# Questions tagged [empirical-cumulative-distr-fn]

Empirical cumulative distribution function: a step function increasing by $1/n$ at each unique $X$-value that occurred in the sample.

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### Adjustment needed for multivariate Dvoretzky–Kiefer–Wolfowitz inequality on MCMC samples?

I was thinking about studying bounds on the multivariate empirical cumulative distribution function for samples from an MCMC chains. The multivariate Dvoretzky–Kiefer–Wolfowitz inequality would seem ...
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### What are the simplest examples of nonlinear statistical functionals?

I am reading Wasserman's book "All of Statistics" in which he defines a statistical functional as any function $T(F)$ of the cumulative distribution function $F(x)$ that outputs a real ...
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### Picking a specific estimated CDF from a set of CDFs provided by an ECDF

Let $F_X$ be a CDF of an unknown random variable $X$. If we have independent samples $x_1, x_2, \ldots, x_n$ of $X$ then we can estimate $F_X$ non-parametrically using an ECDF $\hat{F}_n$. By Central ...
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### Notation for ECDF

I'm reviewing statistical functionals and U-statistics, trying to make notes, and I am tripping on notation. From my understanding, $X$ is used to denote a random variable and $x$ is used to denote an ...
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### Density estimation from ECDF - numerical derivatives and scaled domains

Suppose we want to get a density estimate of some data X. One way is to compute the empirical CDF, ...
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### Confidence Interval of p-Quantile from Empirical CDF

I am trying to provide an interval estimate for the 0.8-quantile of some numeric data, which is assumed to be an IID sample from some unknown, continuous distribution. I constructed an Empirical CDF ...
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### Empirical estimation of conditional distribution $Y|X$ at the boundaries of X

I want to estimate conditional distributions of Y | X. Where X contains several continuous covariates. I'm coding in R. I tried several methods so far, but none gives me entirely satisfactory results ...
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1 vote
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### Does the Glivenko-Cantelli theorem work back and forth?

If we have a sample $X_1, X_2, \ldots, X_n \sim F$ then $\hspace{1mm}sup_x|F_n(x) -F(x)|\xrightarrow{a.s./p}0$. Now, if I can come up with a theoretical cdf $F$ such that \$\hspace{1mm}sup_x|F_n(x) -F(...
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