Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

1
vote
0answers
16 views

Is it the case/is there a proof that the convergence in distribution for the CLT is monotonic?

So for instance, if I compare $\bar{x}_n$ and the comparable normal distribution, and $\bar{x}_m$, $m > n$, and the comparable normal distribution, would I expect the difference in former (e.g. the ...
0
votes
0answers
25 views

Bayesian model initial values impact posterior values

I using Winbugs and having trouble getting the model to converge, but I think real question is understanding what is going on with the bayesian model and the initial values which is why I post on ...
0
votes
0answers
12 views
0
votes
1answer
27 views

Policy iteration does not converge to optimal policy [on hold]

I have simple environment of 4 timesteps and at each timestep agent receives e tuple (e1, e2). Agent is able to perform 4 ...
2
votes
1answer
32 views

What is a good aproximation in asymptotic normality?

I have a conceptual doubt. For example, suppose I have $X_i \stackrel{iid}{\sim} N(\theta^*,1)$ and I know that (I have the information) $\theta^{*}\geq 0$. So I have the Constrained Maximum ...
5
votes
1answer
35 views

What does the distribution of samples from an MCMC method converge to without repeated samples?

Suppose I have an absolutely continuous distribution with density $f(x)$ and I use an mcmc sampler which has accept/reject step to sample from this distribution. In the final samples, there are some ...
0
votes
0answers
31 views

Derivation of AMISE and Bandwidth

Given: Let $K(\cdot)$ be a bona fide kernel. Let $f$ be a pdf and $\widehat{f}_n$ is kernel density estimator with bandwidth $h$ based on a sample $X_1,X_2,\cdots,X_n$ of size $n$ draw iid from $f$. ...
1
vote
1answer
45 views

R: singular convergence in mixed effect model

I have an experiment that is designed as 6 blocks of 4 plots each, with two treatments (W_add and P_add) plus combination of treatments and control. The data are flux measurements taken during 9 ...
0
votes
1answer
18 views

Limits and constraints for Q-learning

I have simple implementation of Q-learning algorithm and I'm trying to run it on States space size = 36865 Actions space size = 25 So my resulting Q-table is ...
0
votes
0answers
21 views

On the Relationship between Data Size, Number of Epochs, Number of Iterations and Convergence of a Model

I did the following two experiments with a model on a dataset: Experiment 1: Training on a small dataset (~50 examples) The model took around 60 epochs to overfit just this small dataset. Each epoch ...
0
votes
1answer
27 views

Convergence in Distribution, Argument Converging in Probability

Suppose $\lim_{n\to\infty}P(X_{n}\leq x) = P(X\leq x)$ and that $A_{n} \stackrel{p}{\longrightarrow} a$, where $a$ is a continuity point of $F_{X}(x) = P(X\leq x)$. Is it the case that $\lim_{n\to\...
1
vote
0answers
24 views

Clarification regarding proof of convergence of online EM

Online EM algorithm was proposed by Olivier Cappé in Link to paper. They assume that complete data likelihood $f(x ; \theta)$ belongs to exponential family i.e. $f(x;\theta) = h(x) \exp \left\lbrace ...
1
vote
1answer
22 views

Difference between finiteness and boundedness of a random variable

In a stochastic processes class, we're studying a theorem which required that a random variable $T$ have finite mean. The notes presented a counterexample where a R.V. $T$ was such that $P(T<\infty)...
8
votes
3answers
123 views

When does $X_n\stackrel{d}{\rightarrow}X$ and $Y_n\stackrel{d}{\rightarrow}Y$ imply $X_n+Y_n\stackrel{d}{\rightarrow}X+Y$?

The question: $X_n\stackrel{d}{\rightarrow}X$ and $Y_n\stackrel{d}{\rightarrow}Y \stackrel{?}{\implies} X_n+Y_n\stackrel{d}{\rightarrow}X+Y$ I know that this does not hold in general; Slutsky's ...
0
votes
0answers
25 views

“Good” MCMC trace plot

I have ran ensemble MCMC using emcee sampler package. For parameters, most of them had uniform prior U[a,b](chosen from known info). When looking at the traceplots, the chain seems to continually ...
3
votes
1answer
335 views

Why second order SGD convergence methods are unpopular for deep learning?

It seems that, especially for deep learning, there are dominating very simple methods for optimizing SGD convergence like ADAM - nice overview: http://ruder.io/optimizing-gradient-descent/ They trace ...
1
vote
0answers
18 views

Acceptance-Rejection using Functional

Setup Let $X\in L^1(\Omega,\mathcal{F},\mathbb{P})$. As far as I've seen, Monte-Carlo methods generate $x_1,\dots,x_n$ from the distribution of $X$ and uses the Glivenko-Cantelli theorem to conclude ...
2
votes
2answers
39 views

Asymptotic Expectation of Ratio of Sample Averages

I have two random variables: $X$ and $Y$. I know that: \begin{equation} E[X]=E[Y]=\mu>0 \end{equation} I know that variance of both can be bounded: \begin{equation} \operatorname{Var}[X]<k, \...
4
votes
1answer
33 views

Centering in longitudinal linear mixed modeling - center by participant mean, timepoint mean, or participant by time grand mean?

EDIT: I was incorrectly looking to center my outcome variables. Only center predictors, and decide on group mean or grand mean centering by how you want to interpret your intercept. I have 150 ...
0
votes
1answer
31 views

Prove convergence of a sum of random variables

I am trying to grab on to some intuition about the area where random variables start looking a bit more like calculus. I've learned about random variables and the weak law of large numbers, but seem ...
0
votes
0answers
13 views

Spatio-tempral Bayesian Poisson model convergence investigation

I am fitting a spatio-temporal Bayesian Poisson model with 22 explanatory variables, an offset variable, 2200 observations and non-informative priors. I am using the package ...
1
vote
1answer
30 views

Random variables - proof of convergence in probability

I've got this exercise from lecture notes, but I couldn't find an answer. For each positive integer $n$, let $X_{n}$ be a non-negative random variable with $\mathbb{E}[X_{n}] < \infty$. Prove that ...
1
vote
2answers
32 views

Question about expectation in OLS?

Consider the linear model $$y_i = x_i^T\beta + \epsilon_i.$$ In ordinary least squares it is assumed that the errors satisfy $E[\epsilon_i]=0$. This implies that that $\dfrac{X^T\epsilon}{n} \to 0$ ...
2
votes
1answer
189 views

abusing convergence in distribution notation

If I have $\sqrt{n} (X_n - c) \xrightarrow[]{d} N(0,v) $ does it make any sense at all to say this implies that $X_n \xrightarrow[]{d} N(c, \frac{v}{n})$. If not, what is the accurate way/notation ...
1
vote
0answers
19 views

Approximating AR(1) by finite order MA process - convergence results

I am currently struggling with a result pertaining to the finite order MA approximation of a simple AR$\,(\,1\,)$ process defined on a double sided time-index set $\,T=\mathbb{Z}$. I would be very ...
1
vote
0answers
14 views

Brownian Motion proof: difference converging to 0 almost surely

I am reading a proof where it is assumed that $$ \lim_{n \to \infty} \sup_{0<s\leq s_0}\left| \frac{t_n(s)}{s}-1 \right|=0 , \hspace{30mm} (1)$$ where $t_n(.)$ is some sequence of functions. ...
0
votes
1answer
113 views

statsmodels logistic regression with binned variables has large coefficients and standard error for some variables

I'm fitting a logistic regression (binary) using Python's statsmodels, and here's a snippet of summary from the model: I have noticed that the large coefficients ...
0
votes
1answer
66 views

glmer model convergence question

We are working with a longitudinal dataset, with three variables: WAIP, BPSRRI and group. WAIP and BPSRRI are measured repeatedly for 10 times and group refers to the group assignment of our subjects ...
0
votes
0answers
14 views

Cannot seem to converge beyond a loss of 3 on an object detector being trained on YOLO

Data The you only look once YOLO algorithm is used for object detection. I have scoured the internet for resources on how to tackle this problem, but there seems to be a lot of resources that point ...
0
votes
0answers
10 views

How does network structure (model complexity) affects covergence speed?

I trained Bi-GRU and HAN (Hierarchical Attention Networks) on my own datasets, and found HAN converges faster than Bi-GRU, within less number of epochs. What would be the reason for this? I guess ...
7
votes
1answer
126 views

Convergence of the Matérn covariance function to the squared exponential

The Matérn covariance function converges to the squared exponential covariance function. Many sources, amongst them the GPML book and Wikipedia, state this result. None of them provide details. I ...
5
votes
1answer
208 views

Central limit theorem (CLT) writing

Is there a reason why we are used to write the CLT as $\sqrt{n}(\overline{X}_n-\mu)\stackrel{d}{\rightarrow}N(0,\sigma^2)$ and not as $\overline{X}_n\stackrel{d}{\rightarrow}N(\mu, \frac{\sigma^2}{n})$...
2
votes
2answers
46 views

Rate of convergence of sum of two random variables

Let $X_n$ and $Y_n$ be random variables such that $X_n=o_p(1)$, $Y_n=o_p(1)$, $X_n - Y_n = o_p(1)$. Is the following correct? $o_p(X_n) + o_p(Y_n) = o_p(|X_n - Y_n|)$
4
votes
1answer
66 views

Does convergence in distribution imply asymptotic stationarity?

Let ${\bf \tilde{x}}_1, {\bf \tilde{x}}_2, \ldots$ be a (possibly non-stationary) stochastic sequence of $d$-dimensional random vectors that converges in distribution. Does it immediately follow that ...
0
votes
1answer
25 views

Nested model failing to converge - how to make decisions about random intercept only model?

I have two models: modela <- lmer(perception~1+self+actual+(1|id/rid),data=data) modelb <- lmer(perception~1+self+actual+(1+self+actual|id/rid),data=data) ...
1
vote
1answer
50 views

Bayesian consistency in compact uncountable parameter space

Let $p(y_i \mid \theta)$ be the likelihood we are using of a single data point, $p(\theta)$ be the prior, and $f(y_i)$ the true distribution of the data. Also, let $\theta_0$ be the parameter that ...
1
vote
1answer
59 views

convergence in distribution?

I have a question. Let $X_n$ converge to $X$ in distribution, on the other hand, $Y_n$ converges to $Y$. What can we obtain about convergence of division of $X_n/Y_n$ in distribution? Does it ...
2
votes
1answer
54 views

convergence of an algorithm [closed]

I want to know when we speak about the convergence of an algorithm, what are the conditions that we should check. For example, I was looking for the convergence of the policy iteration algorithm in ...
1
vote
1answer
93 views

Convergence in probability of $\frac{1}{n}\sum_{i=1}^n X_i^2$ when $X_i$'s are i.i.d $N(0,1)$

Question: My approach: And after this I am stuck..How do I put the modulus over here and how do I determine the appropriate value of "k" ? (here k signifies the value of convergence in probability ...
0
votes
1answer
47 views

Can you perform a likelihood ratio test on two linear mixed effects models with different optimizers in lme4?

I ran into an error with my full (but not simple/null) model, so I had to use a different optimizer to avoid the fitting problems. Can I still do an LRT test using those models?
0
votes
1answer
25 views

jackknife estimator with central limit theorem

Let $\hat{\theta}_n$ be an estimator of the parameter $\theta$ from the sample $\Omega_n$ of $n$ observations, satisfying that $\sqrt{n} (\hat{\theta}_n-\theta) \overset{d}{\longrightarrow} \mathcal{N}...
0
votes
0answers
16 views

Convergence radius of random power series

I have a problem with getting how I should interpret the random power series. I am given $X_n$ that are i.i.d random variables. Further the random power series, $\sum_{n=0}^{\infty} X_{n}z^{n}$ ...
2
votes
0answers
31 views

CLT and convergence of Variance

I am looking at a problem where the sum of the individual $X_i$ is $S_n=X_1+\dotsm+X_n$. The probability is given as, $P(X_i=i)=P(X_i=-i)=\frac{i^{-\alpha}}{4}$ and $P(X_i=0)=1-\frac{i^{-\alpha}}{2}$. ...
0
votes
0answers
89 views

policy iteration convergence

There is a question here for 2014 about the convergence of policy iteration algorithm with two answers > Question However, it is not clear for me how we change the value functions after one policy ...
1
vote
1answer
87 views

Proving a remainder term converges to 0 in probability

So we have these definitions: σ̂^2_1= (1/n)∑(Xi−μ)^2 σ̂^2_2= (1/n)∑(Xi−Xbar)^2 I have shown that n^0.5(σ̂^2_2−σ^2)= n^0.5(σ̂^2_1−σ^2)- n^0.5(Xbar-μ)^2 I am trying to show that the remainder term ...
1
vote
1answer
62 views

Convergence of $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$ - central limit theorem

Suppose that $U_n=\frac{1}{\sqrt{2n\sigma^2}}\left(\Sigma X_j-\Sigma Y_j\right)$, where $X_1,X_2,\ldots$ and $Y_i,Y_2, \ldots$ are i.i.d. sequences of random variables with mean $\mu$ and variance $\...
3
votes
2answers
72 views

Prove convergence in distribution for n times the minimum of an unknown positive distribution

Let $Z_1, Z_2, ...$ be independent and identically distributed random variables with some density $f$. Suppose that $P(Z_i > 0) = 1$, and that $$ \lambda = \lim_{x\to 0} f(x) > 0$$ Let $X_n = ...
1
vote
0answers
16 views

Prove bi-directional relationship between convergence in distribution and convergence of probability mass functions

Let $X$ be a random variable that is positive and integer-valued. Let $X_1, X_2, ...$ also be random variables that are positive and integer-valued. Prove that $X_n$ converges in distribution to $X$ ...
0
votes
1answer
29 views

Can we conclude, with the strong law of large numbers, that $n$ random variables are independent? [closed]

Suppose we have a sequence of identically distributed random variables $X_1, \ldots, X_n$, and that we know $(X_1 + \ldots + X_n)/n$ converges almost surely to $\mu = E[X]$ as $n$ approaches infinity. ...
0
votes
0answers
59 views

How to select parameters for ADAM gradient descent

I am using ADAM for performing gradient descent. I am having difficulty in setting the learning rate, $\beta_1$ and $\beta_2$. Along with gradient descent, I am projecting the paramters on $L_1$ ball ...