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How to find the conditional CDF based on observed data in R

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;

3

$begingroup$

If we have two samples (generally their distribution is not known),say $Xsim N(0,1)$, $Y|Xsim N(X,X^2/2)$. Can we recover the conditional CDF of $Y|X$ based on the observed samples in R?

n=1000
x=rnorm(n)
y=rnorm(n,x,x^2/2)

r distributions conditional-probability cdf

share|cite|improve this question

asked 5 hours ago

J.MikeJ.Mike

1415

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  conditional PDF and CDF can be estimated nonparametrically. There is supposedly at least one package available for those purposes.
  $endgroup$
  – Gary Moore
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your kind comment! Do you have the reference for the method of nonparametric estimation and the R package?
  $endgroup$
  – J.Mike
  4 hours ago
  
  

  
  
  
  

add a comment | 

3

$begingroup$

If we have two samples (generally their distribution is not known),say $Xsim N(0,1)$, $Y|Xsim N(X,X^2/2)$. Can we recover the conditional CDF of $Y|X$ based on the observed samples in R?

n=1000
x=rnorm(n)
y=rnorm(n,x,x^2/2)

r distributions conditional-probability cdf

share|cite|improve this question

asked 5 hours ago

J.MikeJ.Mike

1415

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  conditional PDF and CDF can be estimated nonparametrically. There is supposedly at least one package available for those purposes.
  $endgroup$
  – Gary Moore
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your kind comment! Do you have the reference for the method of nonparametric estimation and the R package?
  $endgroup$
  – J.Mike
  4 hours ago
  
  

  
  
  
  

add a comment | 

$begingroup$

If we have two samples (generally their distribution is not known),say $Xsim N(0,1)$, $Y|Xsim N(X,X^2/2)$. Can we recover the conditional CDF of $Y|X$ based on the observed samples in R?

n=1000
x=rnorm(n)
y=rnorm(n,x,x^2/2)

r distributions conditional-probability cdf

share|cite|improve this question

asked 5 hours ago

J.MikeJ.Mike

1415

$endgroup$

n=1000
x=rnorm(n)
y=rnorm(n,x,x^2/2)

share|cite|improve this question

asked 5 hours ago

J.MikeJ.Mike

1415

share|cite|improve this question

asked 5 hours ago

J.MikeJ.Mike

1415

asked 5 hours ago

J.MikeJ.Mike

1415

asked 5 hours ago

J.MikeJ.Mike

1415

2 Answers
2

active

oldest

votes

2

$begingroup$

You can't determine the CDF from samples, but you can easily get an empirical estimate:

set.seed(1359)
n <- 1000
x <- rnorm(n)
y <- rnorm(n, x, x^2/2)

LM <- lm(y ~ 0 + x) # no intercept because you know this, though usually you won't
coef(LM)

Gives me $hatbeta = 1.076$, or $haty = 1.076 cdot x + epsilon$ (about $1times x$, as you specified).

Similarly, you can get an empirical estimate of the standard deviation you supplied with sd(resid(LM)).

---

If you don't know anything about their distributions, you could try a non-parametric approach.

share|cite|improve this answer

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer! Do you have the reference for the nonparametric approach?
  $endgroup$
  – J.Mike
  4 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

Finding the conditional distribution of a variable $Y$ conditional on another observed variable $X$ is the entire subject matter of regression analysis (construed in its wide sense to include linear and nonlinear regression models, GLMs, GLMMs, etc.). This is a huge subject and a core part of statistical education. If you would like to learn more about it, I would recommend starting with some material on linear regression analysis, and then building up from there.

share|cite

answered 9 mins ago

BenBen

28.8k233129

$endgroup$

add a comment | 

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2

$begingroup$

You can't determine the CDF from samples, but you can easily get an empirical estimate:

set.seed(1359)
n <- 1000
x <- rnorm(n)
y <- rnorm(n, x, x^2/2)

LM <- lm(y ~ 0 + x) # no intercept because you know this, though usually you won't
coef(LM)

Gives me $hatbeta = 1.076$, or $haty = 1.076 cdot x + epsilon$ (about $1times x$, as you specified).

Similarly, you can get an empirical estimate of the standard deviation you supplied with sd(resid(LM)).

---

If you don't know anything about their distributions, you could try a non-parametric approach.

share|cite|improve this answer

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer! Do you have the reference for the nonparametric approach?
  $endgroup$
  – J.Mike
  4 hours ago
  

  
  
  
  

add a comment | 

2

$begingroup$

You can't determine the CDF from samples, but you can easily get an empirical estimate:

set.seed(1359)
n <- 1000
x <- rnorm(n)
y <- rnorm(n, x, x^2/2)

LM <- lm(y ~ 0 + x) # no intercept because you know this, though usually you won't
coef(LM)

Gives me $hatbeta = 1.076$, or $haty = 1.076 cdot x + epsilon$ (about $1times x$, as you specified).

Similarly, you can get an empirical estimate of the standard deviation you supplied with sd(resid(LM)).

---

If you don't know anything about their distributions, you could try a non-parametric approach.

share|cite|improve this answer

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for your answer! Do you have the reference for the nonparametric approach?
  $endgroup$
  – J.Mike
  4 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

You can't determine the CDF from samples, but you can easily get an empirical estimate:

set.seed(1359)
n <- 1000
x <- rnorm(n)
y <- rnorm(n, x, x^2/2)

LM <- lm(y ~ 0 + x) # no intercept because you know this, though usually you won't
coef(LM)

Gives me $hatbeta = 1.076$, or $haty = 1.076 cdot x + epsilon$ (about $1times x$, as you specified).

Similarly, you can get an empirical estimate of the standard deviation you supplied with sd(resid(LM)).

---

If you don't know anything about their distributions, you could try a non-parametric approach.

share|cite|improve this answer

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

$endgroup$

set.seed(1359)
n <- 1000
x <- rnorm(n)
y <- rnorm(n, x, x^2/2)

LM <- lm(y ~ 0 + x) # no intercept because you know this, though usually you won't
coef(LM)

share|cite|improve this answer

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

answered 5 hours ago

Frans RodenburgFrans Rodenburg

3,6471529

1

$begingroup$

Finding the conditional distribution of a variable $Y$ conditional on another observed variable $X$ is the entire subject matter of regression analysis (construed in its wide sense to include linear and nonlinear regression models, GLMs, GLMMs, etc.). This is a huge subject and a core part of statistical education. If you would like to learn more about it, I would recommend starting with some material on linear regression analysis, and then building up from there.

share|cite

answered 9 mins ago

BenBen

28.8k233129

$endgroup$

add a comment | 

1

$begingroup$

Finding the conditional distribution of a variable $Y$ conditional on another observed variable $X$ is the entire subject matter of regression analysis (construed in its wide sense to include linear and nonlinear regression models, GLMs, GLMMs, etc.). This is a huge subject and a core part of statistical education. If you would like to learn more about it, I would recommend starting with some material on linear regression analysis, and then building up from there.

share|cite

answered 9 mins ago

BenBen

28.8k233129

$endgroup$

add a comment | 

$begingroup$

Finding the conditional distribution of a variable $Y$ conditional on another observed variable $X$ is the entire subject matter of regression analysis (construed in its wide sense to include linear and nonlinear regression models, GLMs, GLMMs, etc.). This is a huge subject and a core part of statistical education. If you would like to learn more about it, I would recommend starting with some material on linear regression analysis, and then building up from there.

share|cite

answered 9 mins ago

BenBen

28.8k233129

$endgroup$

share|cite

answered 9 mins ago

BenBen

28.8k233129

answered 9 mins ago

BenBen

28.8k233129

answered 9 mins ago

BenBen

28.8k233129