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The sign test based on ranked set sampling
is proposed for testing hypotheses concerning the quantiles of a
population characteristic. Both balance and selective designs are
considered and the relative performance of different designs is
assessed in terms of Pitman's asymptotic relative efficiency. For
each quantile, the sampling allocation that maximizes the efficacy
of sign statistic is identified and shown to not depend on the
population distribution.
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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.
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In this paper, a new class of distributions,
namely asymmetric Marshall-Olkin Laplace (AMOL) distribution, is
introduced, some properties and numerical characteristics of AMOL
are obtained, and a necessary and sufficient of autoregressive model
with AMOL as marginal distribution is derived.
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The purpose of this paper is to propose
a new weak dependence coefficient between two random variables under
integral probability metric. We show that our coefficient may be
also used to obtain covariance inequality and strong law of large
numbers, and we can further investigate moment inequalities for
associated r.v.s..
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In this paper, under a general loss function
$\psi(y-f(x))$, when $\psi(z)$ is a continuous function, error
estimation of regression problem is discussed.
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This paper, adopting the recursive multiple-priors
utility with fluctuated discounting rate, studies the optimal
consumption and portfolio choice in a Merton-style model with
anticipation when there is a difference between ambiguity and risk.
In the case of a power utility function, the paper characterizes the
optimal investment which is affected by both ambiguity and
anticipation. The optimal portfolio is derived in terms of backward
stochastic differential equation and Malliavin derivatives.
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Based on type II censored data, generalized
lower confidence limit is constructed by two different procedures
for the reliability life of a left truncated two-parameter
exponential distribution, using the concept of generalized pivotal
quantity and generalized confidence interval due to Weerahandi. One
procedure is to define the restricted generalized lower confidence
limit for the reliability life of a left truncated two-parameter
exponential distribution using the generalized lower confidence
limit constructed in the case that the location parameter is not
restricted. The other is to find the conditional generalized lower
confidence limit for the reliability life based on the conditional
distribution of generalized pivotal quantity. We investigate the
properties of the two lower confidence limits respectively and
present simple numerical calculation procedures. Simulation study
showns that restricted generalized lower confidence limit gives good
coverage probability, coverage probability of conditional
generalized lower confidence limit is related to the values of the
parameters, but it's mean is bigger and it's variance is smaller in
some cases compared with the restricted generalized lower confidence
limit.
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By use of maximum likelihood ratio means,
we present in this paper a Wilks test rule of each fixed effects in
the equilibrium design and multiple-way classification model with
repeated survey; then deduce a means to test each fixed effects
simultaneously. At last, we deduce the function relation between
non-central parameter and original parameter to reflected efficiency
of this test rule.
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This paper proposes a differential
geometric framework for nonlinear models for Failure Time Data. The
framework may be regarded as an extension of that presented by Bates
\& Wates for nonlinear regression models. As an application, we use
this geometric framework to derive three kinds of improved
approximate confidence regions for parameter and subset parameter in
terms of curvatures. Several results such as Bates and Wates (1980),
Hamilton (1986) and Wei (1998) are extended to our models.
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In this paper an insurer is assumed to invest his
reserve in a financial market, which consists of a risky asset and a
risk-free asset. The random impulsive model for stock prices is used
to depict the price of risky security. A controlled diffusion risk
process is presented to describe such a dynamic setting. Explicit
and closed-form solutions for the optimal dynamic choice are derived
when excess-of-loss or proportional reinsurance is incorporated with
an investment under the optimization criteria of maximizing the
expectation of quadratic utility of the terminal wealth at a fixed
terminal time, respectively. Based on the explicit solutions, the
influence of the dependence between the finance risk and insurance
risk on the optimal dynamic choice is illustrated numerically.
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Longitudinal data arises when subjects are
followed over a period time. In this paper, we applied block
empirical likelihood in partially linear regression model accounting
for the within-subject correlation. For any working covariance
matrix, an empirical log-likelihood ratio for the parametric
components, which are of primary interest, is proposed, and the
nonparametric version of the Wilk's theorem is derived. Simulations
show that performance can be substantially improved by correctly
specifying the correlation structure. At last, we illustrate the
proposed method by analyzing an example in epidemiology.
