# Questions tagged [nonparametric-regression]

Nonparametric regression is a form of regression analysis where the form of the functional dependence of the response on the predictors is not assumed. It subsumes many kinds of models, like spline models, kernel regression, gaussian process regression, regression trees or random forrests, and others.

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### How to test whether a nonparametric function is equal to 0?

There is an unknown function $h(x)=E(Y|X=x)$ which I estimated with a nonparametric series estimator (also called sieve estimator) $\widehat{h}(x)$ using data $\{Y_i,X_i\}_{i=1}^n$. I'm interested in ...
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### nonparametric model for longitudinal data analysis

For the longitudinal data provided below, we have the following variables: the response variable 'y', the time variable 'week', 'grp' (with two levels: treatment and control), and 'subject'. My ...
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### 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 ...
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### Convergence rate of a nonparametric estimator

Optimal rate of convergence for a nonparametric estimator is well-known. This rate is derived for when we don't anything about functional form (expect perhaps degree of smoothness). Suppose we know ...
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### Variable independece in marginal integration estimator

This is an exercise of the textbook Nonparametric and Semiparametric Models by Wolfgang Hardle Exercise 8.1. Assume that the regressor variable $X_1$ is independent from $X_2, \cdots, X_d$. How does ...
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### References: convergence rates of kernel regression, exchangeable data

I have been studying Kernel estimation; in particular, the Nadaraya-Watson estimator. I am interested in studying the rate of convergence in L^p of the NW (or similar) estimators for subgaussian ...
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### Rates of convergence with asymptotically negligibly noisy observations

Apologies in advance if this question is not completely well defined. Suppose that I am estimating a nonparametric model for a conditional expectation function $\mathbb E[Y_i | X_i]$ using some i.i.d. ...
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### Why isn't every nonparametric model with random model design an additive noise model?

Let $Y$ be a real random variable and $X$ be a real random vector. In a nonparametric model with additive noise, we assume the relationship $$Y = f(X) + \epsilon$$ for some unknown regression function ...
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1 vote
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### R: "family" and "degree" specification in loess fitting

I can't understand the difference between the possible specifications of the family option in the loess command in R. This is ...
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### why is the nadaraya watson estimator unbiased?

Say I have the model $Y_{i} = m(x_{i}) + \epsilon_{i}$ and $Y_{i}$ and $X_{i}$ are two mutually independent i.i.d. sequences. Then, how can I show that the Nadaraya Watson estimator is unbiased for ...
1 vote
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### Is the distinction between parametric and non-parametric statistics always clear-cut?

Is the distinction between parametric and non-parametric statistics always clear-cut or do examples of a statistic exists which cannot clearly assigned to one of these categories?
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### can I estimate density function of 2d/3d data with kernel smoothing (e.g. ks package R), or are there better estimation methods

I have a 2d matrix of positive values (non integer), where the values can be thought of intensity at an x,y coordinate indexed by the row and column. I want to estimate a density function across this ...
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### The nonparametric estimation in generalized regression model

Let $Y_t \in \mathbb{R}$ be a response variable and $X_t$ a $d$-dimensional explanatory variable. Assume we observe the process that $(X_1, Y_1), \cdots, (X_n, Y_n)$. Y_{t} = \mu(...
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### Gaussian and Epanechnikov Kernel Regressions giving drastically different estimations

sorry if this is the wrong place to be asking this question. I'm trying to implement kernel regression for a specific dataset I'm working with, but I'm noticing that the trendlines generated by my ...
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### Nonparametric Regression

Suppose I have response y, continuous independent variable x and binary variable z. ...
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### Can I use/make prediction/regression if my data is not normally distributes? Are non-parametric test for prediction?

My data is not normally distributed, and I`m confused what tests can I use (non-parametric, of course), but is there any way, to analyse prediction if the data is not normally distributed? I read ...
1 vote
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### About Generalized Additive Models - First parametric estimations, after nonparametric estimations for the remaining components

I wonder is it possible to construct a generalized linear modelin in that way, First, I will exclude the intercept term, which is standard for GAMs. Second, I will predict my interested dependent ...
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### A particular method for estimating the gradient of a log-density from samples

Suppose I have $N$ samples $x^1, \ldots, x^N$ which were drawn iid from an unknown density $P(x)$. Suppose I am interested in estimating the vector-valued function $g(x) = \nabla \log P (x)$. One ...
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### Examples for integration estimator

suppose I'm interested in estimating $C=\int_{a}^{b}g(x)dx$, where $a$ and $b$ are known, and $g(x)=E(Y|X=x)$ is an unknown function of $x$. The data I have is $\{Y_{i},X_{i}\}_{i=1}^{n}$, then a ...
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### rate of convergence for cross derivative estimation in local linear regression

Suppose $Y_{i}=m(X_{1i},X_{2i})+\epsilon_{i}$, with $E(Y_{i}|X_{1i},X_{2i})=m(X_{1i},X_{2i})$ where $m(\cdot,\cdot)$ is an unknown smooth function. If the estimator $\widehat{m}(x_{1},x_{2})$ is ...
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### Intuition of the regression model under fixed design case (nonparametric regression)

Let $(x_1,Y_1), \dotsc, (x_n,Y_n)$ be a random sample from the regression model $$Y_t=m(x_t)+\epsilon_t.$$ When authors want to develop the asymptotic properties of the local linear estimator of $m$ ...
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### Rates of convergence for estimating population mean squared error

Suppose I have an i.i.d. sample $\{(Y_i, X_i)\}_{i=1}^n$ on which I am trying to estimate a conditional expectation model: $$Y = g(X) + \varepsilon,\quad \mathbb E[\varepsilon | X] = 0$$ There is a ...
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### How robust is coxph when the proportional hazards assumption is violated?

How robust is the coxph when I don’t have proportional hazards? How common is non prop hazards and how do I fix it? Does transforming variables help? Does non parametric survival analysis handle non ...
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### How Semiparametric regression works?

I am working on semiparametric regression models; $$y=\beta x_1 +m(x_2)+e$$. I can understand this combination of Parametric and Nonparametric but how to estimate the responses ($\hat y$)? What is ...
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### Multiple regression for left-censored independent and dependent variables

I am interested in developing a predictive multiple regression model which predicts a concentration of one compound based on the measured concentrations of several other compounds. Both the dependent ...
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### For non-parametric regression which one has better interpretation and properties, GAM or quantile regression?

As in the topic. I want to interpret data for which I have no clues about the distribution. It's neither count, percentage, continuous. I don't want any transformations. Instead I would like to ...
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