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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11
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333 views

Penalized spline confidence intervals based on cluster-sandwich VCV

This is my first post here, but I've benefited a lot from this forum's results popping up in google search results. I've been teaching myself semi-parametric regression using penalized splines. ...
7
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1answer
940 views

Computing a bootstrap confidence interval for the prediction error with the percentile and the BCa method

I have two related questions regarding the computation of a non-parametric bootstrap confidence interval for the prediction error. Setting: I have a sample S from a data population P and a learner L, ...
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1answer
169 views

What to do if your regression residuals aren't normally distributed, cannot be transformed and do not conform even when outliers are removed?

I ran a regression on R and my shapiro wilk test showed that some of my residuals are not normally dsitributed. I cannot transform the data to fit a normal distribution and even when i remove outliers,...
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146 views

Minimizing MISE to find consistent estimator

Consider kernel regression estimation of the mean function $m$ of the process $$y_t = m(x_t) + \epsilon_t,$$ where $\epsilon_t$' s are correlated with covariance function $R(s,t) = \exp \{-\lambda|s-...
5
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0answers
64 views

Non-uniform p-values from hoeffd function in Hmisc when data sets are independent

When using the function hoeffd in the CRAN package Hmisc I get unusual p-values for pairs of data sets that are independent. The function hoeffd is an implementation of Hoeffding's $D$ statistic. ...
5
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399 views

How general is the backfitting algorithm?

Hastie \& Tibshirani's original approach to fitting generalized additive models was the backfitting algorithm. For a model of the form $$ y = \alpha + \displaystyle\sum_k f_k(x_k) + \epsilon $$ ...
5
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268 views

Interpolation and Sample size when Visualizing distributions

Let's assume a stochastic simulation or test with a control variable. The task is to visualize the distribution to demonstrate the effect that is being researched. The objective is to get smooth plot, ...
5
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1answer
107 views

What is an example of data where the permutation test succeeds but a normal t-test fails?

In literature, I normally see authors use a two sample permutation test on normal data to show that it works as well as the two sample t-test. However, the real power for permutation tests should be ...
5
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45 views

Estimate fraction of a known distribution in a mixture with unknown second distribution

Suppose I have a set of bulbs, which are known to be healthy. For each bulb I have a value of its brightness. The underlying distribution is not necessarily normal, and possibly have some complex ...
5
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362 views

All vs all post-hoc after Aligned Friedman (k classifiers over multiple datasets)

I have k classifiers and n datasets, and I have only one accuracy measurement (which is actually the average of three independent repetitions of the 5-fold-CV, i.e. average over 15 accuracy values) ...
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3k views

Differences between poisson.test and E-test when testing Poisson parameters

Suppose we have two independent Poisson-distributed variables $X_1$ and $X_2$. We want to test whether the Poisson parameters are equal, i.e. whether $\lambda_1=\lambda_2$. Now we have 4 distinct ...
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4k views

Calculate Mantel-Haenszel test in R

I would like to have a reality check of my understanding of the MH statistic. I have been trying to reproduce an example of the Mantel-Haenszel test provided in Conover (1999, p. 192-194). The data ...
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98 views

Simultaneous Non-parametric regression and Non-parametric density estimation

Given a collection of $(x,y)$ data, one might do a non/semiparametric regression of $y$ on $x$ to understand how to predict the $E(Y|X)$. Similarly, if one has enough data, it might be useful take a ...
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96 views

Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

I am writing my master's degree thesis on a novel method for fixing knots in an adaptive way and while reading the literature I've found many references to the so-called Chebyshev sites. This sites or ...
4
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1answer
609 views

How to do a stratified nonparametric test?

I'm trying to use the "coin" (conditional inference) package to perform a stratified nonparametric test for difference in distribution (for count data). I tried a stratified Mann-Whitney-Wilcoxon ...
4
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1answer
933 views

Surface Fit Using Tensor Product of B-Splines

I am trying to teach myself surface fitting with splines using tensor products. I am trying to construct a toy example but I can't seem to get my example to work. I will try to explain the best I can ....
4
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76 views

all regressions: coefficients interpretation

good morning to all, I open this topic with the intention of being useful to me but also to many in my situational. I would like to clarify the "interpretation" of the coefficients in the regression. ...
4
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195 views

multiple Kruskal-Wallis instead of ANOVA for non-normally distributed data

Apologies in advanced if I supply too little or vague information, since I am a complete newbie in stats and using this forum. So I did a study which evaluated psychopathic personality traits, ...
4
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0answers
81 views

Nonparametric estimation of the logarithm of a density

I was wondering whether there is an equivalent to Kernel Density Estimation to estimate nonparametrically the logarithm of a density. Or if there is any nonparametric method for that. (Taking the ...
4
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2answers
133 views

Nonparametric Identification from Order Statistics

Suppose a vector of random variables $(X_1,...,X_n,Y_1,...,Y_m)$ is such that $X\sim F(\cdot)$ and $Y\sim G(\cdot)$. So $X$ are distributed independently and identically as $F(\cdot)$ and $Y$ as $G(\...
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1k views

In a permutation test, how to get a confidence interval for the estimated p-value?

Suppose that I have two groups of data of size $50$ and $51$. Assuming that I did an approximate Monte Carlo permutation test with 10,000 permutations randomly drawn, is there a way to find a ...
4
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365 views

Kolmogorov-Smirnov vs. Kuiper test

I would like to compare two 2D distributions with quantitative variables, illustrated here: For each "x", they are several measures "y". I can't assume these distributions are parametric. A ...
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1k views

Where is the maximum bias and variance in a histogram as non-parametric density estimator?

I am a little bit confused about bias and variance of non-parametric density estimators and hope you can help me. Assuming a constant bandwidth and sample size, I am wondering at which points of the ...
4
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0answers
91 views

Rank deficient bootstrap resamples

Despite years of stat courses I'm afraid I may still not completely understand bootstrapping. My question here relates to nonparametric boostrapping of regression models. As i understand it you draw ...
4
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130 views

Nonparametric test for largely skewed count data

My research design looks as follows: an experimental game with 4 participants (human subjects), repeated for 20 rounds. During each round, participants are allowed to form bilateral coalitions which ...
4
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0answers
453 views

Confusion related to Parzen window

I was going through this tutorial related to Parzen window at http://www.cs.utah.edu/~suyash/Dissertation_html/node11.html. However, I have some confusion related to Parzen window with gaussian kernel ...
4
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1answer
145 views

Fast multivariate unimodal density estimator

I have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$ dimensional density $f(\boldsymbol{x})$ and I would like to estimate this unknown density. In addition I know that $f(\boldsymbol{...
3
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0answers
79 views

Parameter estimation when the likelihood function does not exist

The observations $Z_1,Z_2\cdots$ are i.i.d. We have $$Z_k = \sum_{i=1}^\infty \frac{X_{ki}}{2^k}.$$ where the $X_{ki}$'s are i.i.d. with a Bernouilli$(p)$ distribution. If $p=\frac{1}{2}$ then $Z_k$ ...
3
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28 views

non-parametric circular statistics

I am working on a research question of color preference (which can be represented in a circular space). I have divided the circular space into 16 equally spaced bins and done a pairwise comparison ...
3
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0answers
227 views

Multiple comparisons between two groups (non-parametric)

Update Added more details about the Experimental setup. My experiment comprised two groups, control (N=25) and experimental (N=26). Each participant belonged to one group. Their performance has been ...
3
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1answer
41 views

solve an exercise of two samples using Kolmogorov-smirnov

I'm looking for books and information like crazy and I can not find what I need. Well the example proposed is about methods that have been used in literature students and these are the data collected: ...
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62 views

Best Test For Generalized/Nonparametric Behrens-Fisher Problem

First, because there seems to be a confusion of what the generalized Behrens-Fisher problem is a description adapted from [1]. We have $X_1,\ldots,X_m$ i.i.d. from distribution $P$ and $Y_1,\ldots,...
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42 views

Algebraic Manipulations in Mann-Whitney-Wilcoxon Test Statistics

Given Let $\Delta > 0 $ be positive real number. Consider the Wilcoxon-Mann-Whitney upper tail test $H_0: \Delta \leq 0 \,\,\, \text{vs} \,\,\, H_a: \Delta > 0$ aimed at testing the difference ...
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41 views

Statistical test for first sample greater than given sample?

Does anyone know of a name for the following statistical test/whether there is a name/whether the following line of reasoning is just bogus? Say I have a value $x$, and a way to generate samples from ...
3
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0answers
30 views

Bounds for the expected value of the Kolmogorov-Smirnoff loss function

Let $$ \mathcal{F}=\{F:\mathbb{R}\longrightarrow\mathbb{R}: \text{$F$ is the CDF of some probability measure on $\mathbb{R}$}\}. $$ Consider the loss function, $L:\mathcal F\times\mathcal F\to\mathbb ...
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114 views

Can non-parametric tests, e.g. Mann-Whitney U, be used on non-normally distributed statistics off of bootstrap samples?

I have some return data from some different portfolios which I would like to compare using risk vs return ratios. The standard Sharpe ratio has a nice solution for calculating the significance of the ...
3
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0answers
141 views

Can “non-parametric” tests be achieved with generalized linear models?

I recently read @Kodiologist's answer to a post here looking for clarification on the relation between GLMs and non-parametric tests. His answer is along the lines of "the approach is not non-...
3
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0answers
409 views

p-values for permutation tests

Let's say I want to test whether the average performance of two individuals who work together (let's say in the same room) is different to their performance when they would not have worked together. ...
3
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0answers
215 views

Kernel density estimation with FFT for a univariate non-parametric regression

The non-parametric regression model to be estimated looks like the following x_t = b(x_t-1) + epsilon_t Forfinding the optimal bandwith h in the kernel ...
3
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0answers
276 views

Minimum sample for non parametric test?

Exactly how many sample to be minimum size for non parametric test? Right now i have 3 data with really2 small sample size 1. 5 pairs for wilcoxon signed rank test (pretest and postest in 1 place) 2. ...
3
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0answers
62 views

Calculating variance with unknowable mean

I commonly hear the above statement or something like it in gambling circles. When applied to a game with a known set of parameters, it is true. But when applied to something like a sporting event, I ...
3
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0answers
56 views

Alternative to ANOVA (beginner)

I have run 15 experiments to compare the effect of different hormone combinations on the maturation on Xenopus oocytes (immature eggs). I am hoping to find the best performing variable. I have 4 ...
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0answers
2k views

Nonparametric equal variance tests

I have two large, non-normal samples as evidenced by the Kolmogorov-Smirnov test. I now wish to test for equality of variance nonparametrically. I'm confused as to which nonparametric test is ...
3
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0answers
479 views

Multiple comparison of non-normal, heteroscedastic data. What test should I use?

I have a set of brain pathology data. These were obtained by counting certain parameters in the brain. Due to availability of human brains, the amount of cases vary a lot across the different groups ...
3
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0answers
36 views

German tank variant: estimate resolution of camera given cropped photo sizes

Make whatever assumptions you like, but I like the flavor of nonparametric techniques. I have a list of the $x_i$ by $y_i$ resolutions of a number of photos, all cropped from photos taken at the same ...
3
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0answers
187 views

Endogenous interactions in nonparametric instrumental variables

I'm interested in estimating a model along the lines of $$ pr(y==1) = g^{-1}\left(f(x_1,x_2)+X'\beta\right)+\epsilon $$ where $g$ is logit and $f$ is some smooth function. I'm using GAM's in ...
3
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0answers
338 views

Is this how a Bayesian bootstrap works?

I am a bit new to the whole nonparametric and Bayesian idea, so tell me if this is correct: to estimate, say, the mean of a dataset's population we do the following: We define a function $f(x)$ that ...
3
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0answers
44 views

upper bound for expected maximum of difference of two kernel-Estimations

I'm searching for an upper bound for a function like $$ E\left[ \max_{x \in R} \left( \frac{ \sum_{i=1}^n K(\frac{x-X_i}{f(x,X_1, \dots X_n)}) \cdot Y_i } { \sum_{i=1}^n K(\frac{x-X_i}{f(x,...
3
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0answers
633 views

Non-parametric effect size

Effect size, as estimated by Cohen's $\delta$, is: $d=\frac{\hat x_1 - \hat x_2}{\hat s_{pooled}}$ Since the numerator is an estimate of difference in location, and the denominator is an estimate ...
3
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0answers
897 views

Can I use wilcoxon signed rank test for time series data

I have a question about wilcoxon signed rank test. I have 2 different speed profiles (speed starts from time 0 to 100 sec) of the same participant that was given 2 different treatment. I would like to ...

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