# 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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### Nonparametric Order Statistics - Does this Exist?

I was reading about Order Statistics (https://en.wikipedia.org/wiki/Order_statistic) : Apparently, if we have a sample with "k" number of elements (e.g. x1, x2, ...xk) and assume a ...
1 vote
36 views

### Nonparametric mixed-design ANOVA

I have an experiment design with one "within subject" factor and one "between-subject" factor. So I have to use mixed-model ANOVA, but empirical distributions are not approximated ...
1 vote
10 views

### How does the Friedman test extend the sign test?

Every book/article claims this as if it's self-evident, but I have a hard time figuring out why. How do you get from the sum-of-squares style statistic of Friedman to the difference statistic involved ...
22 views

### Question regarding Kernel Density Estimation bandwidth selection (Scott's rule)

I'm studying KDE and got trouble understanding Scott's rule or Silverman's rule for bandwidth selection. I saw that the optimal bandwidth is the value that minimizes Mean Integrated Squared Error (...
18 views

### Sample size planning method differs from analysis method

I have seen some articles using one method for sample size estimation(two sample comparison for means or proportions) and subsequently using regression analysis/non parametric methods. If I have a ...
1 vote
26 views

### How to conduct a boostrapped or a permutation wilcoxon test (in R)

I have a total of 18 mice, 9 from Healthy group and 9 from Sick group. Since I have a very poor sample size I would like to use boostrapping or permutation test. Is there a way to conduct a ...
55 views

### NA p-value in R cor.test

$R$ gives "NA" for the p-value when I try to run Kendall's test with an "exact p-value" flag set on a larger data set (n=170 seems to be the cutoff). Is this just a computation ...
2k views

### Why is my data not normally distributed while I have an almost perfect QQ plot and histogram?

I am doing a thesis and I am stuck with my statistics on time series data. And when I run a Shapiro test, or any test, it says: ...
43 views

### good intermediate-level textbook for undergraduate applied statistics in data science?

I will be teaching an applied statistics course for the first time and the main audience will be 2nd and 3rd year undergraduates, mostly data science majors. They will have an intro statistics course ...
22 views

### Comparing objects with mostly unknown parameter values

Imagine that you have a picture of an apple and a picture of grapes. You need to decide what picture has the higher contrast. You know that there should be a significant enough difference between the ...
41 views

### Hierarchical ranking/clustering algorithm?

Consider two situations: 1st situation You ordered a number of cubes by their weight (from light to heavy). Then you notice that most of the cubes are grey, but there're a lot of the cubes with ...
1 vote
34 views

### alternative to ANOVA or simplifying approximations for multi-factor,, batch design with binomial data (advanced beginner)

this is my first post. I did already read various didactic materials and related posts here, but still had trouble figuring this one out. Sorry this is so long but I am trying to be as specific as ...
16 views

### Pros and cons of Nadaraya–Watson estimator vs. RKHS method?

Recently I've been reading some materials about nonparametric methods. Two methods related to the word "kernel" rasied my interest-- Nadaraya–Watson estimator and RKHS method. What's the ...
1 vote
40 views

### How to handle ties in pairwise wilcoxon rank-sum test?

I am willing run the wilcoxon rank sum test for different combination of variables, and using the base R code, I get a lot of warnings. The reason is that there are so many (about 30% of the whole ...
223 views

### Is there a non-parametric form of a 3-way ANOVA?

I am currently in the process of writing a publication about the home range of cat shark species in South Africa. However, I am currently struggling with how to create an interaction model of shark ...
1 vote
7 views

### Design points of local polynomial regression

Let the random set $\{(Y_{t},X_t)\}_{t=1}^n$ follow the model: $$Y_t=m(X_t)+\epsilon_t,\quad t\in\{1,\cdots,n\}\quad (1)$$ where $\epsilon_t$ is a random error term and $m(\cdot)$ is an unknown smooth ...
1 vote
25 views

### Wilcoxon Rank Sum test - appropriate to compare frequency of events between two sources?

I have some data on the frequency that a particular claim is referenced by two distinct types of sources. The first is traditional news media, and the second source are conspiracy theory sites. I want ...
1 vote
20 views

### Cross-validation on the HP filter for penalty selection

I'm looking for a bit more clarification on the selection of the $\lambda$ value for the Hodrick-Prescott Filter, aka HP filter. Which stems from a time-series in the form of $$y_t=g_t+\epsilon_t$$ ...
22 views

### How to prove symmetry of a Uniform kernel?

I am trying to prove this kernel is valid, $$K(x) = \frac{1}{2}I(-1 < x < 1)$$ So far I can integrate to 1, but how do I prove $$k(x) = k(-x)$$ Also, how do we satisfy that k(x) is $\ge$ 0 for ...
6 views

### Test differences between sub-populations with different data size

I am working with an environmental dataset with >300 observations collected randomly between five different zones. For each observation (station), 15 parameters (variables) were measured. Those ...
1 vote
19 views

### Seasonality test for poissonian counts

I have a count $N_i$ of rare evevents for each season, where $i$ identifies the season. The counts' rates are not high enough to justify a normal distribution aproximation of the poissonian. I want to ...
43 views

### How to validate the effect of the type of Task on participants' performance using count data

We conducted a user testing with two groups of participants (Group_A, Group_B). Group_A performed Task_A (a writing) under Condition_A. Group_B performed Task_B (a writing) under Condition_B. Group_A ...
1 vote
32 views

### How to extract the penalty term from the GAMM function in R and what is used to estimate the penalty terms

I'm working on some log GDP data and I am testing out a Generalized Additive Mixed Model for it with a penalized cubic regression spline. I am using the GAMM function from the mgcv package in R and I ...
17 views

### An estimator $\hat f$ such that $\hat f(x) : =y_{i^*}$ where $i^* := \operatorname{argmin}_i |x-x_i|$

I'm think of such an estimator $\hat f$ defined as below. It is inspired from the continuity of $f$. Let $f:\mathbb R \to \mathbb R$ be continuous and $(X_0, y_0)$ a square-integrable random vector ...
12 views

### How to correct for an underestimating (yet consistent) nonparametric step function estimator of survival?

I am working with a specific type of data where the non-parametric step-function estimator of the survival function is underestimating the true survival function for small sample sizes yet I can prove ...
24 views

### Test for non-parametric repeated measures for replicated block data

I asked 133 students to rate 12 audio-samples (on a hedonic scale from 1 to 9): 4 of those samples were generated by myself (human), 4 of those by an algorithm (machine), 4 of those are random ...
19 views

### Compare whether one group are significantly closer to real observations than other

I have two groups consisting of non-parametric estimated data of a phenomenon. I want to compare these two groups of estimations with a third group of real observations of the same phenomena. ...
11 views

### Bandwidth selection when comparing different local constant regression models

Let's say that I want to compare two alternative specifications of a Local Constant least squares model. If I had a single model, I would select my optimal bandwidth by cross validation. However, ...
16 views

### Kruskal-Wallis versus Friedman - Paired data, but not repeated measures/blocks?

I'm trying to compare the difference in behaviour of an animal with no enrichment to the same animal with two (or more) types of enrichment. (Total active behaviours before/total active behaviours ...
1 vote
18 views

### What statistical analysis should I use [duplicate]

I have been measuring flux of CO2 in (mmol m-2 d-1) from two different rivers and I now want to do a statistical analysis using IBM SPSS but Im not sure where to start. One lake is showing negative ...
1 vote
12 views

### validation and calibration of crop yield data using conditional inference trees

I am trying to validate and calibrate the conditional inference tree model using the crop yield data, and I started by splitting my dataset into training and test sets. After splitting, I had to ...
1 vote
100 views

### Statistical analysis of carbon dioxide flux data

I have been measuring flux of CO2 in (mmol m-2 d-1) from two different rivers and I now want to do a statistical analysis using IBM SPSS but I'm not sure where to start. One lake is showing negative ...
1 vote
56 views

### Comparing Z-Scores from Different Wilcoxon Signed Rank Tests

I have paired dependent data that represent pre-intervention/post-intervention ordinal values for the participants of a study. As part of the study, I have three separate groupings of participants: A, ...
1 vote
41 views

### What non parametric should I choose?

I Have an hypothesis that say : " London have more jobs posts more than other cities " , I have dataframe with column of the cities and the number of jobs posts (c(London,Manchester,Bristol.....
196 views

### Inference of nonparametric tests as linear models

I found some statements throughout the web that suggest that most common statistical tests can be performed as general(ized) linear models (cf. here). For a Wilcoxon test the author of the referenced ...
1 vote
35 views

### Welch's t test vs Mann-Whitney for very unequal groups

I have two vastly unequal groups (n1=18 and n2=400), and want to test mean differences between the groups for some 700 parameters (more specifically, RNA expression levels for 700 genes). While I ...
22 views

### Jonckheere-Terpstra test for DEPENDENT samples with an ordered alternative hypothesis

I have a question about the tests that consider an a priori ordering (the alternative hypothesis is ordered - testing the hypothesis u1 ≤ u2 ≤ ... ≤ un). We want to compare a variable in the same ...
10 views

### Minimax testing vs estimation for normal means (and other parametric problems)

Suppose $X_1,\ldots,X_n\sim N(\mu,\Sigma)$ with $\Sigma$ known (equivalently, $\Sigma=I$). Consider the problems of (a) Estimating $\mu$ (say, in $\ell_2$) and (b) Testing  H_0: \mu=0\, \\ H_1: \mu\...
52 views

### Looking for the Holy Grail of nonparametric regression

Unfortunately, to state precisely the question, I need some formal preliminaries. Let $d \in \mathbb{N}$. For each $d^* \in \{1,\dots,d\}$, define $\mathcal{M}_{d^*}$ be the set of probability ...
1 vote
92 views

### Help finding the right test

I am running an experiment and now it is time to do some analysis, but I am having a hard time figuring out the right way to analyze my data. I have a number of questions, but first let me give you ...
11 views

### Detecting Mean differences on streaming data

Im taking online measurements on highly skewed real valued data of two possibly unrelated distributions. The precision is low, which means small values tend to come in duplicates, while large values ...
24 views

### Similarity measures for Probability Mass Functions

I am trying to predict whether two sets of papers are written by the same author by looking at the distribution of papers over the years (number of papers published in a given year). Suppose we have ...
366 views

### Can non-parametric data have mean value and standard deviation?

I understand that for non-parametric data, the probability density function (pdf) cannot be obtained using parameters like (mean value) and (standard deviation), and I understand that we use Kernel ...
13 views

### How to represent ranked ANCOVA in a violin plot?

When I did ANCOVA, I did not find normality and equality, so I did ranked ANCOVA(nonparametric tests) using SPSS. well.. I think that if I use just ANCOVA(parametric tests), I could create the violin ...
52 views

### Use of both parametric and non-parametric tests in the same study

Suppose we are investigating whether there is a significant difference in dependent variables A and B between two treatments in a population. Let's assume that the data provide parametric assumptions (...
129 views

### Wilcoxon signed-rank test for just one sample: R vs. Python

I have tried to solve a simple college exercise about WSR test: first by hand, then in Python and finally in R. But I'm having an issue with the statistic I get. I have a small sample of 21 numbers: 4,...
21 views

### Nonparametric repeated measures with uneven number of subject repeats

I came across a dataset with some properties that make me uncertain what statistical tests would be appropriate for testing significance and effect size between certain conditions. Trying to keep the ...
1 vote
73 views

### How to create a B-spline basis without intercept and linear trend included?

I want to fit the following model using splines: \begin{align} Y(t) = \beta_0 + \beta_1t + \sum_{j=2}^{d} \beta_jB(t)_j \end{align} where $B_j$ are the basis functions. However, when I run the ...