# 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 of estimated Survival Functions

Q1 part A&B I have so far $$\underset{n\rightarrow\infty} {\lim} \frac{1}{n}\sum_{i=1}^nI(T_i>x)$$ since we are summing an indicator variable we can say it has a Bernoulli distribution with ...
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### Is convergence in probability implied by consistency of an estimator?

Every definition of consistency I see mentions something convergence in probability-like in its explanation. From Wikipedia's definition of consistent estimators: having the property that as the ...
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### Finite bracketing integral implies convergence in probability

In a paper I am reading, the following result is used. If $(\mathcal{X},\mathcal{F})$ is a measurable space, $\mathcal{G}$ is a class of functions with elements $f : \mathcal{X} \to \mathbb{R}$. We ...
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### Conditions needed for the convergence of Bayesian posterior distribution to point mass (posterior consistency)?

The following 2 theorems (from Bayesian Data Analytics 3rd edition by Gellman, appendix B) show proofs for why Bayesian posteriors converge to a point mass around θ0. Where θ0 is the true parameter ...
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### Convergence of Sample Distributions for Periodic vs Chaotic Systems

Say we have a stochastic process from which we take finite samples to build up some sample probability distribution. As we include more time steps, the sample distribution converges to that of the &...
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### Convergence almost surely of Bernoulli distributed random varibles

I proved that given a sequence of Bernoulli distributed random variables $X_n$ with parameter $1/n$ they do NOT converge to $X=0$ a.s. using the Borel-Cantelli lemma. My doubt is: If I have the space ...
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### Nonconvergence of some parameters in MCMC of Hierarchical Bayesian Model

In short: MCMC is used to construct posterior distributions for parameters of central tendency and all parameters used in the formula for this central tendency. I only care about the parameters of ...
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### Convergence criteria for random field

I am iteratively solving a stochastic equation by generating a random field and using the resulting generation to move toward an equilibrium. I know that the system converges but I want to use an ...
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### Proving uniform convergence of moment restriction score function in GMM asymptotic normality proof

I am asked in a homework question to prove asymptotic normality for the generalized method of moments estimator. The assumptions (which i think are necessary to solve this particular subproblem) given ...
Let's say we have two categorical variables the first with categories $j = 1,..., J$ and the other with categories $k = 1,...,K$. Often in Bayesian hierarchical linear regression, we might have a ...