Koenker, R., Bassett, G. J., Regression quantiles, Econometrica, vol. 46 (1), pp. 33-50, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....t, Cauchy, and Burr distributions, while corresponds to # 0 the distributions such as the normal, lognormal, exponential, and gamma, whose tails decay exponentially. The case includes distributions like the uniform and beta, with finite upper # 0 bound. The quantile regression methods of Koenker and Bassett (1978) represent an alternative, robust approach to the estimation of conditional quantile functions. These methods estimate forecasting relationships at a particular quantile of the conditional distribution of y by choosing estimates of its parameters as the solution to the minimisation problem min ....

Koenker R, Bassett G. 1978. Regression quantiles. Econometrica 46:33-50.

....a test to establish the quality of the estimate. 3 In this paper we address each of these issues. We propose a conditional autoregressive specification for VaR t , which we call Conditional Autoregressive Value at Risk (CAViaR) The unknown parameters of the CAViaR models are estimated using Koenker and Bassett s (1978) regression quantile framework. Building on White (1994) and Weiss (1991) we extend the results of the linear regression quantile to the nonlinear dynamic case, providing the asymptotic distribution of the estimator and a procedure to estimate the variance covariance matrix. We also show how to ....

....X a OLS OLS c q q d d While this measure of performance is quite useful, its distribution in sample is affected by the fact that the Hits are functions of estimated parameters. We will discuss this problem in section 6. 5. REGRESSION QUANTILES Regression quantiles models were introduced by Koenker and Bassett (1978). They show how a simple minimization problem yielding the ordinary sample quantiles in the location model can be generalized to the linear regression model. Consider a sample of independent observations on random variables y 1 , y t distributed according to (12) t y t t x F x y t t = ....

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Koenker, R. and G. Bassett (1978), Regression quantiles, Econometrica, 46: 33-50.

....asymmetric least absolute deviation (ALAD) first suggested in 1 Throughout the paper, we use risk and volatility interchangeably. 2 Taylor effect states that the absolute return has the highest autocorrelations among all of its power transformation. See Section 4 in Granger and Ding (1995) 3 Koenker and Bassett (1978) in the context of robust estimation. Further details can be found in the next section. For comparison, we also consider a conventional autoregressive conditional heteroskedasticity like (ARCH like) model called Asymmetric Power ARCH (A PARCH) first suggested in Ding et al. 1993) More ....

Koenker, R. and G. Bassett (1978), "Regression Quantiles," Econometrica 46, pp.33-55.

....paper, we examine first and second order asymptotic theory for two estimators in a linear quantile model in the case where the response is observed multiple times at fixed covariate vectors x 1 ; Delta Delta Delta ; x k . The first estimator is the regression quantile estimator introduced by Koenker and Bassett (1978) while the second estimator is a least squares estimator on the sample quantiles of the response at each x i . In particular, it is shown that, under an i.i.d. error model, the two estimators are asymptotically equivalent to first order but have different second order behaviour. Key words and ....

....an i.i.d. error model, the two estimators are asymptotically equivalent to first order but have different second order behaviour. Key words and phrases: Bahadur Kiefer representations, regression quantiles, least squares estimation. 1 Introduction Quantile regression estimation was introduced by Koenker and Bassett (1978) as a means of estimating conditional quantiles in linear regression models. It has become a widely used and accepted technique in many areas; for example, Koenker (2000) gives a survey of applications in economics while Haire et al. (2000) apply quantile regression estimation to a problem in ....

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Koenker, R. and Bassett, G. (1978) Regression quantiles. Econometrica. 46, 33-50.

....distribution are unimportant. However, this may prove inadequate in some research agendas. If exogenous variables influence parameters of the conditional distribution of the dependent variable other than the mean, then an analysis which disregards this possibility will be severely weakened (see Koenker and Bassett, 1978). Unlike OLS, quantile regression models allow for a full characterisation of the conditional distribution of the dependent variable. 11 , 12 10 An alternative quote might be taken from Mosteler and Tukey, 1977, p. 266, quoted in Mata and Machado (1996) What the regression curve does is give ....

Koenker, R. and G. Bassett (1978) `Regression quantiles', Econometrica, 46, 33-50.

....the exogenous variables on the independent variable along the conditional distribution are unimportant. If the independent variables in uence parameters of the conditional distribution of the dependentvariable other than the mean, then an analysis which disregards this possibility will be weakened (Koenker and Basset, 1978). In contrast to OLS, quantile regression models allowtoanalyze the conditional distribution of the dependent variable. As we have outlined above, employer learning seems to be important only for blue collar workers. Two reasons can put forward to explain this nding. First, employers are unable ....

....the importance of employer learning for the returns to schooling is di erent at di erent quantiles of the wage distribution, i.e. we hypothesize that employer learning is only important for jobs at the lower end of the earnings distribution. The quantile regression model can be written as (see Koenker and Basset, 1978; Buchinsky, 1994, 1995) # # = # # # # # ### #### ##### # (# # ## # ) # # # # # (4) where # # is a vector of exogenous variables and # # is the vector of parameters to be estimated. ##### # (# # ## # ) denotes the #th conditional quantile of # # given # # . The #th regression quantile, 12 0 ....

Koenker, R. and G. Bassett (1978): \Regression Quantiles," Econometrica, ##, 33-50.

....a significant part of the effect of union membership on wages. Assuming a linear specification of the conditional quantile of the logarithm of wages (lnW) the conditional quantile of lnW may be denoted as 13 More detailed expositions of the theory and uses of quantile regression can be found in Koenker and 7 Basset (1978), Deaton (1997) and Buchinsky (1998) STATA s sqreg command is used. It allows simultaneous estimation of different quantile equations 8 and yields an estimate of the entire variance covariance matrix of the estimators by bootstrapping. All t values are calculated based on bootstrapped ....

Koenker, R., and G. Bassett. 1978. Regression quantiles. Econometrica 46 (1): 33-50.

....of regression quantiles for a more complete picture of the data at hand. Some interesting examples of quantile regression in linear models and nonparametric models can be found in Efron (1991) Hendricks and Koenker (1992) and He, Ng and Portnoy (1995) The formulation of regression quantiles by Koenker and Bassett (1978) opened a new window for regression analysis. Instead of taking the squared distance in (1.1) we minimize n X i=1 ae ff (Y i Gamma X T i fi Gamma g n (T i ) 1:2) where g n is a function in a m dimensional B spline space and ae ff (s) jsj (2ff Gamma 1)s (1:3) is used to obtain an ....

Koenker, R. and Bassett, G. (1978), Regression quantiles, Econometrica, 46, 33-50.

....of # 0 under this restriction was defined by Newey and Powell (1990) as # = arg min # 1 n n X i=1 # # (y i min x # i #, c i ) 2.12) where # # (u) # [# 1 u 0 ] u; 2. 13) this estimator is the censored data analogue to the regression quantile estimator proposed by Koenker and Bassett (1978) for the linear model. Under regularity conditions, it was shown that the estimator # solves a set of estimating equations obtained as approximate first order conditions from this minimization problem: o p (n 1 2 ) 1 n n X i=1 [# 1 y i # x # i # ] 1 x # i # c i x i ....

Koenker, R. and G.S. Bassett (1978), "Regression Quantiles," Econometrica, 46, 33-50.

.... the th conditional quantile of y given x can be estimated by x 0 fi n where fi n minimizes n X i=1 ae (z i Gamma minfx 0 i fi; cg) 3:3) with ae (r) rI(r 0) Gamma (1 Gamma )rI(r 0) The fact that the quantiles solve an optimization problem through ae was first recognized by Koenker and Bassett (1978) for linear regression models. Powell (1986) proposed the above formulation (3.3) for censored regression quantiles. The regression quantile approach avoids any parametric distributional assumption on u. In fact, the estimate is consistent even when the conditional distribution of y given x varies ....

Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica, 50, 1577-1584.

....10 P.J.ROUSSEEUW AND A.STRUYF This is equivalent to med(Y jX = x 0 ) x 0 ; 1) which says that the conditional median of Y given x 0 is linear in x 0 . This is an essential requirement for the applicability of methods like least absolute deviations regression and regression quantiles (Koenker and Bassett 1978). An interesting property of the model (3.2) is that it allows for skewed error distributions and heteroscedasticity. Since the median of Y jX = x 0 need not be unique, we could expand definition (3.2) to P 2 H , P(E 0jX = x 0 ) P(E 0jX = x 0 ) for all x 0 2 IR p : However, we need to go ....

Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica 46 33--50.

....Generalized Linear Models (cf. e.g. Liang Zeger 1986 and Zeger et al. 1988) 7. L q ESTIMATION In this section, we consider a linear estimating equation in which g i (y i ,#)isnot di#erentiable with respect to #. Such situations arise in nonparametric and semiparametric models (cf. e.g. Koenker Bassett 1978 and Hettmansperger 1984) and in robust regression (e.g. Huber 1981) We consider the general regression model (28) and suppose that # is to be estimated by minimization of n # i=1 y i f(x i ,#) a for some a,1#a#2. When a = 2, this yields the least squares estimator, but for other ....

....# is to be estimated by minimization of n # i=1 y i f(x i ,#) a for some a,1#a#2. When a = 2, this yields the least squares estimator, but for other values of a, a more robust procedure than least squares is obtained. For 25 example, a = 1 yields the median regression; cf. e.g. Koenker Bassett (1978). In general, we have the following estimating equation, n # i=1 sign y i f(x i ,#) A(x i ,#) y i f(x i ,#) a 1 =0. 34) We consider a =1.5 for which both the multidimensional and nuisance parameter problems can be addressed. We confine attention to simple linear regression, f(x i ....

R. Koenker & G. J. Bassett (1978). Regression quantiles. Econometrica, 84, 33--50.

....fi 0 under this restriction was defined by Newey and Powell (1990) as fi = arg min fi 1 n n X i=1 ae (y i Gamma minfx 0 i fi; c i g) 2.12) where ae (u) j [ Gamma 1fu 0g] Delta u; 2. 13) this estimator is the censored data analogue to the regression quantile estimator proposed by Koenker and Bassett (1978) for the linear model. Under regularity conditions, it was shown that the estimator fi solves a set of estimating equations obtained as approximate first order conditions from this minimization problem: o p (n Gamma1=2 ) 1 n n X i=1 [ Gamma 1fy i x 0 i fig] Delta 1fx 0 i ....

Koenker, R. and G.S. Bassett (1978), "Regression Quantiles," Econometrica, 46, 33-50.

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Koenker, R., Bassett, G. J., Regression quantiles, Econometrica, vol. 46 (1), pp. 33-50, 1978.

No context found.

R. Koenker and G. Bassett, "Regression quantiles," Econometrica, vol. 46, no. 1, pp. 33--50, 1978.

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Koenker, R., and G. Bassett (1978), "Regression Quantiles," Econometrica, 46, 33-50.

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Koenker, R. and Bassett, G. (1978) Regression quantiles. Econometrica. 46, 33-50.

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Koenker, R. and G. Bassett (1978), Regression quantiles, Journal of the American Statistical Association 82, 851-857.

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Koenker, R. and G.S. Bassett Jr. (1978) "Regression Quantiles", Econometrica, 46, 33-50.

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Koenker, R. and G.S. Bassett Jr. (1978), \Regression Quantiles", Econometrica, 46, 33-50

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Koenker, R. and G.S. Bassett Jr. (1978), "Regression Quantiles", Econometrica, 46, 33-50

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Koenker, R. and Bassett, G. Jr. (1978). Regression quantiles. Econom. 46, 33--50.

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Koenker, R. and G.S. Bassett Jr. (1978) "Regression Quantiles", Econometrica, 46, 33-50.

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Koenker, R. and G.S. Bassett Jr. (1978), "Regression Quantiles", Econometrica, 46, 33-50

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Koenker, R. and Bassett, G. (1978). Regression Quantiles, Econometrica, 46, 33-50.

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