# Questions tagged [convergence]

Convergence generally means that a sequence of a certain sample quantity approaches a constant as the sample size tends to infinity. Convergence is also a property of an iterative algorithm to stabilize on some aim value.

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### Convergence issues with lme4 1.1-20 for models that converged when using earlier version of lme4

I am encountering convergence problems with some models after updating to lme4 1.1-20 that I did not encounter with earlier versions of lme4 (in particular, lme4 1.1-15). I am encountering these new ...
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### MCMC convergence, analytic derivations, Monte Carlo error

I'm trying to figure out some convergence statements on an MCMC example. The setup is: I'm generating data samples as observations from a (known) deterministic parameter, say $s$ (using a forward ...
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### Momentum updates average of g, Adagrad also of g^2 - any other interesting updated averages for SGD convergence?

Updating exponential moving average is a basic tool of SGD methods, starting with of gradient $g$ in momentum method to extract local linear trend from the statistics. Then e.g. Adagrad, ADAM family ...
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### A dynamical systems view of the Central Limit Theorem?

(Originally posted on MSE.) I have seen many heuristic discussions of the classical central limit theorem speak of the normal distribution (or any of the stable distributions) as an "attractor" in ...
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### How to show that an estimator is consistent?

Is it enough to show that MSE = 0 as $n\rightarrow\infty$? I also read in my notes something about plim. How do I find plim and use it to show that the estimator is consistent?
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### Convergence of F(n,n) distribution to normal

Suppose that $X \sim F(n,n)$, an F distribution on $n$ and $n$ degrees of freedom. I'm trying to figure out why some literature state that $X$ converges in distribution to a normal distribution. My ...
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### Proving that the product of 2 samples, when sorted in order, converges to the variance of the population

I have a question regarding the average value of the pairwise product of 2 ordered samples that are drawn from a random variable, $X$, which in this case is zero-mean Gaussian ($X \sim N(0,\sigma_x)$)...
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### Convergence in probability and distribution

Let $P(K=k)=(1-\beta)^k\beta ; k=1,2,3,...$ Then it is required to show $\beta K$ converges in distribution to an exp (1) random variable as $\beta$ tends to zero. For this they have started with ...