Convergence generally means that a sequence of a certain sample quantity approaches a constant as the sample size tends to infinity.

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7 views

How to test whether a time series of measurements have converged to an equilibrium

I have a time-series of data that looks like this (as a couple of examples): This mean energy is the mean over a number of Monte Carlo test particles. The number of particles vs. time is not ...
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10 views

canonical benchmark on convergence measures for neural networks

This is in reference to an answer to a previous question (here), and to a related question (here). I know there are a truck-load of data sets out there (link). I know there is very wide variety of ...
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8 views

How to decide about the number of looks (window size for ensemble averaging) in SAR images?

This question has frustrated me for a while. In order to find an answer I sent an email to prof. Yamaguchi, the author of the paper Four-Component Scattering Power Decomposition With Rotation of ...
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0answers
44 views

Convergence in distribution and degenerate random variable

Let $\{Y_n\}$ be a sequence of random variables with an associated sequence of CDFs $\{F_n\}$ given by : $$F_n(y) = \begin{cases} 0 & \textsf{for}&y <0 \\ (\frac{y}{\theta})^n & ...
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2answers
39 views

Inverse gamma convergence in probability

I am trying to prove the consistency of MLE for a beta distribution. The problem now reduces to the following: Assume $Y=\frac n X$ and $X$ ~ Gamma(n,$\frac 1 \theta$), prove that $Y$ converges to ...
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8 views

SPSS: GLMM and(adjusted) odds ratio

I am performing a retrospective study and the relative statistic analysis. I am studying the the risk factors for the occurrence of complications during medical procedures. I have 50 subjects ...
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0answers
10 views

Improving convergence of simulated annealing

I have a complex curve that I need to approximate with a parametric model (5 parameters). The parametric model itself is highly non-linear, and small changes in parameters can lead to big changes in ...
3
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0answers
23 views

Convergence of a sequence of Binomial variable with changing probability

Consider a $t\in(0,1)$. Consider, for $\Delta>0$ the random variable $X_t^{(\Delta)}$ defined as $$ \mathbb{P}[X_t^{(\Delta)}=1]=\left(1-\lambda\,\Delta\right)^{\left\lfloor ...
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1answer
67 views

convergence of Cauchy distribution

It is known that the Large Number Theorem does not apply to Cauchy distribution since it does not have an expectation value. That said, $S_n / n$ does not converge in any sense (almost sure, in ...
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0answers
21 views

Asymptotic normality for nonsmooth objective functions

Assume that $f ({\bf x}; \theta): \mathbb{R}^p \times \Theta \to \mathbb{R}$, where ${\bf x}$ is the vector of inputs (with some distribution) and $\theta$ is the vector of parameters. Also, assume ...
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1answer
20 views

Continuous mapping theorem for convergence in probability

I have seen the continuous mapping theorem (CMT) used to justify the convergence in probability of the difference of two sequences of random variables when it is known that each sequence converges in ...
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3answers
273 views

Statistical test to verify when two similar time series start to diverge

As from title I would like to know if exist a statistical test that can help me to identify a significant divergence between two similar time series. Specifically, looking the figure below, I would ...
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1answer
58 views

Convergence in probability question

Being a novice to this topic, I am not being able to properly write down a step by step solution to this problem. For each integer $n$, let $X_n$ be a non negative random variable with finite ...
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1answer
38 views

Is there a central limit theorem for i.n.i.d. variables when normalised by inconsistent variance estimate?

I am wondering whether there exists a central limit theorem for the following situation. Consider the sum of normally distributed variables $\epsilon_i$ with unequal variances according to ...
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0answers
27 views

A convergence problem

Let Xn be a sequence of random variable that converges in distribution to a random variable X, Let Yn be a sequences of random variables with the property that for any finite number c, ...
4
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2answers
109 views

Chebychev’s Weak Law of Large Numbers

This theorem is on Econometric Analysis (7th edition) by Greene (2012), Page 1071. It states that "If $x_i$, $i=1,2,...,n$ is a sample of observations such that $E(x_i)=\mu_i<\infty$ and ...
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2answers
307 views

Is Slutsky's theorem still valid when two sequences both converge to a non-degenerate random variable?

I am confused about some details about Slutsky's theorem: Let $\{X_n\}$, $\{Y_n\}$ be two sequences of scalar/vector/matrix random elements. If $X_n$ converges in distribution to a random ...
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0answers
117 views

Topologies for which the ensemble of probability distributions is complete

I have been struggling quite a bit with reconciling my intuitive understanding of probability distributions with the weird properties that almost all topologies on probability distributions possess. ...
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1answer
100 views

Law of large numbers and convergence

Suppose $X{\sim}N(\mu_1,\sigma_1^2)$ and $Y{\sim}N(\mu_2,\sigma_2^2)$, $x_1,...x_n$ and $y_1,...,y_n$ are i.i.d samples from X and Y, respectively. Consider the estimator ...
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1answer
27 views

How similar is the WLLN to “converges in probability”?

How similar is the weak law of large numbers to convergence in probability? It seems that one can use WLLN to display convergence in probability. Like displayed here: ...
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1answer
142 views

The antithesis of “converges in probability”?

A sequence $X_n$ converges in probability to $X$ if $$\lim_{n\rightarrow \infty}P(|X_n-X|>\epsilon)=0$$ when $n \rightarrow \infty$ for all $\epsilon >0$. How do you formulate that antithesis ...
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0answers
50 views

How do i compare two Self Organizing Maps?

I have results (weights) for multiple runs of self organizing map. I am trying to compare these results to check if my algorithm gets to the same solution from different random initial weights. I have ...
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14 views

kmeans convergence text data

I'm using kmeans to cluster text data. My tfidf matrix is approximately 5700 documents x 3900 features, and sparse as is typical with text data. I have set max iterations to converge = 100. I've ...
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11 views

Convergence for oscillating trends

I am working with an algorithm studying the response of a system to an external factor (Phenomenon A). The system can either respond perfectly, or can be completely disrupted. I am plotting the ...
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1answer
140 views

Convergence to normal distribution

Let $X_{1},X_{2},...$ be independent random variables such that $X_{k}$ is Po(k)-distributed for k=1,2... Show that: $$Z_{n}=\frac{1}{n}\sum_{k=1}^{n}\left(X_{k}-\frac{n^{2}}{2}\right)$$ ...
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55 views

Prove $\int_E |f| d\mu < \infty$, $\lim \int_E f_n d\mu \to \int_E f d\mu$

Suppose we have a measure space $(\Omega, \Sigma, \mu) = (\mathbb R, \mathscr B(\mathbb R), \lambda)$ (Alternatively, we can consider a similar probability space on some subset of $\mathbb R$ that has ...
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1answer
28 views

Convergence in probability: Does squeeze theorem apply?

Does squeeze theorem apply in convergence in probability? My statistics reference (where it talks about convergence in probability and its condition) does not cite it (but does seem to apply it), but ...
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2answers
160 views

Is $\mathbb{P}(X^2>a)=\mathbb{P}(X>\sqrt{a})$, $a>0$?

Let $X$ be a r.v. and $a>0$ Is $$\mathbb{P}(X^2>a)=\mathbb{P}(X>\sqrt{a})$$ ? As seen in the comments, no. It should be: $$\mathbb{P}(X^2>a)=\mathbb{P}(|X|>\sqrt{a})$$ But why ...
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1answer
129 views

Meaning of $\lim\limits_{n\rightarrow \infty}\mathbb{E}(X_n^2)=0$?

This is related to convergence in probability: What's the meaning of $\lim\limits_{n\rightarrow \infty}\mathbb{E}(X_n^2)=0$ for random variables $X_1,X_2,...$.
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1answer
42 views

Distribution and convergence of two random variables

Find two sequences $(X_n)$ for $n\in\mathbb{N}^{+}$, and $(Y_n)$ for $n\in\mathbb{N}^{+}$ of random variables such that all the following conditions are satisfied: (a) For every $n \in ...
4
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1answer
52 views

Convergence of expectation

Suppose we have $X_n \overset{D}\to X$ for some sequence $X_{1},\dotsc, X_{n}$. Is it the case that if $E(X_{n}^2) \to E(X^2)$ we have it that $E(X_n) \to E(X)$, and when would it hold? My first ...
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19 views

Convergence in MCMC [duplicate]

I am using the gelman.diagfunction in R to check the convergence of MCMC. This is the result: ...
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23 views

Does the asymptotic distribution of sample median follow from statistical functionals?

I know that if $F_n$ is the empirical distribution function and $F$ is the true distribution function, then, with $T$ being any statistical functional (satisfying the von-Mises derivative conditions), ...
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4answers
171 views

What is the difference between bias and inconsistency?

I am trying to learn about bias in simple linear regression. Specifically, I want to see what happens when the $cov(e,x) = 0$ assumption of the simple regression is violated. If this assumption is ...
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1answer
51 views

Interpreting GLM regression analysis result

I'm using the following code in R to predict votes (e.g. non-negative integer count data). ...
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17 views

Convergence in distribution of constrained MLE?

Consider a sample of i.i.d. random variables $\{X_i\}_{i=1}^N$ with $X_i$ distributed as $N(\mu,1)$. The MLE estimator of $\mu$ subject to $\mu \geq 0$ is $\mu_{mle, constrained}=\max ...
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0answers
33 views

What is the information-theoretical lower bound for estimating $E[f(X)]$

Given i.i.d. realizations $X_1,\ldots,X_n$ of $X$, what is the information-theoretical lower bound of the convergence rate for estimating $E[f(X)]$? Here $f$ is a function from $[0,1]$ to $[0,1]$. ...
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2answers
89 views

Predictive Variance of a Gaussian Process

Suppose $f$ is a function of some variable say $x$ ($x$ could be multi-dim). Then the GP assumption is written as follows $$f∼GP(m,k)$$ where $m$ is the mean function and $k$ is the covariance ...
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0answers
25 views

Convergence diagnostics for binary variables

I am running MCMC for binary/categorical variables. I know that a decent method to check for convergence is to look at the traceplot of the variance, but I don't know a good citation for this. Does ...
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2answers
61 views

Gaussian Process Proofs and Results

I am building a model based on Gaussian processes and want to assume something like as my sample size $n$ gets large my prediction error goes to 0. In other words,a re there any proofs or theorems ...
3
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0answers
32 views

Check if one particular distribution is $\mathcal{L}^2$

I am regularly doing econometrics on various distributions. But I wonder if one should theoretically think of the regularity of this distribution. To be more, clear, should not one "check" that a ...
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13 views

GAM convergence error in for-loop

I am running a gam model as shown in the code below: gam=list() for (j in 1:1000){ ...
3
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1answer
54 views

Convergence in probability of an estimator

I'm asked to verify if the following estimator of $\mu$: $$\hat{\mu}=\frac{1}{n+1}\sum_{t=1}^{n}y_t$$ converges in probability by computing its $p \lim$ (note that $E[y_t]=\mu$). I've made the ...
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1answer
80 views

Converge in probability, always zero variance?

Suppose a sequence of random variables $X_n$ converges in probability to a random variable $X$. Is it always the case that $\mathrm{Var}(X)=0$?
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1answer
27 views

How does R calculates convergence tolerance and what does it stands for?

I'm using R for the first time for estimating parameters of a vector function. In the summary of the method I used (nls to be precise), the information on "achieved convergence tolerance" appeared. ...
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19 views

SPSS Linear Mixed Models converging extremely slowly, 24+ hours [closed]

This is my first question here, I will do my best to not break any rules. My question is about Mixed Models in SPSS 19. I have used these models before with datasets n=2200 and my processing time ...
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1answer
31 views

Almost sure convergence of sample variance with iid sample

Consider $\{X_i\}$ i.i.d. sample of multivariate (in $\mathbb{R}^J$) with mean $\mu$ and variance $\Sigma$. I've been asked to show that $\hat{\Sigma}\equiv\frac{1}{n}\sum_{i=1}^n (X_i-\bar{X}_n) ...
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58 views

Convergence error in r.squaredGLMM() but not glmer() fit

I am fitting binomial generalized linear mixed effects models with 2-8 fixed continuous variables and one random effect with 8 levels. The data set has about 700 points. I am using package lme4, ...
1
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1answer
30 views

Convergence of vector of RV iff convergence of each RV

I'm trying to show that: $$ (X_n,Y_n)\to^p(X,Y)\iff X_n\to^pX,Y_n\to^p Y $$ where $\to^p$ means convergence in probability ($P(||X_n-X||>\varepsilon)\to 0,\forall\varepsilon>0$). I managed to ...
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0answers
32 views

calculation of the log-likelihood evolution for my MCMC simulation resulted in infinite values

i want to plot the log-likelihood evolution for my MCMC simulation results. i was estimated a Dirichlet mixture model parameters using the Gibbs sampling method in R environment and utilizing the ...