• Title, Summary, Keyword: F-statistics

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Stochastic Comparisons of Order Statistics

  • Kim, Song-Ho
    • Journal of the Korean Statistical Society
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    • v.22 no.1
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    • pp.13-25
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    • 1993
  • The purpose of this paper is to investigate the properties of order statistics under various stochastic relations. We study the stochastic comparison of order statistics in a single sample. And we consider two sample case too. For example, F(t) > G9t) for t > 0 when X and Y are random variables symmetric about 0, with c.d.f.s F and G. Two examples are provided.

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Comparing the performance of likelihood ratio test and F-test for gamma generalized linear models (감마 일반화 선형 모형에서의 가능도비 검정과 F-검정 비교연구)

  • Jo, Seongil;Han, Jeongseop;Lee, Woojoo
    • The Korean Journal of Applied Statistics
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    • v.31 no.4
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    • pp.475-484
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    • 2018
  • Gamma generalized linear models are useful for non-negative and skewed responses. However, these models have received less attention than Poisson and binomial generalized linear models. In particular, hypothesis testing for the significance of regression coefficients has not been thoroughly studied. In this paper we assess the performance of various test statistics for gamma generalized linear models based on numerical studies. Our results show that the likelihood ratio test and F-type test are generally recommended and that the partial deviance test should be avoided in practice.

Functional ARCH (fARCH) for high-frequency time series: illustration (고빈도 시계열 분석을 위한 함수 변동성 fARCH(1) 모형 소개와 예시)

  • Yoon, J.E.;Kim, Jong-Min;Hwang, S.Y.
    • The Korean Journal of Applied Statistics
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    • v.30 no.6
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    • pp.983-991
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    • 2017
  • High frequency time series are now prevalent in financial data. However, models need to be further developed to suit high frequency time series that account for intraday volatilities since traditional volatility models such as ARCH and GARCH are concerned only with daily volatilities. Due to $H{\ddot{o}}rmann$ et al. (2013), functional ARCH abbreviated as fARCH is proposed to analyze intraday volatilities based on high frequency time series. This article introduces fARCH to readers that illustrate intraday volatility configuration on the KOSPI and the Hyundai motor company based on the data with one minute high frequency.

MAGNIFYING ELEMENTS IN A SEMIGROUP OF TRANSFORMATIONS PRESERVING EQUIVALENCE RELATION

  • Kaewnoi, Thananya;Petapirak, Montakarn;Chinram, Ronnason
    • Korean Journal of Mathematics
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    • v.27 no.2
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    • pp.269-277
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    • 2019
  • Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

Overfitting Probabilities using Dependent F-tests in Regression

  • Park, Chan-Keun
    • Communications for Statistical Applications and Methods
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    • v.8 no.3
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    • pp.589-601
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    • 2001
  • Probabilities of overfilling for model selection criteria are derived for several different situations. First, one candidate model with one extra variable is compared to the current model. This is expanded to m candidate models. We show that these comparisons are not independent and discuss ovefitting probabilities. Correlation between two F-tests is derived. Finally, probabilities are computed using the dependent F distributions and F distributions based on order statistics of independent Chi-squares.

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Minimum Distance Estimation Based On The Kernels For U-Statistics

  • Park, Hyo-Il
    • Journal of the Korean Statistical Society
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    • v.27 no.1
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    • pp.113-132
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    • 1998
  • In this paper, we consider a minimum distance (M.D.) estimation based on kernels for U-statistics. We use Cramer-von Mises type distance function which measures the discrepancy between U-empirical distribution function(d.f.) and modeled d.f. of kernel. In the distance function, we allow various integrating measures, which can be finite, $\sigma$-finite or discrete. Then we derive the asymptotic normality and study the qualitative robustness of M. D. estimates.

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THE CONDITIONAL BOREL-CANTELLI LEMMA AND APPLICATIONS

  • Chen, Qianmin;Liu, Jicheng
    • Journal of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.441-460
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    • 2017
  • In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\mathfrak{F}$-independent random variables sequences, the convergence of sums of $\mathfrak{F}$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

FRACTIONAL DIFFERENTIATION OF THE PRODUCT OF APPELL FUNCTION F3 AND MULTIVARIABLE H-FUNCTIONS

  • Choi, Junesang;Daiya, Jitendra;Kumar, Dinesh;Saxena, Ram Kishore
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.115-129
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    • 2016
  • Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and usefulness in many branches of science, engineering, technology, earth sciences and so on. Saigo et al. [9] evaluated the fractional integrals of the product of Appell function of the third kernel $F_3$ and multivariable H-function. In this sequel, we aim at deriving the generalized fractional differentiation of the product of Appell function $F_3$ and multivariable H-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional differentiation, for example, Riemann-Liouville, $Erd\acute{e}lyi$-Kober and Saigo operators, associated with multivariable H-function and Appell function $F_3$ are shown to be deduced as special cases of our findings.

Strong Representations for LAD Estimators in AR(1) Models

  • Kang, Hee-Jeong;Shin, Key-Il
    • Journal of the Korean Statistical Society
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    • v.27 no.3
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    • pp.349-358
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    • 1998
  • Consider the AR(1) model $X_{t}$=$\beta$ $X_{t-1}$+$\varepsilon$$_{t}$ where $\beta$ < 1 is an unknown parameter to be estimated and {$\varepsilon$$_{t}$} denotes the independent and identically distributed error terms with unknown common distribution function F. In this paper, a strong representation for the least absolute deviation (LAD) estimate of $\beta$ in AR(1) models is obtained under some mild conditions on F. on F.F.

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Case influence diagnostics for the significance of the linear regression model

  • Bae, Whasoo;Noh, Soyoung;Kim, Choongrak
    • Communications for Statistical Applications and Methods
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    • v.24 no.2
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    • pp.155-162
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    • 2017
  • In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination $R^2$ and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in $R^2$ and F-statistic.