Questions tagged [nadaraya-watson]

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Nadaraya-Watson regression alternative for binary outcome

I am looking for pointers as to what would be the non-parametric equivalent of Nadaraya-Watson regression when modelling a binary outcome. I have been googling and ended up with Generalized Additive ...
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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 ...
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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 $(X_1, Y_1), \cdots, (X_n, Y_n)$. \begin{equation} Y_{t} = \mu(...
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In kernel regression, what are the common theoretical motivations for using a kernel that is Lipschitz continuous?

I read a few papers on Nadaraya-Watson kernel regression in which I saw assumptions that require the kernel function being Lipschitz continuous without explanation ( and without citation of such ...
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Suppose $\widehat{m}'(x)$ is the derivative of Nadaraya-Watson estimator, can I get its uniform rate from the rate for its numerator and denominator?

Suppose $E(Y|x)=m(x)$ is the regression function that is twice differentiable, $f(x)$ is the density of $X$ that is also twice differentiable. Suppose $Y_i=m(X_i)+e_i$. $m'(x)$ is the derivative of ...
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About the validity of two statements

Let $f(x)$ be some smooth univariate density, and let the leave-one-out Nadaraya-Watson estimator $\widehat{f}_{-i}(x)$ be defined as follows: $\widehat{f}_{-i}(x)=\frac{1}{(n-1)h}\sum_{j=1,j\neq i}^...
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Why taking an average makes convergence to zero faster?

Let $f(x,y)$ be some density, and let the leave-one-out Nadaraya-Watson estimator $\widehat{f}_{-i}(x,y)$ be defined as follows: $\widehat{f}_{-i}(x,y)=\frac{1}{(n-1)h^2}\sum_{j=1,j\neq i}^nK(\frac{(...
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Can we apply the Nadaraya–Watson kernel regression estimator when $X$ is discrete?

Suppose $Y_i=g(X_i)+e_i$ with $E(e_i|X_i)=0$, $g(\cdot)$ being an unknown function and $X_i\in S=\{1,2,3,4\}$ with equal probability of taking each value. We want to estimate $g(x)$ using data $\{Y_i,...
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Derive an expression for the decision rule for a binary classification classifier

I want to derive the decision rule for the local constant logistic regression: Consider the log-likelihood for the GLM (general linearised model) \begin{equation} l( \beta_{0}, \beta_{1})= \sum_{i=1}^{...
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Optimal grid for Nadaraya-Watson CV bandwidth selection

Is there any rule of thumb or optimization technique for number of grid points for Kernel Regression? I am doing Nadaraya-Watson on 10 years data (2500 daily observations) of Swap rate. While ...
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Nadaraya Watson regression increasing bandwidth

I'm working with the Nadaraya Watson estimator and read the book of Wand and Jones (Kernel Smoothing, 1995) for introduction. On page 117 (for those who have the book) there is written that with ...
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How can I implement univariate Nadaraya–Watson regression for prediction?

How can I implement univariate Nadaraya–Watson regression for prediction? And what is the $x ,x_i$, and $y_i$? How can I select the $x ,x_i$, and $y_i$? The sample for prediction and the shape of ...
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Multivariate plug-in bandwidth estimator local constant regression

Has someone good references for multivariate plug-in bandwidth estimators in local constant regression? All I'm finding is for the univaraite case. And is there maybe already an implementation in R? ...
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Nadaraya Watson Bandwidth-Variance

I'm working with the Nadaraya Watson estimator and calculate the optimal bandwidth h with leave one out cross validation. Now I'd like to get the variance of h (not the variance of the NW estimator)....
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Nonparametric Quantile Regression for AR(1)-ARCH(1) process

I would like to estimate the conditional scale function $(\sigma_\tau(X_t))$ in a QAR-QARCH model represented by: \begin{equation} Y_t = \mu_\tau(X_t) + \sigma_\tau(X_t)\epsilon_t,\, t = 1,2,\ldots \...
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How to choose appropriate bandwidth for kernel regression?

I'm trying to understand how to choose an appropriate bandwidth for kernel regression. Note that this is NOT about kernel density estimation (unless someone can ...
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Nadaraya-Watson Optimal Bandwidth

I am currently working on a statistical project where I need to estimate a conditional expectation $E[Y|X=x_i]$ using the Nadaraya-Watson estimator. For doing that, I have the sample $(x_1,y_1),...,(...
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What is Nadaraya-Watson Kernel Regression Estimator for Multivariate Response?

Given a regression setting with covariates $X_{n \times m}$ and response $Y_{n \times p}$ where $p>1$, i.e the responses are vector-valued or multivariate, is there a Nadaraya-Watson estimator for ...
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