Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [bounds]

231 questions
30
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3 answers

Statistical methods for data where only a minimum/maximum value is known

Is there a branch of statistics that deals with data for which exact values are not known, but for each individual, we know either a maximum or minimum bound to the value? I suspect that my problem stems largely from the fact that I am struggling to…
user2390246
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6 answers

Can mean plus one standard deviation exceed maximum value?

I have mean 74.10 and standard deviation 33.44 for a sample that has minimum 0 and maximum 94.33. My professor asks me how can mean plus one standard deviation exceed the maximum. I showed her many examples about this, but she doesn't understand.…
Boyun Omuru
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2 answers

How can we bound the probability that a random variable is maximal?

$\newcommand{\P}{\mathbb{P}}$Suppose we have $N$ independent random variables $X_1$, $\ldots$, $X_n$ with finite means $\mu_1 \leq \ldots \leq \mu_N$ and variances $\sigma_1^2$, $\ldots$, $\sigma_N^2$. I am looking for distribution-free bounds on…
MLS
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3 answers

How to model bounded target variable?

I have 5 variables and I'm trying to predict my target variable which must be within the range 0 to 70. How do I use this piece of information to model my target better?
user333
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1 answer

Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by $$C(u_1,...,u_d)\leq \min\{u_1,..,u_d\}.$$ Is there a similar (in the sense that it depends on the marginal densities) upper bound for the copula…
Coppola
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16
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2 answers

What is the variance of the maximum of a sample?

I'm looking for bounds on the variance of the maximum of a set of random variables. In other words, I'm looking for closed-form formulas for $B$, such that $$ \mbox{Var}(\max_i X_i) \leq B \enspace, $$ where $X = \{ X_1, \ldots, X_M \}$ is a fixed…
Peter
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6 answers

Linear regression when Y is bounded and discrete

The question is straightforward: Is it appropriate to use linear regression when Y is bounded and discrete (e.g. the test score 1~100, some pre-defined ranking 1~17)? In this case, is it "not good" to use linear regression, or it's totally wrong to…
Master Shi
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13
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2 answers

Hypothesis testing and total variation distance vs. Kullback-Leibler divergence

In my research I have run into the following general problem: I have two distributions $P$ and $Q$ over the same domain, and a large (but finite) number of samples from those distributions. Samples are independently and identically distributed from…
M.B.M.
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12
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1 answer

Dealing with regression of unusually bounded response variable

I am attempting to model a response variable that is theoretically bounded between -225 and +225. The variable is the total score that subjects got when playing a game. Although theoretically it is possible for subjects to score +225. Despite this…
Jonathan Bone
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11
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1 answer

Expected number of times the empirical mean will exceed a value

Given a sequence of i.i.d. random variables, say, $X_i \in [0,1]$ for $i = 1,2,...,n$, I'm trying to bound the expected number of times the empirical mean $\frac{1}{n}\sum_{i=1}^n X_i$ will exceed a value, $c \geq 0$, as we continue to draw samples,…
fairidox
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11
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2 answers

Tail bounds on Euclidean norm for uniform distribution on $\{-n,-(n-1),...,n-1,n\}^d$

What are known upper bounds on how often the Euclidean norm of a uniformly chosen element of $\:\{-n,~-(n-1),~...,~n-1,~n\}^d\:$ will be larger than a given threshold? I'm mainly interested in bounds that converge exponentially to zero when $n$ is…
Ricky Demer
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11
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0 answers

Reference for $\text{Var}(X)\le (b-a)^2/4$

I am not a statistician, but am working a proof for the upper bound of an expression which contains the variance of a variable which obtains its values from a closed interval, [0,1]. I have seen in several places (mostly forums and web pages) the…
Adam Russell
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10
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2 answers

Understanding Hazard Function Values Exceeding 1

I keep running into problems in understanding hazard rates. I know, for example, that in a strict sense a hazard rate is not a probability and it is continually mentioned that because of this the hazard rate has no upper bound. Am I right in…
T Bonnett
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10
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2 answers

Regression results have unexpected upper bound

I try to predict a balance score and tried several different regression methods. One thing I noticed is that the predicted values seem to have some kind of upper bound. That is, the actual balance is in $[0.0, 1.0)$, but my predictions top at about…
Mennny
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9
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1 answer

Bounds on the difference of correlated random variables

Given two highly correlated random variables $X$ and $Y$, I'd like to bound the probability that the difference $ |X - Y| $ exceeds some amount: $$ P( |X - Y| > K) < \delta $$ Assume for simplicity that: The correlation coefficient is known to be…
Avanti89
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