# Questions tagged [nonlinear]

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### Auto-correlation for irregular non-linear sample

I have irregular sampled residuals resulting from solving a non-linear optimization problem. Currently I am gridding them into a regular grid and calculating the auto-correlation to check the ...
60 views

### How to fit logistic regression to circular data?

I've made a script that can do normal logistic regression with sigmoid(linear model). However, I have data that has a circular decision boundary and looks like this. My question is how I can modify ...
28 views

### Degrees of freedom for a $\chi^2$ with non-linear polynomial model

I have a $\chi^2$ below for some model function $F$: $$\chi^2 = \sum_{i=1}^{i=M} \frac{\left(y_{i}-F\left(x_i;\vec{a}\right)\right)^2}{\left(\Delta y_{i}\right)^2}$$ I know that non-linear model ...
29 views

### If X^2 is not significant but X is significant, do I have to remove X^2 and run again the regression analysis?

Model DV ~ W+PDSR+Corr+(FAGDP1+FAGDP2)+log(PCGDP)+Exp+Pop+Health FAGDP2=FAGDP1^2 Result: After removing FAGDP2(FAGDP1^2) from the model, FAGDP1 turns to be insignificant Am I right in removing FAGDP^...
1k views

### RMSE vs MSE loss function - the optimization solutions are equivalent?

If we optimize a function $f$ with respect to loss $L$, which is defined as RMSE; Are we going to get the same solution as optimizing MSE ? Even, if the function $f$ is non-linear (e.g. a neural ...
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### Parameter estimation of a model with exponential almon lag structure

Suppose I have the following model: $$y_t = \beta_0\sum_{i=0}^p w(\delta;i)x_{t-i}$$ Where $\displaystyle w(\delta;i)=\frac{\exp(\delta_1 i+ \delta_2 i^2)}{\sum_{i=0}^p \exp(\delta_1 i+ \delta_2 i^2)}$...
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### How to calculate the bandwidth of the Diks and Panchenko(2006) nonlinear granger causality test?

I am doing the nonlinear causality test of the crude oil futures and spot prices, and I want to use the method introduced by Diks and Panchenko(2006), but I am confused about how to choose the optimal ...
122 views

### Quantile regression with an exponential function

The following equation: y = a*x**b where y is a nonlinear function of x. By taking logs, the equation can be expressed as: ln(y) = ln(a) + bln(x). I would like to run a quantile regression instead of ...
11 views

### Non-linearly separable decision boundaries

This ANN uses tanh in the hidden layers and softmax activation in the output layer. I am trying to figure out if the network can learn nonlinearly separable decision boundaries and if so what ...
17 views

### standar error of non-linear regression

I'm trying to compute the standar error of a non-linear regression fit, I find the answer in this post Non-linear regression confidence interval But i did't find that formula in any other place,and I ...
10 views

### Candidate methods for maximizing multivariable constrained nonlinear loglikelihood function

I want to approximate the maximum value of a nonlinear loglikelihood function with 53 strictly positive variables via numerical methods that do not use derivatives. According to literature there are ...
16 views

### Problem with nonlinear regression with proportional data [closed]

I am trying to do a nonlinear regression with proportional data, but it doesn't work in Minitab or SPSS. The variables are independent and sum up to 100 but there seems to be a problem with variables ...
13 views

### "Nonlinear" random spatial field: an example

I want to generate a "nonlinear" random spatial field in the sense that the autocorrelation function in function of the lag/distance $h$, $\rho(h)$, should be not equal to the $R(h)$ ...
107 views

### Isn't ReLU just a linear function? [duplicate]

I am doing Andew Ng's Deep Learning course and he says that ReLU is better than Sigmoid, but it makes no sense to me at all. The biggest advantage of activation functions are too get a non-linear ...
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### How to determine if a functional connectivity method can detect linear or nonlinear effects?

I am currently calculating the functional connectivity of EEG data using cross-correlation, phase lag index (a phase synchronization method), and mutual information. From what I understand, cross-...
26 views

### How to fit a non-linear model to data using a predefined function

I tried to fit a Difference of Gaussians (DoG) function to my data that has a non-linear relationship. The DoG function is as follows: ...
37 views

### Why do we use Relu if it's mostly linear

We use activation functions in neural nets to introduce some non-linearity. Now I understand that Relu is a non-linear function and I had no problems with it. But today I learned that when the output ...
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### When does a Linear regression stop being a good fit?

I'm testing a couple of hypotheses and I have a non normally distributed continuous response variable (residuals are not normally distributed as well). I have been given mixed suggestion on what model ...
547 views

### Effect of nonlinear transformations on the mean

Suppose I have a continuous random variable $X$ and a random variable $Z = f(X)$, where $f$ is a nonlinear monotonic transformation. How can I prove the following relation between the mean and the ...
33 views

### Statistical Testing of Non-linear Model Parameters

I have produced three non-linear 4-parameter logistic curves based on some experimental observations using three different measurement devices. Each curve shows the measurement of density decline ...
124 views

### How do I evaluate correlation, that appears non-linear

Directed here from StackOverflow Let's say I want to assess if there is a correlation between two fields, one of which I know to have a power distribution. A lot of the information I read assumes ...
92 views

### L-BFGS-B. Forces early stop with no 0 gradient

I am minimizing a non-linear function which is close to linear with L-BFGS-B with scipy.optimize. The issue is that I have a non zero jacobian, low levels of tolerance but the algorithm keeps early ...