Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [nadaraya-watson]

18 questions
7
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1 answer

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 $(x_1,y_1),...,(x_n,y_n)$, where $n=14$, and I have chosen the…
JJFM
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6
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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 convince me that the same techniques can be used). Here's my thinking on this: The…
makansij
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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 \end{equation} where $\epsilon$ is zero (0)…
Logamou Seknewna Lema
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1 answer

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 larger bandwidth h the estimate tends towards the…
To Mate
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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 kernel regression in this setting? This boils down…
hearse
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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 assumption in the proof), so I'm wondering what are…
T34driver
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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 regression function. We have i.i.d. data…
T34driver
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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: $\widehat{f}_{-i}(x,y)=\frac{1}{(n-1)h^2}\sum_{j=1,j\neq i}^nK(\frac{(X_j,Y_j)-(x,y)}{h})$, where $K(\cdot,\cdot)$ is…
T34driver
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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 $\{Y_i,X_i\}_{i=1}^{n}$. Can we estimate $g(x)$ with the…
T34driver
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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})=…
Stochastic
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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 Models, but I think these impose functional forms?
Papayapap
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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 this model, regardless of the bandwidth? And what…
user34031
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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(X_{t})+\sigma(X_{t})\varepsilon_{t}, \quad…
香结丁
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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: $\widehat{f}_{-i}(x)=\frac{1}{(n-1)h}\sum_{j=1,j\neq i}^nK(\frac{X_j-x}{h})$, where $K(\cdot)$ is the…
T34driver
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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 performing cross-validation for optimal bandwidth…
Alex
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