Smoothing methods in data analysis, like splines or kernel smoothers. See https://en.wikipedia.org/wiki/Smoothing, which has a long list of various smoothing methods.

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Trouble deriving nonparametric regression result

I'm working through Computational Statistics, Second Edition by Givens and Hoeting and I cannot reproduce a result stated in the book. We're considering a nonparametric regression problem where the ...
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Is the Laplace/Lidstone smoothing parameter (talking about Multinomial/Bernoulli Naive Bayes) related to the particular structure of the dataset?

I'm working with Multinomial and Bernoulli Naive Bayes implementation of scikit-learn (python) for text classification. I'm using the 20_newsgroups dataset. From the scikit documentation we have: ...
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66 views

What are the published methods to smooth a time series of weights?

I am looking for methods to smooth a time series of human weights, in particular I would like to know methods that are quoted or described in articles published in peer-reviewed journals. I am also ...
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34 views

Difference between smoothing spline and penalised spline

I have read many documents, and I am confused about the difference between smoothing splines and penalised splines. Are those two the same? Can someone please suggest any good document which can ...
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1answer
38 views

Smooth Non Normally Distributed Data

I have ~16,000 probability sets of goals scored [maximum of 12] like below [some % are rounded hence do not add up to 100%]: ...
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27 views

Calculating bias and variance in a LOESS fit

I have datasets that can form several different curvy patterns between the dependent and independent variables. The 'true' relationship likely depends on a large number of factors that aren't easily ...
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25 views

Time Series Shocks with Exponential Decay

Imagine a piano key played in an auditorium: The amplitude of the sound wave is perhaps highest in the first milliseconds, then slowly decays to zero if no other notes are played. If other notes are ...
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1answer
45 views

Alternate distance metrics for two time series

I have time-series data of different houses. Assume it is power consumption data. Now, I want to cluster the houses following similar power consumption pattern utmost. So, the various distance metrics ...
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46 views

R forecast ets initial level and trend

I am trying to understand how the ets function of R in the forecast package computes initial level $l_0$, and initial trend $b_0$. I was under the impression that they are set to the intercept and ...
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14 views

How to deal with frequencies that don't appear in the held-out set?

The held out probability is defined as $$P_{HO}\left(x\right)=\frac{t_{r}}{N_{r}\cdot\left|S^{H}\right|}$$ where: $t_{r}$ is the total number of times events that appeared $r$ times in the training ...
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5 views

Fast bivariate smoother?

I need a nonparametric regression for two explanatory variables that is faster than GAM. lm = gam(X3 ~ s(X1,X2,k=8),data=dataset) If the sample size is about ...
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18 views

Fit mixture of distributions vs. smoothing to time series data in R

I have a time series data and I want to represent this as in the right side of below plot: Authors of the paper claim that they fit a mixture of models to raw power data using mclust function. I ...
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32 views

What methods can be used to pick the optimal kernel smoothing width parameter

Kernel smoothers for a function f(x) usually have a parameter which control the width of the region which is used to smooth the value of the function, say at a ...
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93 views

When to choose GAM over LOESS?

I am smoothing the relationship between a binary variable y and a continuous variable x. For this I've looked into both GAM and ...
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46 views

Influence matrix in Cross validation

I am trying to implement cross validation to find the apropriate smoothing parameter value for smoothing spline I am able to implement the leave out one , in which one data point is left out , then ...
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41 views

Use Kalman Filter to post-process an elevation profile?

I'm so sorry that I haven't studied mathematics or physics. Now I have to smooth an elevation profile (the altitudes of a GPX track), because there are really nasty outliers. I've implemented a ...
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64 views

Robustness Weights in LOESS behaving strangely

I've been playing around with writing my own LOESS module in Python (2 reasons: first, I wanted the practice, and second, the implementation in statsmodels doesn't ...
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1answer
83 views

LOESS for subset of data

I want to analyze the performance of two classifiers. For that I have a dataset with 30000 observations that each have an independent variable interactions and a ...
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28 views

How to smooth standard deviations?

So, I have some idea how to smooth a set of points to produce a smooth estimate of the conditional mean. Suppose that I want to estimate the standard deviation locally. That is, I have a set of ...
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62 views

centering constraints on ti() terms in MGCV

I have some raw data on which I compute percent changes, and I calculate rolling averages of two different lengths on the percent changes. I want to use a tensor interaction of the two rolling ...
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54 views

Truncated power basis function and continuity in b-splines

I do not understand how adding a truncated power basis function leads to continuity in B-Splines. Could someone please provide a low level explanation?
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20 views

how forecast with penalized b-spline

I have inflasi data, and i will forecast future with penalized b-spline, but I have problem after having found lambda. Do you know syntax to uose in SAS for forecasting values from a penalized ...
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1answer
57 views

why add one in inverse document frequency

My textbook lists the idf as $log(1+\frac{N}{n_t})$ where $N$: Number of Documents $n_t$: Number of Documents containing term $t$ Wikipedia lists this formula as a smoothed version of the actual ...
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52 views

Does a radial basis function network work in high dimensions?

It seems that a single-layer radial basis function network with normalized weights is the same thing as kernel smoothing (see e.g. Haykin Neural Networks: a Comprehensive Foundation, Section 5.12). ...
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Is it possible to use spatial autocorrelation test to determine the tuning parameter in the thin plate spline smoother?

I am currently working with some insurance data and try to estimate spatial structure of claims frequencies. The common approach is to perform some kind of regression on the non-spatial data then ...
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33 views

Smooth.monotone function in the Berkeley Female Growth Data

I am learning functional data analysis by myself. But I come across one problem when I implement the example of the growth girl study example. Below is the code from the book "Functional data ...
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1answer
80 views

How to calculate Hat matrix for penalized spline regressions?

The book "Semiparametric Regression" by Ruppert et al. (2003) provided a computationally fast algorithm for Penalized Spline Regression. I put a part of the algorithm here. Does anybody can do algebra ...
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62 views

Is there a way to smooth cohort demography data in R? [closed]

I have a set of mortality data that I'd like to smooth so that I can run it through a Lee-Carter model for forecasting. The set of data focuses on the cohorts of aged 1-11 people for the years of ...
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1answer
30 views

Applying a non-parametric ANCOVA to the interactive effects of multiple explanatory variables.

I am having a few issues processing some data in that the number of samples is far less than originally anticipated. In a control and impacted design, there are 11 samples each. I thought this seemed ...
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48 views

What does monotone polynomial plot represent?

I am trying to understand monotone and isotonic regression. I believe they will produce curve which are monotonely increasing or decreasing. In most of what I read on the net, the change is shown in a ...
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31 views

How to determine the optimal time averaging window

I have two large time series datasets with some background noises. I would assume the two datasets are either lag correlated or lead correlated. I tried to use time averaging to smooth out the dataset ...
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17 views

Good Turing smoothing

which smoothing algorithm is easy and effective in case of implementation point of view... My training corpus is a hex dump looks like, 64 FA EB 63 31 D2 62 22 19 BD 64 B5 63 17 4F 48 62 A8 64 11 0F ...
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1answer
71 views

Smoothing a particle filtered 2D trajectory

I am currently developing a very basic particle filter for a 2D robot localization task. My process is defined by a really simple velocity / steering angle based motion model. I am re-weighting the ...
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15 views

How can I smooth a set of distributions?

I have a set of results from MCMC modelling of a variable at discrete time points and I would like to know what kind of approaches I could take to smooth the results, given I would expect some kind of ...
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54 views

Tensor product smooth and Isotropic smooth

In 'mgcv', it is possible to fit two or more dimensional thin plate regression splines but not basis like cubic and P-splines. However, with tensor product smooth (te), we can use all the basis. My ...
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49 views

Choosing smoothing parameters across multiple Naïve Bayes classifiers with different number of categories

I would like to train multiple Naïve Bayes classifiers with different number of categories, and also have a global threshold for how certain one classifier must be in order for the classification to ...
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1answer
91 views

strange predicted values from LOESS model

I am trying to predict density function using LOESS in R. However, the predicted values I got are not in the estimated LOESS line. ...
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140 views

The correct use of tensor product in gam (mgcv) function

I want to resurrect a question that I asked two months ago (Comparing gam models using ti( )), but adding more explanations. The aim of my analyses was to compare several gam models with different ...
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1answer
75 views

can I apply loess or spline regression in mixed model?

My situation right now is that I have the mixed model with quadratic term but it doesn't perform very well. So I am wondering if I can apply loess or spline regression to the mixed model instead of ...
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135 views

Spike detection and removal in position data

Is there any good filter to remove big spikes in position data? I think lowpass filter should be good but is it possible to filter 2D position data with assumption its joint distributed? I mean, not ...
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609 views

Smoothing - when to use it and when not to?

There is quite an old post on William Briggs' blog which looks at the pitfalls of smoothing data and carrying that smoothed data through to analysis. The key argument is namely: If, in a moment of ...
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31 views

What is the effective kernel for smoothing methods?

I'm learning different smoothing methods and the term "effective kernel" came up and I don't really understand it. By definition, for a smoothing method, the vector of estimates ...
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55 views

Beginner level: How to plug in the smoothing equations into E step (Part 2)

Considering Gaussian Linear Dynamical system, $x_{t+1} = Ax_t + w_t$ $y_t = Cx_t + v_t$ $w_t = N(0,Q)$, $v_t = N(0,R)$ By Kalman Filter we are estimating the state variables and the state estimate ...
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643 views

Beginner level: Help in learning Kalman Smoother (Part 1)

Parameter estimation of Linear Dynamical system is a tutorial which explains Kalman Filter, Smoothing, and Expectation Maximization. I have followed the derivation for Kalman Filter. But cannot ...
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89 views

Symmetry in moving average smoothing in “Forecasting: principles and practice”

In the textbook Forecasting: principles and practice by Hyndman and Athana­sopou­los, in the moving average smoothing section (Sec 6.2), the authors speak of even order moving average smoothing not ...
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81 views

Why is locally weighted regression is a nonparametric method? How is it implemented in R?

I'm wondering where does the "nonparametric" label of locally weighted regression like LOESS or LOWESS comes from, i.e. why they are nonparametric methods? Also, I would like to know in general how ...
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53 views

Base sales in multivariate time series | MCMC model

I have been looking around online for good resources that explain how one would go about calculating base sales when preforming marketing mix modeling. I was told by a colleague that essentially they ...
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23 views

Smoothing of a 2D Empirical Distribution

I have a number of data points $\theta \in \mathbb{R}^2$ with corresponding values $x \in \mathbb{N}$. I am assuming the $x$ are realisations from a distribution $f(X | \theta)$. Given I have a lot ...
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4k views

How to use Pearson correlation correctly with time series

I have 2 time-series (both smooth) that I would like to cross-correlate to see how correlated they are. I intend to use the Pearson correlation coefficient. Is this appropriate? My second question ...
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132 views

“Future-independent” smoothing methods (as exponential smoothing)

I'm searching for time series smoothing algorithms, which give "future-independent" results - each next smoothed value depends only on previous data (smoothed or not smoothed), but not on any future ...