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    A new approach to quantile regression
    (Maltepe Üniversitesi, 2009) Ardalan, Arash; Mardani-Fard, H. A.
    In this paper, we present a new approach to the quantile regression context that combine classical quantile regression approach given by Koenker and Bassett (1978) which estimates quantiles by specialized linear programming techniques, with expectile regression given by Efron (1991) and Newey and Powell (1987) which is very much related to the classical quantile regression. We try to compare these three methods. It is known that the quantiles also coincide with the maximum likelihood solution of the location parameter in a class of asymmetric distribution. In this regard, we present a new class of asymmetric distributions and investigate the properties and asymptotic behavior of maximum likelihood estimators of the parameters.
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    What are copulas?
    (Maltepe Üniversitesi, 2009) Mardani-Fard, Heydar Ali; Ardalan, Arash
    A copula is, in fact, a multivariate distribution function with standard uniform margins. Sklar (1959) proved that for a d?variate distribution function F with univariate margins F1, . . . , Fd, there exists a d?copula, CF , such that F (x) = F (x1, . . . , xd) = CF (F (x1), . . . , F (xd)), for all x ? R d . Studying multivariate distribution functions with given margins coincides with studying copulas. For example, looking for bounds on a specified class of multivariate distribution functions with given margins coincides with trying to find bounds on a class of copulas with related conditions. Also,CF can be stand for the joint information of F , against its marginal information (that are all in its marginal distribution functions). As a result, in the studying of association of two random variables, it is useful to restrict our attentions to the copula-based measures. In this work we give some interpretations and properties of copulas and present some ways to construct a copula. Also, some applications of copulas were presented. In many parts of this work, the particular case d = 2 is discussed.