• Title, Summary, Keyword: empirical CLT

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An empirical clt for stationary martingale differences

  • Bae, Jong-Sig
    • Journal of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.427-446
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    • 1995
  • Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.

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The Differential Effect of PC vs. Mobile on User Behavior : An Empirical Study based on Construal Level Theory(CLT) (데스크톱과 모바일 기기의 차이가 사용자의 행위에 미치는 영향 : 해석수준 이론을 적용한 실증 연구)

  • Suh, Kil-Soo;Kang, Hyunjeong
    • Journal of Information Technology Services
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    • v.18 no.5
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    • pp.31-51
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    • 2019
  • Construal level theory (CLT) have been researched in wide range of disciplines such as marketing, organizational study, psychology, or education. Current study asserts that CLT would explain the effect of different devices of PC and smartphone on interaction between human-computer interfaces and information systems use. In CLT, those who are far from an object in terms of physical, temporal, social or psychological distance, they construe their understanding as abstract (high level) and vice versa. We hypothesized different size of digital device will increase psychological distance and result in behaviors that correspond to present construal level. The analysis result shows that users of PC recognized that they are socially distant from the device and those of smartphone felt that they are socially close to the device. However, the device did not have significant effect on attention to essential information, advertisement preference, and immediacy. The implication to academia, practice and future research and limitations are also discussed.

THE EMPIRICAL LIL FOR THE KAPLAN-MEIER INTEGRAL PROCESS

  • Bae, Jong-Sig;Kim, Sung-Yeun
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.269-279
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    • 2003
  • We prove an empirical LIL for the Kaplan-Meier integral process constructed from the random censorship model under bracketing entropy and mild assumptions due to censoring effects. The main method in deriving the empirical LIL is to use a weak convergence result of the sequential Kaplan-Meier integral process whose proofs appear in Bae and Kim [2]. Using the result of weak convergence, we translate the problem of the Kaplan Meier integral process into that of a Gaussian process. Finally we derive the result using an empirical LIL for the Gaussian process of Pisier [6] via a method adapted from Ossiander [5]. The result of this paper extends the empirical LIL for IID random variables to that of a random censorship model.

THE UNIFORM CLT FOR MARTINGALE DIFFERENCE ARRAYS UNDER THE UNIFORMLY INTEGRABLE ENTROPY

  • Bae, Jong-Sig;Jun, Doo-Bae;Levental, Shlomo
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.1
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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.

Biological Distribution by Water Temperature and Refocus on the Theory of Critical Environmental Variation Quantum (수온환경변화에 따른 생물분포와 어업피해결정을 위한 임계환경변화량이론의 재조명)

  • Kang, Young-Joo;Kim, Ki-Soo
    • The Journal of Fisheries Business Administration
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    • v.45 no.1
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    • pp.1-16
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    • 2014
  • The study attempts to show that the theory of critical environmental variation quantum(CEVQ) has a sound logical basis and empirical support. It is well known that the theory of critical environmental variation quantum is derived from the theory of biological probability distibution function and the central limit theorem(CLT) in statistics. The study uses the case study of fisheries damages compensation caused br the public marine construction undertaken in the area do Anjeong Bay in the city of Tongyeong for empirical test of theory of CEVQ. The results shows that the CEVQ theory perfoms a good job in measuring quantatively fjsheries damages caused by outflow of cold water due to the operation of LNG company since 2002. Therefore the study proves that the CEVQ theory is a good theory having internal consistency and empirical applicability.

An Empirical Central Limit Theorem for the Kaplan-Meier Integral Process on [0,$\infty$)

  • Bae, Jong-Sig
    • Journal of the Korean Statistical Society
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    • v.26 no.2
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    • pp.231-243
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    • 1997
  • In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

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