Skip to main content

Questions tagged [ranks]

Ranks are ordinal numbers of the quantitative data values sorted ascendingly or descendingly. Various methods to assign ranks to equal values (ties) exist. Transform of values to ranks is often done in nonparametric data analysis. (Not to confuse with [ranking] task..) (See related: [order-statistics])

Filter by
Sorted by
Tagged with
0 votes
0 answers
18 views

How to analyze rank data? Any books/tutorials recommended? [closed]

Suppose I have kept record of a certain group of players on a specific game, which only generates ranks without any scores (e.g. which player has gone the 2nd farthest by the end), over a long enough ...
Paw in Data's user avatar
1 vote
2 answers
35 views

How to create a rank from ranks?

I have calculated ranks for each row based on a condition on each column. Now I have, ...
Windy Day's user avatar
3 votes
1 answer
47 views

Suppose $(X,Y)$ have copula $C(u,v)$, does $(aX,aY)$ have the same copula for $a>0$?

Suppose $(X,Y)$ have copula $c(u,v)$ in the sense of $Pr(X\leq x,Y\leq y)=Pr(F_X(X)\leq F_X(x),F_Y(Y)\leq F_Y(y))=Pr(U\leq u, V\leq v)=c(u,v)$, where $u\equiv F_X(x)$ and $v\equiv F_Y(y)$ and $c(u,v)$ ...
ExcitedSnail's user avatar
  • 2,966
3 votes
0 answers
42 views

What is the minimum Pearson sample correlation given a perfect sample rank correlation with no ties? [duplicate]

Let $(X, Y)$ be a random sample of finite size $n$ from a bivariate continuous distribution with unknown parameters $(\rho_{XY},\mu_X,\mu_Y,\sigma_X,\sigma_Y)$. Assume observed values are real numbers ...
virtuolie's user avatar
  • 632
0 votes
0 answers
28 views

comprasion of data (ranks) to a certain data sample

Excuse me for mistakes, non-native here. I'll describe my uni research and the problem i have troubles solving. I study perception of composition in paintings, for this i have two independent groups: ...
Spaceparticle's user avatar
0 votes
0 answers
83 views

Conditional expectation given the rank of the variable

Suppose that we have a random variable $X$ with distribution $F_X(x)$. Define the rank of the variable as $R = F_X(X)$. What can we say about $\mathbb{E}[X \mid R]$? If $F_X(X)$ is strictly ...
ecnmetrician's user avatar
4 votes
1 answer
90 views

How can I compare the elements of two lists (in terms of overall similarity and order) in R?

I have a list of the 'actual' top 25 authors and I want to compare this to lists of predicted top 25 authors (I have 5x repeats of the predicted list). I want to compare actual and predicted both in ...
banananada's user avatar
1 vote
0 answers
14 views

Hoeffding’s formula for Locally most powerful rank tests

Suppose we have a testing problem with $$H_0: X_1,X_2, . . . ,X_n \ \text{are i.i.d. random variables with a continuous cdf} \ F(x) \ \text{and pdf} \ f(x)$$ and $$H_1: X_1,X_2, . . . ,X_n \ \text{are ...
user771946's user avatar
0 votes
0 answers
18 views

Give the distribution of an asymptotically Normal statistic, conditional on a function of sample ranks, and describe regression parameters

I'd like to write the following, about conditioning a normal r.v. on a rank statistic, but I'm unable to recall a specific theorem or theorems I can cite: "Let $\hat{\rho}$ be an asymptotically ...
virtuolie's user avatar
  • 632
2 votes
0 answers
43 views

rank aggregation with partial ranking lists

My question is about rank aggregation, which is in relation with statistics and decision sciences. (if this question is off the topic of this site, plz let me know.) The question is that I have N ...
Maul Seil's user avatar
1 vote
0 answers
105 views

Example probability model predicting vectors of ranks?

Background I'll confess, I like Richard McElreath's lectures so much that I've been watching his backlog of lectures (even though I've already seen all of the recent lectures of the same course). In ...
Galen's user avatar
  • 9,412
0 votes
0 answers
43 views

General rigorous justification of validity/power of bootstrap and ranking test?

Suppose we have data $X_1,\ldots, X_n$ and we want to do some Hypothesis test based on the value of a statistic $T.$ Let's say that the larger the value of $T,$ the more "likely" the ...
Ma Joad's user avatar
  • 163
0 votes
0 answers
33 views

Analysis of multivariate ranking data

I have data on companies, each company ranks how important are the following 4 elements (price leadership, quality, innovation, and customization) for its competitive strategy. There are 4 dependent ...
Giovanni's user avatar
0 votes
0 answers
4 views

Comparing ranks from differently sized sets across conditions

I performed a treatment-control experiment, with $r$ repeats per group. Each repeat $i$ consists of a set of $n_i$ observations. Each observation $j$ consist of a rank $x_{ij}$ and a class indicator $...
Knarpie's user avatar
  • 1,648
0 votes
1 answer
183 views

Distribution of rank differences for a paired dataset

I guess I have a rather simple question but I couldn't find the answer in previous posts. I have a paired dataset in which the same objects are ranked under two different conditions, here A and B: <...
Meisam's user avatar
  • 101
4 votes
1 answer
197 views

Kolmogorov-Smirnov test with median ranks instead of traditional empirical distribution function

I know that Kolmogorov-Smirnov test uses the empirical distribution function of the sample studied $\widehat{F}(X_i) = \frac{i}{n}$ and then measures the adequacy of function $\widehat{F}$ to function ...
Martin's user avatar
  • 43
1 vote
0 answers
21 views

Are paired matches in ranked data independent, if the original, unranked, continuous pairs are independent?

Let $(X, Y)$ be a randomly drawn sample of $n$ paired observations from a bivariate continuous population. It is clear that each pair is independent of the others, both pairwise and mutually. Let $R(X,...
virtuolie's user avatar
  • 632
1 vote
1 answer
136 views

Full-rank approximation to a square matrix

Let $\bf A$ be an $n \times n$ matrix with rank $r$ where $r<n$. How can I get a full-rank approximation for $\bf A$? In other words, I want to find the rank-$n$ $\bf X$ that minimizes the ...
MMM's user avatar
  • 850
0 votes
0 answers
52 views

Does the rank transform preserve signum of Spearman correlation between parameter estimates across samples?

Suppose we have real-valued random variables $X$, $Y$, with noise $\epsilon$ that is independent of $X$ and $Y$ and $\mathbb{E}[\epsilon] = 0$, and measurable function $f$. I am thinking about ...
Galen's user avatar
  • 9,412
2 votes
0 answers
117 views

Inference for Spearman's Correlation

Assume a set of variables $x_1,...,x_p$ and their variable importance indices given by two different predictive models. Regardless of the importance metric itself (as long as we use the same metric ...
Spätzle's user avatar
  • 4,012
3 votes
0 answers
49 views

How to statistically compare two rank correlations?

Lets suppose I have three random variables: $X$, $Y$, and $Z$. I can use the Spearman Rank Correlation to measure the degree of monotonic relation between any two of them. However what if I want to ...
naveace's user avatar
  • 115
0 votes
0 answers
24 views

How to simulate data with ties in R

I am using R to investigate the effect of tied values on rank-based correlation statistics I wish to simulate correlated bivariate standard normal data with some specified proportion of tied values (...
stweb's user avatar
  • 437
8 votes
4 answers
2k views

What is a rank?

I've been thinking about unifying some notions related to ranking, order theory, ordinal data, and graded posets. While the notion of a grade in order theory is quite general, in some sense the way we ...
Galen's user avatar
  • 9,412
0 votes
1 answer
179 views

How to compare two ranked lists of genes with ranking values?

I have 80 independent sets of genes with 6000 genes in each. Gene expression values are ranked and scaled from 0 to 1. So, a set looks like this: Gene1 1 Gene2 0.98 Gene3 0.85 ... Gene5998 0.002 ...
Yulia Kentieva's user avatar
6 votes
1 answer
526 views

How to interpret rank bar plot of a MCMC trace?

I am learning how to use PyMC for Bayesian inference. I coded up a random intercept $Y = \gamma + \sum_{j=1}^3 \beta_j \mathbb{I}_j + \epsilon$ and looked at the trace plots. Here is a ...
Galen's user avatar
  • 9,412
0 votes
0 answers
30 views

What is the relationship between the manifest correlation between ranked variables and the latent, continuous correlation?

Suppose you draw n pairs of observations from a real-valued bivariate distribution. You then convert each observation to its ascending rank order. Given the population correlation for the real-valued ...
virtuolie's user avatar
  • 632
1 vote
0 answers
20 views

Ranking log-linear distributions and the Lucas numbers

The wikipedia page on rank-size distributions claims: "When any log-linear factor is ranked, the ranks follow the Lucas numbers, which consist of the sequentially additive numbers 1, 3, 4, 7, 11,...
agnosticmantis's user avatar
3 votes
1 answer
61 views

assessing which random sample agrees more with a preferred ranking

I am not a mathematician or a statistician. But, I think the question I have is related to statistics. I will start with a made up example. If I can grade apples into,say four grades from 1 to 4, one ...
Ajith's user avatar
  • 33
0 votes
1 answer
94 views

Ranking by specific percentile

Is there a name for ranking categories by their value in a specific percentile (e.g., 66th percentile)? A fictitious example: Goethe published 9 books, Schiller published 7, and Herder published 3. We ...
anpami's user avatar
  • 111
2 votes
1 answer
49 views

Two-Sample Rank Statistics

Assume we got two models, either regression or RF or whatever. I'm trying to observe the relative importance of each feature by using ranks. That is, if we look at a regression model, we have a t-test ...
Spätzle's user avatar
  • 4,012
0 votes
0 answers
18 views

Algorthm for discerning which top X values in a list are statistically ranked higher than the bottom Y

Given a ranked list, which contains values with high uncertainty, I would like to remove as many of the middle values that have high overlap in uncertainties as possible, and be left with more or less ...
Charlie Crown's user avatar
2 votes
1 answer
2k views

What is the best way to represent Spearman’s correlation graphically?

For my thesis research I have to do Spearman’s correlation tests on a set of ordinal variables. I would like to represent the correlations graphically to include them in the report and give a clearer ...
balzy's user avatar
  • 139
1 vote
0 answers
35 views

Quantifying agreement of ordinally ranked sequences

I've been using a very particular set of closely related metrics to quantify how well two ranked sequences agree with one another. I'd like to know if this way of thinking is well-known and if any of ...
Mike Battaglia's user avatar
2 votes
2 answers
151 views

Testing for differential ranking between lists relative to a reference list

I am interested in comparing ranked lists in order to find elements that are differently ranked. Suppose we have 10 lists, each ranked (and for simplicity assuming the elements overlap and only the ...
ATpoint's user avatar
  • 29
0 votes
0 answers
247 views

Interaction between variables to create a ranking system

I was wondering if there is a standard way to rank cases by multiple variables. When we have only 1 quantitative variable, the ranking is trivial, you sort the cases by comparing the magnitude between ...
gabriel's user avatar
  • 93
6 votes
2 answers
1k views

Why Spearman's rank correlation ranges from from -1 to 1

$$\rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}$$ $\rho$ = Spearman's rank correlation coefficient $d_i$ = difference between the two ranks of each observation $n$ = number of observations Given the ...
william007's user avatar
  • 1,087
1 vote
1 answer
173 views

Correlation Test Between a Categorical Variable and an Ordinal (In the form of a ranking) Variable

I have a dataset of book sales by rank and the color of the cover. I would like to find a relationship between the rank of the book and the color of the cover. I'd like to know how to do this analysis ...
Lucas Tejedor's user avatar
8 votes
0 answers
319 views

Are there any surveys of the opinions of statisticians on the usefulness of classical rank-based nonparametric statistics?

The following comes from a YouTube video: Robustness in Statistics, which I have tried to quote verbatim. In Biology and Medicine these procedures are extremely popular, and I don't know why. They're ...
Galen's user avatar
  • 9,412
4 votes
2 answers
113 views

Is there a common notation for "the rank of $x_i$"?

Such as $x^{\text{r}}_{i}$, or $\text{rank}(x_{i})$, or something like that? (I just pulled those out of my bum, probably haven't seen them before.)
Alexis's user avatar
  • 30.3k
0 votes
1 answer
102 views

bootstrap time series using the rank

Don Walpola wrote a good overview of the bootstrap techniques used for time series (https://stats.stackexchange.com/a/450894). I searched through the literature, and did not find a single method ...
François Ritter's user avatar
0 votes
0 answers
20 views

Do statistical models allow for "ranking their outputs"?

Suppose you create a regression model that predicts the hourly salary based on age and height. Suppose you have some new age and height measurements for 5 new people. The regression model predicts the ...
stats_noob's user avatar
1 vote
1 answer
159 views

Which items in two ranked lists are ranked significantly different?

I have 91 items ranked by different demographic groups of questionnaire participants. The rank lists for each group are all the same length and contain identical items. I understand that I can perform ...
Routh_Gilson's user avatar
3 votes
2 answers
327 views

Why are extreme correlations so common in this Monte Carlo simulation? [duplicate]

Consider the following simple Monte Carlo: ...
Galen's user avatar
  • 9,412
0 votes
1 answer
103 views

How can I determine the rank of matrix $X$ given the LSE of $X\beta$?

I am given the LSE of $X\beta$, but I need to find the rank of $X$. Is there any result or theorem that allows me to obtain $r(X)$?
Oski's user avatar
  • 5
1 vote
0 answers
16 views

utilising ipsative measures

I am using a data set containing ipsative measures resulting from forced ranks. For example, respondents are asked to rank in terms of importance various methods of employee development (training, ...
Giovanni's user avatar
0 votes
0 answers
869 views

How to weight ranks?

I have a set of responses ranked by my participants. For example, they gave responses A, B, C and ranked them as 3, 2, 1 (or C, B, A). I computed relative frequencies of each responses (A, B, C) and ...
Petr Palíšek's user avatar
4 votes
2 answers
672 views

How to calculate Hodges-Lehmann estimator of slope in rank regression?

Suppose we have $n$ paired observations $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$, where $y$ is the response variable and $x$ is the covariate. Consider a simple linear regression model $$y_i=\alpha+\...
StubbornAtom's user avatar
  • 11.4k
1 vote
1 answer
138 views

Consistency of Wilcoxon rank sum statistic

In Chapter 1 of E. L. Lehmann's book Nonparametrics, he refers to the Wilcoxon Rank Sum test in treatment-control experiments. Using Lehmann's notation, let $N$ be the total number of units, $n$ the ...
Student_718's user avatar
1 vote
1 answer
117 views

Invertibility of $E(X^\top X)$ and $\tilde{X}^\top \tilde{X}$

Consider the linear regression model with 3 regressors $$ Y=\beta_1 Q+\beta_2 W+\beta_3 Z+\epsilon $$ Let $X\equiv (Q, W, Z)$ and $\beta\equiv (\beta_1,\beta_2,\beta_3)^\top$. Also suppose that $Q,W,...
Star's user avatar
  • 891
2 votes
0 answers
183 views

Understanding a proof of the relation between Walsh averages and Wilcoxon signed rank test statistic

I am trying to understand a particular proof of the relation between Walsh averages and the Wilcoxon signed rank test statistic, as given in the book Statistical Inference Based on Ranks by T.P. ...
StubbornAtom's user avatar
  • 11.4k