Skip to main content

Questions tagged [nadaraya-watson]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
0 answers
103 views

Is Kernel regression a good idea for time series?

As title. I'm worried about the implications of autocorrelation (the timeseries is not stationary), if should transform it to be stationary, etc. Particularly worried since right now I'm having ...
MDSv's user avatar
  • 33
1 vote
0 answers
31 views

Closeness of two estimators of median under non parametric setup in a large sample situation

Median Regression under non-parametric set-up (Nadaraya Watson Estimate) Data: $\{(Y_i,X_i):1\le i\le n\}$ Interested in estimating $\phi(x)=\text{median}(Y|X=x).$ Possible estimates are Minimize the ...
reyna's user avatar
  • 365
0 votes
0 answers
101 views

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 ...
Papayapap's user avatar
  • 361
0 votes
0 answers
444 views

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 ...
user34031's user avatar
1 vote
1 answer
46 views

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(...
香结丁's user avatar
  • 203
1 vote
0 answers
82 views

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 ...
ExcitedSnail's user avatar
  • 2,914
2 votes
1 answer
426 views

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 ...
ExcitedSnail's user avatar
  • 2,914
1 vote
1 answer
57 views

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}^...
ExcitedSnail's user avatar
  • 2,914
2 votes
1 answer
198 views

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{(...
ExcitedSnail's user avatar
  • 2,914
1 vote
0 answers
538 views

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,...
ExcitedSnail's user avatar
  • 2,914
1 vote
0 answers
166 views

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}^{...
Stochastic's user avatar
0 votes
0 answers
198 views

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 ...
Alex's user avatar
  • 1
2 votes
1 answer
400 views

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 ...
To Mate's user avatar
  • 87
0 votes
1 answer
929 views

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 ...
Bingo Sun's user avatar
0 votes
1 answer
144 views

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? ...
To Mate's user avatar
  • 87
0 votes
1 answer
319 views

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)....
To Mate's user avatar
  • 87
3 votes
0 answers
90 views

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 \...
Logamou Seknewna Lema's user avatar
6 votes
2 answers
12k views

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 ...
makansij's user avatar
  • 2,289
9 votes
1 answer
4k views

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),...,(...
JJFM's user avatar
  • 101
4 votes
1 answer
4k views

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 ...
hearse's user avatar
  • 2,545