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Questions tagged [nonparametric]

Use this tag to ask about the nature of nonparametric or parametric methods, or the difference between the two. Nonparametric methods generally rely on few assumptions about the underlying distributions, whereas parametric methods make assumptions that allow data to be described by a small number of parameters.

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Paired Non-parametric test with more than 3 groups but just two timepoints

I may not have found the right term to search for, so I am asking what might be a straightforward question: Assume we have an experiment with paired non-normal distributed data, called "Pre" ...
StrugglingStatisticEnthusiast's user avatar
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Combining Data from Multiple Participants for Statistical Analysis of a Facial Expression Memory Task

Context of the Query: I am working on a project involving a memory task for facial expressions, consisting of two phases: Encoding Phase: In this phase, participants are exposed to 8 virtual ...
StupefiedByYou's user avatar
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Local linear kernel regression

It is know that the prediction for a given point $x$ is given by: $$\hat{f}_h(x) = \hat{\beta}_0(x)$$ where $$\hat{\beta}(x) = \arg\min_{\beta_0, \beta_1}\sum_{i=1}^nK\left(\frac{x - x_i}{h}\right)(...
user405777's user avatar
5 votes
3 answers
134 views

Non-parametric one-sample mean test for a bounded variable (based on Chebyshev's inequality?)

The problem I have $x_1, \ldots , x_n$ i.i.d. draws from r.v. $X$ such that $0 \leq X \leq 1$, but I can't make any other assumptions about the distribution. I want to test the null hypothesis that $E(...
Martin Modrák's user avatar
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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 ...
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expectation functional property

I'm trying to solve the second statement of the following exercise. It is Exercise 2.5 of "All of Nonparametric Statistics, Larry Wasserman". My try: \begin{align} |T(F)-T(G)| &= \left|\...
urikokp's user avatar
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3 votes
2 answers
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sample size in chi-squared test

The chi-square test of independence is a type of non-parametric test, but in cases of small sample sizes, the Fisher's exact test should be used instead. My understanding of non-parametric methods is ...
Ivan's user avatar
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Statistical test for unequal sample sizes of repeated measures (non-parametric)

I'm looking to understand the differences between various sources (50) that evaluate an event based on 8 ordinal scales (varying from 2 to 4 values) associated with a discrete score between 0 and 10, ...
ron's user avatar
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22 votes
7 answers
2k views

Isn't it problematic to look at the data to decide to use a parametric vs. non-parametric test?

I've seen in some instances of people mentioning that using a parametric vs. non-parametric approach may be decided by looking at the data. For example this question: nonparametric vs. parametric Isn'...
Coris's user avatar
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How do I get from integral to computational formula of Cramér-von Mises statistic step by step?

My question is related to the calculus procedures behind Cramér-von Mises test. How do I get from integral: to computational formula: of Cramér-von Mises statistic, step by step? I understand the ...
Édio Renato Fávaro's user avatar
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Statistical Significance Testing for Nested Cross-Validation in ML Experiment

I am currently working on an ML experiment where I use a nested 5-cross validation procedure and obtain a NDCG@10 scores for each test user. I am comparing 6 different ML algorithms and have data for ...
Bernhard's user avatar
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When is Tukey post hoc test result identical to Games Howell post hoc test for Welch ANOVA?

In what situations is the Tukey post hoc test identical to the Games Howell post hoc test? I have an ANOVA analysis where HOV is violated and I have a statistically significant Welch ANOVA result. I ...
L.S.'s user avatar
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Non-Parametric Two Way Within-Subjects ANOVA

I have a dataset with 4 individuals that are measured twice in each of the 5 groups (so in total 40 observations). Subject ID Group Value 1 1 A 45 1 2 A 62 1 1 B 70 1 2 B 37 ... ... ... ... 4 2 ...
mschal's user avatar
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Does the estimate of a nonparametric function changes when adding a parametric component?

I am estimating a semiparametric and a non-parametric model using a GAM function with the package mcgv in R. In particular I am ...
Bob's user avatar
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Why does the Dunn's test in online calculator rejects the null hypothesis while my manual computations cannot reject it?

In my own manual calculations of the Dunn's Test in google sheet, using the formula from a YouTube video, I managed to calculate the same Test Statistic as the online calculator. However, using the ...
FifthRevelathor's user avatar
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What non-parametric tests can be run to check the mediation analysis, since my data is not normally distributed?

I have two IVs (computed scores from likert scale) and one DV (computed scores from likert scale) IVs are Depression and Anxiety scores and DV is Social Connectedness scores. These are cintnuous. I ...
Muhammad Muneeb -ur-Rehman's user avatar
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Is bootstrapping inherently Frequentist? If so, how do we do a Bayesian non-parametric two-sample test?

I normally use frequentist statistics but I now want to use Bayesian statistics as I want to carry out a two-sample (randomised control trial) test that includes prior information. I have an existing ...
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Appropriate Trend Analysis Test for Small Sample Size

Note: I have read Finding an appropriate trend test but unfortunately this post does not apply for me Suppose I have a small sample of data for 2 numeric variables $T$ and $Y$ where $T$ represents ...
NM_'s user avatar
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2 votes
4 answers
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I want to show by simulation that the Wilcoxon test is more robust than the Student test for non-normally distributed data

I want to test by simulation that the Wilcoxon test is more robust than the Student test for non-normally distributed data. For example, I'm testing the ...
Seydou GORO's user avatar
1 vote
0 answers
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Welch ANOVA for Comparisons of Elevation & altered Sediment Accretion of Sea Ecosystems: Large DEM with no normal distribution & heterogeneity

I am investigating the elevation characteristics and sediment accretion effects of two distinct ecosystems within the Wadden Sea, impacted by the bioinvasion of one species (ecosystem one) and ...
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0 answers
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Non parametric tests for 2 way anova and linear model? [duplicate]

My dissertation is due very soon and I have only just realised a large mistake in my work. I misread the normality test I used, which actually showed non normal data- but I still have homogeneity of ...
Thomas B's user avatar
4 votes
1 answer
52 views

In what ways is Gaussian Process Regression both parametric and non-parametric?

Gaussian Process Regression is considered a "non-parametric" model. However, the term "non-parametric" is often used imprecisely to mean different things, leading to questions ...
socialscientist's user avatar
1 vote
1 answer
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Estimating Confidence in Feature Rankings from Multiple Experiments with Non-Normal Data

Hello dear Cross Validated Community, I am a new doctoral student in bioinformatics, and I am working on a project involving multiple experiments, each generating a single numerical result for each of ...
Thomas Rauter's user avatar
2 votes
1 answer
92 views

Non-Parametric Regression with an Omitted Variable

Suppose we use the Kernel Regression Estimator $$\hat{m}(c)=\frac{\sum_{i=1}^n K\left(\frac{x_i-c}{h}\right)y_i}{\sum_{i=1}^n K\left(\frac{x_i-c}{h}\right)}$$ where $h\to 0$ and $nh\to \infty$ as $n\...
Joseph Basford's user avatar
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0 answers
33 views

Singular Spectrum Analysis Decomposition on single input signal using PyTS module

I read this paper and was curious to apply it on a single-channel audio recording of mixed sources. It is about Singular Spectrum Analysis (SSA). The paper mentions that a key component of the ...
user3320707's user avatar
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0 answers
40 views

How to show $\sup_{x\in [a,b]}|f_n(x)-f(x)|=O_p(\sqrt{\frac{\log n}{nh}}+h^2)$ when the kernel $K(\cdot) $ is of bounded variation?

Consider the kernel estimate $f_n$ of a real univariate density defined by $$f_n(x)=\sum_{i=1}^{n}(nh)^{-1}K\left\{h^{-1}(x-X_i)\right\}$$ where $X_1,...,X_n$ are independent and identically ...
Kevin's user avatar
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2 votes
0 answers
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Controlling for regression to the mean in nonparametric survey response data - pre-post design - difference between groups

I have 920 pre-post responses to 5-point Likert-scale questions evaluating the impact of an educational intervention. I wish to test whether outcomes (change = post - pre) differed across different ...
Rachel's user avatar
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2 votes
1 answer
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Does the sign test only work on location families?

That is, if $G$ is the distribution of the sample, what does it test: \begin{align} \mathcal H_0 : G(x) = F(x) && \mathcal H_1 : G(x) = F(x - \theta), \theta \neq 0 \end{align} where $F$ is ...
Shaikh Ammar's user avatar
1 vote
0 answers
28 views

Strange results using Dunn's test [closed]

I am receiving a result that seems very counter-intuitive using the Dunn's test. My data is illustrated in the plot below. I have 5 groups (labelled muscle1a, muscle1b, muscle2, muscle3 and muscle4). ...
HanLisb's user avatar
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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
3 votes
0 answers
41 views

Can a Gaussian Process predict random events?

I know that we can use Gaussian processes effectively for function approximation and regression. However,suppose there is a sequence of points in time $S = \{s_1, s_2, \dots, s_n\}$, where $s_i$ can ...
Hassan Ali's user avatar
0 votes
0 answers
46 views

ACME Significant in Mediation analysis, but not Proportion Mediated and Fitting terminated with step failure warning

I am running a series of mediation analyses in R using the mediation package and the following code: ...
flâneur's user avatar
2 votes
1 answer
30 views

Biased Sampling from a Non-Normal Dataset

For my analysis, I'm interested in a particular subset from a non-normally distributed population. I would therefore like to generate a sample from that population. The sample will have drastically ...
Linkray's user avatar
  • 21
0 votes
0 answers
10 views

Estimation of bivariate function with one variable being constricted

Suppose the following classical supervised regression setting, $$y_{i} = f(x_{i}) + \epsilon_{i}, \quad i=1,\cdots,n,$$ where $\epsilon_{i}$ are i.i.d. zero mean Gaussian noise. The above regression ...
DoubleL's user avatar
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0 votes
0 answers
13 views

U -statistics for bi variate sample problem

Let $(X_1, Y_1), (X_2, Y_2),....,(X_n, Y_n)$ be iid random variables with joint distribution function $F(x, y)$ and $F(x), G(x)$ be the marginal distribution functions of $X_1$ and $Y_1$ respectively. ...
user771946's user avatar
3 votes
1 answer
66 views

Can I aggregate several continuous variables into percentages and then compare those percentages between groups?

I have a dataset with the concentrations of several lipids. I'm interested in finding lipids that are altered between two conditions, but the lipids are not indepentent from each other and the ...
maglorismyspiritanimal's user avatar
0 votes
0 answers
11 views

How to compare peak location and tail length of two different distributions?

I have the distributions of the fraction of people in each income bracket in a town in 1990 and 2020. The total sample size is the same in both, and assume that the incomes have been adjusted to ...
SNIreaPER's user avatar
0 votes
0 answers
17 views

Asymptotic distribution of $U$-statistics

Let $(X_1, Y_1), ...., (X_n, Y_n)$ be iid random vectors with marginal distributions functions $F(x)$ and $G(x)$ (both are continuous distributions) respectively such that $F(0)=G(0)=\frac{1}{2}$. ...
user771946's user avatar
0 votes
1 answer
30 views

Can I use Mann-Whitney U test for within group analysis?

I am conducting a within-group study where participants rate the perceived helpfulness of ideas on a Likert scale (DV) across two different days (Day 1 and Day 2), serving as the independent variable (...
JBUG's user avatar
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0 votes
1 answer
39 views

Statistical test for small non-parametric dataset with more than 2 dependent groups

I’m trying to figure out the most appropriate test to use for a small water quality dataset (n = 10 sampling visits at 6 river sites, upstream to downstream) with the following characteristics: -not ...
Aisha C's user avatar
0 votes
0 answers
14 views

How to determine goodness-of-fit between non-parametric 2d-datasets

Lets say I have a set of paired x' and y' values and I have a N sets of reference values also consisting of paired x and y values. I would like to determine which reference set best matches by x'y' ...
James London's user avatar
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0 answers
40 views

Estimate the likelihood of two continuous samples of unknown distribution

Consider two continuous and unknown distributions $$X : {x_1, x_2, ..., x_n}$$ and $$Y : {y_1, y_2, ..., y_n}$$ both can be tagged as time series with $n > 8000$. I need to estimate the likelihood ...
joueswant's user avatar
3 votes
3 answers
64 views

About regression analysis with categorical variables

Suppose my dependent variable is a continuous variable and is normally distributed. And I have three IVs: one is a continuous variable, and the other two independent variables are categorical. What ...
Ana's user avatar
  • 31
0 votes
0 answers
23 views

Identifying the type of missing data and the post hoc test that can be carried out for Skillings Mack test

I have a non-normal paired sample dataset. Each row represents a dog that has been tested for an experiment. Each dog was provided with three cues (treatments): 5s cue (aka only face cue), vocalone (...
Rohan Sarkar's user avatar
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0 answers
36 views

Implementing Convolution Function for Gaussian Kernel in Python for PDF Estimation

I am currently working on estimating a probability density function (PDF) nonparametrically using a Gaussian kernel. My goal is to determine the optimal bandwidth $h$ that minimizes the cross-...
Tim's user avatar
  • 273
1 vote
1 answer
121 views

Deriving Sample version of Anderson Darling test statistic from the theoretical version

In literature, I have seen two types of Anderson-Darling test statistic. One is expressed as $A_T^2 = n\int_{-\infty}^{\infty}\frac{(F_n(x)-F(x))^2}{F(x)(1-F(x))}dF(x)$ and the other is given by $A_s^...
DevD's user avatar
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1 vote
0 answers
68 views

$U$-statistics and their limiting distributions

Let $X_1,X_2, . . . ,X_n$ be i.i.d. observations from a continuous distribution $F$. Consider the parametric function $\mathbb{P}([\text{min}(X_1,X_2) > X3])$. Find the U-Statistics and its ...
user771946's user avatar
0 votes
0 answers
51 views

Relation between gini coefficient/accuracy ratio and roc_auc_score when there are many identical predictions

I have been working on ranking metrics related to various estimators lately, and cam a across a curious phenomenon related to the Gini-coefficient which I would like to understand better. I will start ...
user405288's user avatar
1 vote
0 answers
48 views

Doubt on non-parametric ANCOVA with two groups and pre-post scores and pre scores (baseline) as covariate

I have used a non parametric ANCOVA to analyze scores of a questionnaire (BSCS) with factors: Type of intervention(A and B) and timepoint (pre- and post) as well as baseline (same distribution as pre-)...
Fil's user avatar
  • 121
0 votes
0 answers
25 views

Help selecting an interpretable model to measure the impact of customer journey touchpoints on satisfaction

Context I'm working on a project where I need to undestand the impact of customer journey touchpoints on satisfaction. My goal is to create an interpretable model rather than a purely predictive one, ...
João Bugelli's user avatar

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