6. On Bahadur's Representation of Sample Quantiles and on Kiefer's Theory of Deviations between the Sample Quantile and Empirical Processes

1983 ◽  
pp. 67-74
Keyword(s):  
Empirical Processes ◽  
Sample Quantile ◽  
Sample Quantiles

scholarly journals Moderate and Large Deviations for the Smoothed Estimate of Sample Quantiles

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Xiaoxia He ◽  
Xi Liu ◽  
Chun Yao
Keyword(s):  
Large Deviations ◽  
Sample Quantile ◽  
Large Deviations Principle ◽  
Sample Quantiles ◽  
Independent And Identically Distributed

We derive the moderate and large deviations principle for the smoothed sample quantile from a sequence of independent and identically distributed samples of sizen.

scholarly journals Defining Sample Quantiles by the True Rank Probability

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lasse Makkonen ◽  
Matti Pajari
Keyword(s):  
Extreme Events ◽  
Sample Quantile ◽  
Statistical Software ◽  
Standard Definition ◽  
Definition Of ◽  
Sample Quantiles

Many definitions exist for sample quantiles and are included in statistical software. The need to adopt a standard definition of sample quantiles has been recognized and different definitions have been compared in terms of satisfying some desirable properties, but no consensus has been found. We outline here that comparisons of the sample quantile definitions are irrelevant because the probabilities associated with order-ranked sample values are known exactly. Accordingly, the standard definition for sample quantiles should be based on the true rank probabilities. We show that this allows more accurate inference of the tails of the distribution, and thus improves estimation of the probability of extreme events.

Asymptotic Distribution of Sample Quantiles for Exchangeable Random Variables

1971 ◽  
Vol 20 (4) ◽  
pp. 135-142
Author(s):  
K. C. Chanda
Keyword(s):  
Normal Distribution ◽  
Asymptotic Distribution ◽  
Order Statistic ◽  
Multivariate Normal Distribution ◽  
Random Variables ◽  
Multivariate Normal ◽  
Sample Quantile ◽  
Exchangeable Random Variables ◽  
Sample Quantiles ◽  
Special Case

Summary The purpose of this article is to investigate the ‘large sample’ properties of sample quantiles when we assume that the basic random variables are exchangeable (ref. Loève (1960) p. 365). It is shown that under different conditions (to be specified below) on the nature of these exchangeable random variables the distribution of the sample quantile Xr : n where Xr : n is the rth order statistic for the first n exchangeable random variables [Formula: see text] tends, as n → ∞, to different nondegenerate forms. As an example, the special case of random variables with equicor-related multivariate normal distribution is discussed.

Some Comments on Quantiles and Order Statistics

1973 ◽  
Vol 16 (2) ◽  
pp. 289-293
Author(s):  
P. V. Ramachandramurty ◽  
M. Sudhakara Rao
Keyword(s):  
Order Statistics ◽  
Asymptotic Distribution ◽  
Sample Quantile ◽  
Underlying Distribution ◽  
Sample Quantiles

A new concept—that of pseudoconsistency—which seems to be particularly appropriate for the estimation of a quantile is introduced. It is shown without any conditions whatsoever on the underlying distributionthat the sample quantile is strongly pseudoconsistent for the corresponding population quantile. The asymptotic distribution of the sample quantiles and order statistics is derived when the underlying distribution is discrete.

On Bahadur's Representation of Sample Quantiles for Nonstationary Mixing Processes

1978 ◽  
Vol 27 (1-4) ◽  
pp. 23-36
Author(s):  
David A. Sotres ◽  
Malay Ghosh
Keyword(s):  
Remainder Term ◽  
Random Variables ◽  
Regularity Conditions ◽  
Sample Quantile ◽  
Mixing Processes ◽  
Sample Quantiles ◽  
Independent And Identically Distributed

For sequences of independent and identically distributed random variables, Bahadur (1966), obtained, under certain mild coniditions an elegant almost sure represetation of a sample quantile as an average of independent and identically distributed centered random variables plus a remainder term converging to zero almost surely at a faster rate. J. K . Ghosh (1971), obtained, under milder regularity conditions, a weaker version of the result. The present paper obtains under certain conditions Bahadur type results for non-stationary ø-mixing processes and J. K. Ghosh type results for non-stationary strongly mixed processes.

Sign in / Sign up

Export Citation Format

Share Document