# Questions tagged [nonparametric-statistics]

For questions about mathematical-statistical models that involve at least one infinite-dimensional parameter and hence may also be referred to as "infinite-dimensional models." This field is closely related to functional analysis, measure theory, and topology on function spaces.

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### P-value for testing a median to be $M \geq M_0$

I'm trying to solve a question from an introductory textbook on statistics. I am to use the Sign Test and determine if there is significant evidence that the median of a dataset $M$ is "at least&...
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### Nonparametric likelihood function $\mathcal{L}_n(f) = \prod_{i=1}^nf(X_i)$ doesnt attain maximum in set of all densities

Let $X_1, \dots, X_n$ be i.i.d random variables with distribution function $F$, and $\mathcal{L}_n(f) = \prod_{i=1}^nf(x_i)$ it's likelihood function. Let $\mathcal{F}$ be the family of all possible ...
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### Question on literature for contraction rates

I read in some lecture notes the following definition of contraction rate: Definition (Posterior rate of contraction) The posterior distribution $\Pi_n\left(\cdot \mid X^{(n)}\right)$ is said to ...
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### Sum of arrival times of Chinese Restaurant Process (CRP)

Suppose that a random sample $X_1, X_2, \ldots$ is drawn from a continuous spectrum of colors, or species, following a Chinese Restaurant Process distribution with parameter $|\alpha|$ (or ...
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### Does there exist a test for statistical significance to compare two distributions that is independent of sample size?

Essentially, I am generating datasets in which I can make the sample sizes as large as I want. Therefore, any statistical test that I do between the generated sample distributions are somewhat ...
38 views

### Calculate the integral with a normalized kernel

$K$ is a baseline kernel function that is nonnegative, symmetric and supported on [-1,1]; $h$ is a bandwidth in local smoothing .Let $p_j$ denote the marginal density of $X_j$.We define the estimator ...
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### Histogram asymptotic bias

I am reading All of Statistics from Casella. When trying to show the bias for a histogram estimator for some density distribution, he starts developing the formula for pj, that is, the probability ...
1 vote
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### Convergence of sup norm estimate of functions

I am working in the context of Gaussian white noise model (where we observe $n$ trajectories sampled via $d X(t)=f(t) d t+\sigma d W(t)$) and also in the non-parametric regression model (where we ...
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