• 대한수학회보
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• 제47권1호
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.219-224
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• 1995

A central limit theorem with random indices is obtained for stattionary martingale difference sequences.

• 호남수학학술지
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• 제36권1호
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• pp.33-41
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• 2014

Ko(2013, JIA 2013:473) discussed complete convergence for weighted sum of martingale difference field when all indices have the same powers in the normalization. In this paper we generalize this law to the case where different indices have different powers in the normalization.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.417-425
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• 2008

For stationary m-dimensional martingale difference sequences we prove the random functional central limit theorems and propose an almost sure consistent estimator for the limiting covariance matrix.

• 대한수학회논문집
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• 제14권3호
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• pp.581-595
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• 1999

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

• 대한수학회보
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• 제51권2호
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• pp.317-328
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• 2014

In Bae et al. [2], we have considered the uniform CLT for the martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes majorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.359-364
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• 2005

This paper considers a specification test of conditional Poisson regression model for time series count data. Although conditional models for count data have received attention and proposed in several ways, few studies focused on checking its adequacy. Motivated by the test of martingale difference assumption, a specification test via Ljung-Box statistic is proposed in the conditional model of the time series count data. In order to illustrate the performance of Ljung- Box test, simulation results will be provided.

• 대한수학회보
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• 제43권3호
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• pp.543-549
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• 2006

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.

• Kyungpook Mathematical Journal
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• 제32권3_spc호
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• pp.369-374
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• 1992

• 한국병원경영학회지
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• 제11권3호
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• pp.19-41
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• 2006

The Objective of this study was to design the model which predict the future cash flow of hospitals and on the basis of designed model to support sound hospital management by the prediction of future cash flow. The five cash flow measurement variables discussed in financial accrual part were used as variables and these variables were defined as NI, NIDPR, CFO, CFAI, CC. To measure the cash flow B/S related variables, P/L related variables and financial ratio related variables were utilized in this study. To measure cash flow models were designed and to estimate the prediction ability of five cash flow models, the martingale model and the market model were utilized. To estimate relative prediction outcome of cash flow prediction model and simple market model, MAE and MER were used to compare and analyze relative prediction ability of the cash flow model and the market model and to prove superiority of the model of the cash flow prediction model, 32 Regional Public Hospital's cross-section data and 4 year time series data were combined and pooled cross-sectional time series regression model was used for GLS-analysis. To analyze this data, Firstly, each cash flow prediction model, martingale model and market model were made and MAE and MER were estimated. Secondly difference-test was conducted to find the difference between MAE and MER of cash flow prediction model. Thirdly after ranking by size the prediction of cash flow model, martingale model and market model, Friedman-test was evaluated to find prediction ability. The results of this study were as follows: when t-test was conducted to find prediction ability among each model, the error of prediction of cash flow model was smaller than that of martingale and market model, and the difference of prediction error cash flow was significant, so cash flow model was analyzed as excellent compare with other models. This research results can be considered conductive in that present the suitable prediction model of future cash flow to the hospital. This research can provide valuable information in policy-making of hospital's policy decision. This research provide effects as follows; (1) the research is useful to estimate the benefit of hospital, solvency and capital supply ability for substitution of fixed equipment. (2) the research is useful to estimate hospital's liqudity, solvency and financial ability. (3) the research is useful to estimate evaluation ability in hospital management. Furthermore, the research should be continued by sampling all hospitals and constructed advanced cash flow model in dimension, established type and continued by studying unified model which is related each cash flow model.