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2019 Vol.35 Issue.6,Published 2019-12-26

551 Hausdorff Dimension for Range and Graph of Multi-Parameter Operator Stable L\'{e}vy Processes
CHEN Xiaoping; LIN Huonan

The lower Hausdorff dimension results for the range and the graph of multi-parameter operator stable L\'{e}vy processes are established. The consequences are completely determined by the eigenvalues of its exponent matrix.

2019 Vol. 35 (6): 551-557 [Abstract] ( 160 ) [HTML 1KB] [ PDF 425KB] ( 277 )
558 Statistical Inferences of Risk Premium under the Generalized Exponential Premium Theory
DU Mengying; WEN Limin

The principle of exponential premium is an important premium principle in non-life actuarial science. This paper proposes an improved exponential premium principle. This premium principle can not only include the principle of exponential premium as a special case, but also the generalizations of Esscher premium principle and net premium principle, which has many excellent properties as a premium principle. We study the maximal likelihood estimates, nonparametric estimates and Bayesian estimation of risk premium, and discuss the statistical properties including asymptotic unbiased, coincidence, and asymptotic normality. In addition, the asymptotic confidence interval for this risk premium is given. Finally, the convergence rate of maximum likelihood estimation and nonparametric
estimation is compared by numerical simulation method. The results show that the nonparametric estimation has a small mean square error when the sample
size is small.

2019 Vol. 35 (6): 558-572 [Abstract] ( 165 ) [HTML 1KB] [ PDF 750KB] ( 315 )
573 Penalized Empirical Likelihood Estimation for Partially Linear Single Index Panel Model with Fixed Effects
DING Feipeng

This paper constructs a penalized empirical likelihood estimation method via quadratic inference function method, filter method and empirical likelihood estimation method. Under some regular conditions, we derived the large sample properties of estimators and show that the proposed empirical likelihood ratio is asymptotically to chi-square distribution. Furthermore, the infinite sample performance of the proposed method is evaluated by Monte Carlo simulation and real
data analysis.

2019 Vol. 35 (6): 573-593 [Abstract] ( 153 ) [HTML 1KB] [ PDF 751KB] ( 303 )
594 Bayesian Variable Selection for Median Regression
HU Danqing; GU Yongquan; ZHAO Weihua

When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.

2019 Vol. 35 (6): 594-610 [Abstract] ( 172 ) [HTML 1KB] [ PDF 1067KB] ( 312 )
611 When the Sum is a Minimal Sufficient Statistics for the Parameter of a Discrete Distribution with Finite Values?
ZHANG Yingying; RONG Tengzhong; LI Manman

We prove three theorems for iid discrete randomvariables taking two values, three values, and k (3\leq k<\infty) valuesby using the technique of indicator function. Under some specifications of the probabilities, we prove that the sum is a minimal sufficient statistics for the unknown parameter of interest of the discrete random variable taking two values, three values, and k (3\leq k<\infty) values. For the dice example, a figure shows that the specifications of the six probabilities are between 0 and 1 and sum to 1, and a fair dice is possible.

2019 Vol. 35 (6): 611-620 [Abstract] ( 149 ) [HTML 1KB] [ PDF 503KB] ( 257 )
621 Testing for Covariance Matrices in Panel Data Models with Interactive Fixed Effect
CHEN Ranran; LI Gaorong

In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data.

2019 Vol. 35 (6): 621-638 [Abstract] ( 157 ) [HTML 1KB] [ PDF 705KB] ( 437 )
639 A Distribution-Free Phase II EWMA Control Chart for Joint Monitoring of Location and Scale
SONG Zhi; LIU Yanchun; TAO Guihong

A single distribution-free (nonparametric) Phase II exponentially weighted moving average (EWMA) chart based on the Cucconi statistic, referred to as the EWMA-Cucconi (EC) chart, is considered here for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous process. A comparison with some other existing nonparametric EWMA charts is presented in terms of the average, the standard deviation and some
percentiles of the run length distribution. Numerical results based on Monte Carlo analysis show that the EC chart provides quite a satisfactory performance. The effect of the Phase I (reference) sample size on the IC performance of the EC chart is studied in detail. The application of the EC chart is illustrated by two real data examples.

2019 Vol. 35 (6): 639-653 [Abstract] ( 137 ) [HTML 1KB] [ PDF 546KB] ( 329 )
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