# 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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### 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 ...
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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 ...
256 views

### Question about the answer to “Local polynomial regression: Why does the variance increase monotonically in the degree?” [duplicate]

I appreciated Marco's elegant answer explaining why the variance of a local polynomial regression increases monotonically in the degree. However, in the end of the proof, I find difficult to calculate ...
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### Local polynomial regression: Why does the variance increase monotonically in the degree?

How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has ...
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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 ...
388 views

### Reporting the results of Nonparametric regression using kernel weights

I am wondering how I can present the results of nonparametric regression. I performed the nonparametric tests using R, and R package 'np'. The commands used for this are freq <- npreg(Respno ~ ...
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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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### 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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### 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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### What is the density of $X$ under fixed design?

We observe an i.i.d. sample $(X_1, Y_1), \ldots (X_n, Y_n).$ Let $m(x) = E(Y|X=x),$ $\sigma^2(x) = \operatorname{Var}(Y|X=x)$ and let $f(\cdot)$ be the density of $X.$ Under some regularity ...
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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 ...