula model with shot noise, where we can not
only describe the impact of common economic conditions characteristics but
also describe the credit name's characteristic. In this proposed model, we
study martingale property of the model and the collateralized CVA of credit
default swaps, and furthermore, we perfer some numerical calculations on
the collateralized CVA and examine the impact of some model parameters on
the CVA.
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In this paper, we first study the strong law of large
numbers for the frequencies of occurrence of random ordered couples of states
for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then
the strong law of large numbers are studied for functions of the nonhomogeneous
bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain
the shannon-McMillan theorem for these Markov chains with finite state space.
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In this paper, the semiparametric generalized partially
linear models (GPLMs) for longitudinal data is studied. We approximate the
nonparametric function in the GPLMs by a regression spline, and use quadratic
inference functions (QIF) to take the within-cluster correlation into account
without involving direct estimation of nuisance parameters in the correlation
matrix. We establish the asymptotic normality of the resulting estimators.
The finite sample performance of the proposed methods is evaluated through
simulation studies and a real data analysis.
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We propose a new estimation method for the parameters
of a partial functional linear model when the parameter curve is subject
to monotone constraint. The proposed estimators are implemented under the
nonlinear mixed effects model framework. The small sample properties are
illustrated through a simulation experiment.
