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Topic: Quantile

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Beta distribution

Quartile

Percentile

Correlation ratio

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Calibration (statistics)

Descriptive statistics

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	quantile algorithm
		Quantiles in between 0.125 and 0.875 are evaluated by linear interpolation: the 0.25, 0.50, and 0.75 quantiles are 17.5, 26, and 46, respectively.
		Quantiles between 0 and 0.125 or between 0.875 and 1 are evaluated by linear extrapolation from the lowest or highest pair of values: the 0% quantile is estimated as 15 - 1/2 (20 - 15) = 12.5, and the 100% quantile is estimated as 60 + 1/2 (60 - 32) = 74.
		The 0.10 quantile is estimated as 12.5 + (15 - 12.5)·(0.10 - 0.0)/(0.125 - 0.0) = 14.5.
	www.fon.hum.uva.nl /praat/manual/Quantile_algorithm.html (514 words)

	Quantile - Wikipedia, the free encyclopedia
		Quantiles are essentially points taken at regular intervals from the cumulative distribution function of a random variable.
		For an infinite population, the kth quantile is the data value where the cumulative distribution function is equal to k/q.
		Closely related is the subject of least absolute deviations, a method of regression that is more robust to outliers than is least squares, in which the sum of the absolute value of the observed errors is used in place of the squared error.
	en.wikipedia.org /wiki/Quantile (886 words)

	Quantiles
		The quantiles of principal interest are the median and the quartiles.
		Quantiles are revealed in the bottom part of the normal quantile plot.
		The dependence of the power quantiles on the ability of the aircraft to land on a carrier can be obtained from a conditioning normal quantile plot.
	www.stat.wvu.edu /SRS/Modules/Quantiles/quantiles.html (411 words)

	VisiCube Quantile Array (Site not responding. Last check: 2007-10-20)
		A quantile plot is a univariate plot in which the distribution of a measure is presented with pertinent statistical values, including quantiles, used as demarcations along the measure's scale.
		This axis is divided into quantiles, typically quarters, and labeled with the fraction (between 0 and 1) which represents the applicable quantile.
		For example, the 0.5 quantile (which is the median) is the quantile for which half of the measurements are on the minimum side of the quantile line.
	www.datamology.com /sample-QA.shtml (304 words)

	ZEW Veranstaltungskalender
		Quantile regression methods offer a powerful and natural approach to analyzing statistical variability caused by heteroscedasticity in the data or inhomogeneity in the population.
		First, the quantiles of the survival function are often of fundamental importance and so direct estimation of the quantiles is especially natural.
		Prior to 2004, this approach had been hampered by not having a conditional quantile estimator for censored data that is directly analogous to the Kaplan-Meier estimator for a single sample.
	www.zew.de /de/veranstaltungen/details.php?LFDNR=403&mi=VER&si=ARC (268 words)

	UNGROUPED QUANTILE ESTIMATION (Site not responding. Last check: 2007-10-20)
		For ungrouped quantile estimation the data are sorted in increasing order on the values of the analysis variable.
		The quantile estimate for the cell is then computed by interpolation between successive cumulative weights.
		This in turn is used to estimate the standard error for the quantile using confidence intervals.
	www.rti.org /SUDAAN/onlinehelp/FlashHelp/sudaanUNGROUPEDESTIMATION_MEDIAN.html (146 words)

	Ed231C: Regression with Measurement Error
		According to Koenker (2000), quantile regression is a statistical technique intended to estimate and conduct inference about conditional quantile functions.
		Quantile regression methods offer a mechanism for estimationg the conditional median function in addtion to other conditional quantile functions.
		Ordinary least squares regression asks the question "How does the conditional mean of Y depend on the covariates X?" Quantile regression asks this question at each quantile of the conditional distribution giving a more complete description of how the conditional distribution of Y given X. In Stata this can be done using the qreg command.
	www.gseis.ucla.edu /courses/ed231c/notes1/quantile.html (1204 words)

	1.3.3.24. Quantile-Quantile Plot
		A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set.
		For a probability plot, the quantiles for one of the data samples are replaced with the quantiles of a theoretical distribution.
		If the data sets are not of equal size, the quantiles are usually picked to correspond to the sorted values from the smaller data set and then the quantiles for the larger data set are interpolated.
	www.itl.nist.gov /div898/handbook/eda/section3/qqplot.htm (628 words)

	ZEW Publikationen
		Quantile regression methods are emerging as a popular technique in econometrics and biometrics for exploring the distribution of duration data.
		Censored quantile regression address the issue of right censoring of the response variable which is common in duration analysis.
		Quantile regression do not impose a proportional effect of the covariates on the hazard over the duration time.
	www.zew.de /de/publikationen/publikation.php3?action=detail&art=12&nr=2654 (188 words)

	Randomized Quantile Residuals: Abstract of Paper
		Quantile residuals are easily computed in computer packages such as SAS, S-Plus, GLIM or LispStat, and allow residual analyses to be carried out in many commonly occurring situations in which the customary definitions of residuals fail.
		Quantile residuals are applied in this paper to three example data sets.
		In the discussion at the end of the paper we briefly indicate how quantile residuals may be extended to models with dependent responses.
	www.statsci.org /smyth/pubs/residual.html (491 words)

	Predicted Values
		The estimated quantile is computed by replacing the unknown parameters with their estimates, including any shape parameters on which the baseline distribution might depend.
		The estimated quantile of the original response is obtained by taking the exponential of the estimated log quantile unless the NOLOG option is specified in the preceding MODEL statement.
		The standard errors of the quantile estimates are computed using the estimated covariance matrix of the parameter estimates and a Taylor series expansion of the quantile estimate.
	www.jmu.edu /docs/sasdoc/sashtml/stat/chap36/sect17.htm (207 words)

	quantile (Site not responding. Last check: 2007-10-20)
		Roughly speaking the pth quantile splits a distribution with p· 100% of the values less than the pth quantile and (1
		The pth quantile of a data vector is found at position 1 + p(n
		the quartiles - the 0, 0.25, 0.5, 0.75 and 1.0 quantiles - are returned.
	www.math.csi.cuny.edu /st/stRmanual/quantile.html (105 words)

	Quantile
		The qth quantile of a data set is defined as that value where a q fraction of the data is below that value and (1-q) fraction of the data is above that value.
		For example, the 0.5 quantile is the median.
		is a number in the interval (0,1) that specifies the desired quantile.
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/quantile.htm (505 words)

	GloriaMundi Resource Detail page
		Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions.
		Other conditional quantile functions are estimated by minimizing an asymmetricaly weighted sum of absolute errors.
		Quantile reguression methods are illustrated with applications to models for CEO pay, food expenditure and infant birthweight.
	www.gloriamundi.org /detailpopup.asp?ID=453055873 (93 words)

	GloriaMundi Resource Detail page
		This paper discusses implementation of a sequential procedure to construct proportional half-width confidence intervals for a simulation estimator of the steady-state quantiles and histograms of a stochastic process.
		It is known that order statistics quantile estimator is asymptotically unbiased when the output sequences satisfy certain conditions.
		An experimental performance evaluation demonstrates the validity of using the QI procedure to estimate the quantiles and histograms.
	www.gloriamundi.org /detailpopup.asp?keywords=heuristic&ID=453058031 (137 words)

	[No title]
		Similarly, the.75 quantile (also referred to as the 75th percentile or upper quartile) is a value such that 75% of the values of the variable fall below that value and is calculated accordingly.
		In this plot, the observed values of a variable are plotted against the theoretical quantiles.
		The lower and upper quartiles (this term was first used by Galton, 1882; also referred to as the.25 and.75 quantiles) are the 25th and 75th percentiles of the distribution (respectively).
	www.statsoft.com /textbook/glosq.html (2080 words)

	Stata FAQ: How do I interpret quantile regression coefficients?
		In the median regression the constant is the median of the sample while in the.75 quantile regression the constant is the 75th percentile for the sample.
		The interpretation for the.75 quantile regression is basically the same except that you substitute the term 75th percentile for the term median.
		The quantile regression coefficent tells us that for every one unit change in socst that the predicated value of write will increase by.6333333.
	www.ats.ucla.edu /stat/Stata/faq/quantreg.htm (1128 words)

	GloriaMundi Resource Detail page
		Quantile estimation has become increasingly important, particularly in the nancial industry, where Value at Risk has emerged as a standard measurement tool for controlling portfolio risk.
		In this paper we analyze the probability that a quantile estimator fails to lie in a pre-speci ed neighborhood of the true quantile.
		Then we consider strati ed quantile estimators and show that the error probability for these estimators can be guaranteed to be 0 with suciently large, but nite, sample size.
	www.gloriamundi.org /detailpopup.asp?keywords=Error&ID=453056368 (118 words)

	Working paper (Site not responding. Last check: 2007-10-20)
		Quantile regression(QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means.
		Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive.
		The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile correlation concept, similar to the relationship between partial correlation and OLS.
	www.eerc.ru /details/WorkingPaper.aspx?handle=RePEc:nbr:nberwo:10428 (234 words)

	Single pass space efficient system and method for generating an approximate quantile in a data set having an unknown ...
		The approximate φ-quantile is guaranteed to lie within a user-specified approximation error ε of the true quantile being sought with a probability of at least 1-δ, with δ being a user-defined probability of failure.
		B buffers, each having a capacity of k elements, initially are filled with elements from the data set, with the values of b and k depending on approximation error e and the probability δ.
		In later iterations (when the height of the tree is at least equal to a predetermined height that depends on δ and ε), the data is sampled non-uniformly to populate the buffers to render the desired performance.
	www.delphion.com /details?pn=US06343288__ (924 words)

	The Quantile Framework for Mathematics
		Quantiles enable educators to target instruction by identifying the mathematical skills a student has mastered, the skills that require more instruction, and new skills the student is ready to learn.
		A Quantile measure (i.e., 850Q) identifies both the difficulty of a mathematical skill or task—called a “QTaxon”—and a student’s mastery of the QTaxons across the following strands: Numbers and Operations, Geometry, Measurement, Algebra, and Data Analysis and Probability.
		The Quantile Framework is instrument-independent, meaning all mathematics tests and instructional programs have the ability to report students’ scores as Quantiles.
	www.quantiles.com /DesktopDefault.aspx?view=ed (217 words)

	GloriaMundi Resource Detail page
		Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the eect of covariates not only in the center of a distribution, but also in the upper and lower tails.
		Specifically, it obtains the large sample properties of extremal (extreme order and intermediate order) quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values.
		In large samples, extreme order regression quantiles converge weakly to argmin functionals of stochastic integrals of Poisson processes that depend on regressors, while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design.
	www.gloriamundi.org /detailpopup.asp?ID=453057227 (184 words)

	Re: st: Is there a fixed effect quantile regression in STATA?
		on page 89: "Useful feaures of the quantile regression and censored quantile regression models can be summarized as follows:......, (e) potentially different solutions at distinct quantiles may be interpretated as differences in the response of the dependent variable to the changes in the regreessors at various points in the conditional distribution of the dependent variable;....."
		Consider the partial derivative of the conditional (theta-th) quantile of y with repspect to one of the regressors, say, x.
		This derivative is to be interpreted as the marginal change in the (theta-th) quantiledue to the marginal change in x.
	www.stata.com /statalist/archive/2004-07/msg00926.html (589 words)

	Strong approximation of quantile processes by iterated Kiefer processes, Paul Deheuvels
		The notion of a $k$th iterated Kiefer process $\mathscr{K}(v,t;k)$ for $k \in \mathbb{N}$ and $v, t \in \mathbb{R}$ is introduced.We show that the uniform quantile process $\beta_n(t)$ may be approximated on [0,1] by $n^{-1/2} \mathscr{K}(n,t;k)$, at an optimal uniform almost sure rate of $O(n^{-1/2 + 1/2^{k+1}+o(1)})$ for each $k \in \mathbb{N}$.
		Functional laws of the iterated logarithm for the increments of empirical and quantile processes.
		Kiefer, J. Deviations between the sample quantile process and the sample d.f.
	projecteuclid.org /getRecord?id=euclid.aop/1019160265 (685 words)

	EmpiricalQuantiles (JMSL Numerical Library)
		The algorithm returns the empirical quantiles and, for each quantile, the two order statistics from the sample that are at least as large and at least as small as the quantile.
		For a sample of size n, the quantile corresponding to the proportion p is defined as
		The quantiles are determined by linear interpolation between adjacent ordered sample values.
	www.vni.com /products/imsl/jmsl/v40/api/com/imsl/stat/EmpiricalQuantiles.html (189 words)

	Uniform consistency of generalized kernel estimators of quantile density, C. Cheng
		Various smoothing methods for quantile density estimation are unified into a generalized kernel smoothing.
		Based on a stochastic upper bound of the derivatives sequence for a sequence of smoothed Brownian bridges, uniform in-probability consistency of generalized kernel quantile density estimators on any closed subinterval of the open unit interval is derived.
		FALK, M. On the estimation of the quantile density function.
	www.projecteuclid.org /Dienst/UI/1.0/Display/euclid.aos/1034713657 (275 words)

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