• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.609-633
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• 2014

From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.959-966
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• 2000

A dimensionality assessment procedure DETECT uses the property of being near zero of conditional covariances as an indication of unidimensionality .This study provides the convergent properties to zero of conditional covariances when the dta is unidimensional, with which DETECT extends its theoretical grounds.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.799-808
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• 2011

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_i{\mid}1{\leq}i{\leq}n$} is a conditional associated given $\mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$, $Cov^{\mathcal{F}}$ (f($X_1$, ${\ldots}$, $X_n$), g($X_1$, ${\ldots}$, $X_n$)) ${\geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $\mathcal{F}$-associated random variables.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.2
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• pp.166-175
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• 2002

In this paper. we predict tracking performance of the probabilistic strongest neighbor filter (PSNF). The PSNF is known to be consistent and superior to the probabilistic data association filter (PDAF) in both performance and computation. The PSNF takes into account the probability that the measurement with the strongest intensity in the neighborhood of the predicted target measurement location is not target-originated. The tracking performance of the PSNF is quantified in terms of its estimation error covariance matrix. The estimation error covariance matrix is approximately evaluated by using the hybrid conditional average approach (HYCA). We performed numerical experiments to show the validity of our performance prediction.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.199-226
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• 2009

We examine the intertemporal relation between risk and return in the Korean stock market and foreign exchange market based on the two factor ICAPM framework. The standard GARCH model and the GJR(1993) model are employed to estimate conditional variances of the stock returns and foreign exchange rates. The covariance between the rates of stock returns and changes in the exchange rates are estimated by the constant conditional correlation model of Bollerslev(1990) and the dynamic conditional correlation model of Engle(2002). The multivariate GARCH in mean model and quasi-maximum likelihood estimation method, consequently, are applied to investigate riskreturn relation jointly. We find that the estimated coefficient of relative risk aversion is negative and statistically significant in the post-financial crisis sample period in the Korean stock market. We also show that the expected stock returns are negatively related to the dynamic covariance with foreign exchange rates. Both estimated parameters of conditional variance and covariance in the foreign exchange market, however, are not statistically significant. The GJR model is better than the standard GARCH model to estimate the conditional variances. In addition, the dynamic conditional correlation model has higher explanatory power than the constant correlation model. The empirical results of this study suggest following two points to investors and risk managers in hedging and diversifying strategies for their portfolios in the Korean stock market: first, the variability of foreign exchange rates should be considered, and second, time-varying correlation between stock returns and changes in foreign exchange rates supposed to be considered.

• Journal of the Korean Statistical Society
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• v.13 no.2
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• pp.87-106
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• 1984

It ${X_t}$ is a sequence of independent identically distributed normal random variables, then the conditional probability density of $X_1, X_2, \cdots, X_n$ given the first p+1 sample autocovariances converges to the maximum entropy probability density satisfying the corresponding covariance constraints as the length of the sample sequence tends to infinity. This establishes that the maximum entropy probability density and the associated Gaussian autoregressive process arise naturally as the answers of conditional limit problems.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.19-30
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• 2003

Spatiotemporal statistical models are used for analyzing space-time data in many fields, such as environmental sciences, meteorology, geology, epidemiology, forestry, hydrology, fishery, and so on. It is well known that classical spatiotemporal process modeling requires the estimation of space-time variogram or covariance functions. In practice, the estimation of such variogram or covariance functions are computationally difficult and highly sensitive to data structures. We investigate a Bayesian hierarchical model which allows the specification of a more realistic series of conditional distributions instead of computationally difficult and less realistic joint covariance functions. The spatiotemporal model investigated in this study allows both spatial component and autoregressive temporal component. These two features overcome the inability of pure time series models to adequately predict changes in trends in individual sites.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.107-128
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• 2004

Bivariate Laplace distributions for which both marginal distributions and Laplace are discussed. Three kinds of bivariate Laplace distributions which are extended bivariate exponential distributions of Gumbel (1960) are introduced in this paper. These symmetrical distributions are compared with asymmetrical distributions of Kotz et al. (2000). Their probability density functions, cumulative distribution functions are derived. Conditional skewnesses and kurtoses are also defined. Their correlation coefficients are calculated and compared with others. We proposed bivariate random vector generating methods whose distributions are bivariate Laplace. With sample means and medians obtained from generated random vectors, variance and covariance matrices of means and medians are calculated and discussed with those of bivariate normal distribution.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.189-200
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• 2013

In this paper, it will be assumed that there are two distinct populations which are multivariate normal with equal covariance matrix. We also assume that the two populations are equally likely and the costs of misclassification are equal. The classification rule depends on the situation whether the training samples include missing values or not. We consider the conditional bootstrap confidence intervals for classification error rate when a block of observation is missing.