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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17 views

Uniform Convergence of Moment under Empirical distribution

Let $X$ be standard Gaussian random variable with cdf $F(x)$. Let $\{X_i\}_{i=1}^n$ be a sequence of i.i.d. standard Gaussian random variables. And let $F_n(x)=\frac{1}{n}\sum_{i=1}^n1_{\{X_i\leq ...
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2answers
27 views

Suspiciously high Multivariate PSRF from gelman.diag()

I am using "Multivariate PSRF" statistics from gelman.diag() function to analyze my MCMC chains. Now I analyzed convergence 471 variables (parameters for each ...
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1answer
35 views

Divergent sequence of random variables with expected value zero

I am trying to think of a sequence of random variables $X_n$ such that $X_n\rightarrow\infty$ as $n\rightarrow \infty$ but $E(X_n)\rightarrow0$. Can you please show me some examples?
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1answer
21 views

Convergence of Sum of Sums of random variables : trivial?

I have a sequence of i.i.d random varaibles $X_1, X_2, ...$ with finite mean $\mu$ and finite variance. I also have another sequence of i.i.d random varaibles $Y_1, Y_2, ...$ with the same finite mean ...
1
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0answers
14 views

Likelihood convexification

I am doing constrained vector optimization using a non-convex non-linear likelihood function. My problem is of the following form: $$\begin{align*}\hat Q &= \underset{\vec Q}{\arg\min} -\log ...
0
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0answers
16 views

pLSA using EM not converging

I have found a lot of questions related to EM but nothing specific to my question. I am using the EM algorithm to fit the pLSA model. As far as I can tell (multiple rounds of checking the code) I can ...
2
votes
0answers
32 views

MCMC convergence: why Heidelberg's test says normal samples are non-stationary?

I am learning about and playing with Heidelberg's convergence test to automatically stop a MCMC sampling. I would have said that if I sample, for instance, from a normal distribution, the test ...
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1answer
39 views

Convergence in distribution with empirical distribution function (EDF)

I'm struggling with the following question: Let $F_n(x)$ denote the EDF of a random sample. Show that $\sqrt{n}(F_n(x)-F(x))\xrightarrow[]{d}N(0,F(x)(1-F(x)))$. I think that the course of ...
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2answers
40 views

What is meant by the term “convergence” in Restricted Boltzmann Machine?

I have come across the term "convergence" in training RBM. Can someone give a brief definition / explanation of it?
3
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1answer
75 views

Show that the sample covariance converges in probability to the $Cov(X,Y)$

Suppose we are given $[(Y_i,X_i)]^{n}_{i=1}$ which is a random sample from the joint distribution of $(Y,X). Show that the sample covariance converges in probability to the $Cov(X,Y)$ My thought ...
8
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5answers
404 views

Intuitive explanation of convergence in distribution and convergence in probability

I am quite unsure of the intuitive difference between a random variable converging in probability versus a random variable converging in distribution. I've read numerous definitions and mathematical ...
4
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1answer
24 views

What to do about very unstable mixed-effects models

I'm working on some poisson mixed effects models for an interrupted time series analysis, and I'm running into two frequent errors. The first I've posted on Stack Overflow, as it appears to be purely ...
3
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1answer
35 views

What is the optimal bandwidth in this problem

Suppose that I have some estimator $\hat f$ for the parameter $f$. I obtain the following convergence rate $$E\|\hat f - f\|^2 = O\left(\frac{1}{nh} + \frac{1}{nh^2} + \frac{1}{\sqrt{n}h} + ...
7
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2answers
287 views

What are some reasons iteratively reweighted least squares would not converge when used for logistic regression?

I've been using the glm.fit function in R to fit parameters to a logistic regression model. By default, glm.fit uses iteratively reweighted least squares to fit the parameters. What are some reasons ...
3
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0answers
81 views

Does $\sqrt{n}(Y_n-1)$ converge in distribution?

Let $n\in \mathbb{N}$ and consider, for each $n$, independent real valued stochastic variables $Z_{1n}\ldots Z_{nn}$, such that $$ P(Z_{nk}=n)=1-P(Z_{nk}=0)=\frac{1}{n} $$ for $k=1,\ldots,n$. Thus ...
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0answers
18 views

Convergence of distributions implies convolution (with itself) converge?

If 2 distributions converge in the limit, then do their convolutions also converge? e.g. I can show that for the Geometric distribution with random variable $T$, the scaled version with parameter ...
3
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1answer
123 views

Convergence from Gamma to Normal Distribution

I came across this problem: Problem If I have $X_1, X_2, ..., X_n$ $n$ iid random variables which pdf is $$ f_X(x) = \begin{cases} \dfrac{x^{\mu-1} e^{-x}}{\Gamma{(\mu)}} &0<x<\infty, ...
3
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1answer
38 views

Converging exponentially in probability implies convergence with probability one ?

When I read the paper On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimate, the theorem 1 in it states something like If for every $\epsilon > 0$ there exists ...
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0answers
39 views

My GARCH model does not converge in Stata

I'm trying to model impact of oil supply shocks on stock prices using GARCH methodology. I have a sample of countries, some for which the GARCH model converges and gives reasonable estimates. For some ...
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0answers
47 views

Correctness of a proof for Hodges' estimator

We know the following is Hodges' estimator: $$ \delta_n = \begin{cases} \bar{X}_n & |X_n| \geq n^{-1/4} \\ a\bar{X}_n & |X_n| < n^{-1/4} \\ \end{cases} $$ where $X_1, ..., X_n \sim ...
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1answer
36 views

Quadratic mean convergence of a biased coin using conditional expectation

I'm a master's degree student and after a lot of research and some days trying I still can't get the answer for a question proposed by my Statistics professor. He asks to toss a coin with a random ...
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0answers
40 views

GLIMMIX convergence problems with ordinal model

I am analyzing a longitudinal data set about hearing loss which has 226 subjects with repeated measures each one (with a maximum of 12 observations per subject) over a follow up time of 22.2 years. I ...
0
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2answers
135 views

Pointwise convergence in probablity of lasso

In the Knight and Fu's paper, in Equation 6 authors consider the pointwise convergence in probability as $$\underset{\phi \in K}{\operatorname{sup}} | Z_n(\phi)-Z(\phi)-\sigma^2| \longrightarrow_p ...
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0answers
27 views

Convergence Time of the EM Algorithm Depending on the Inital Parameter Values

I try to get an intuitive understanding of the convergence properties of the EM-Algorithm. I wrote a code that does the following experiment. We are given three coins: $H$, $A$ and $B$; with ...
3
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1answer
121 views

Convergence of likelihood implying convergence of marginal likelihood?

I will ask my question through a toy motivating example. It is well known that a Poisson process is the continuous time analog to a Bernoulli process (for example: ...
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1answer
16 views

Max fraction of censored values for Cox regression?

I'm not sure whether there's an exact answer to this, but I'm wondering in the simplest case of doing Cox Regression with censoring on one variable, if we have N measurement values, what number (k) of ...
3
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1answer
43 views

Convergence in probability for two statistics of Laplace random variables

Suppose $X_i$ are iid random variables. $X_i \sim \mathrm{Laplace}(\lambda)$. Also define: $$ U_n = \frac{1}{n-2}\sum_{i=1}^n{|X_i|} $$ $$ V_n = \sqrt{\frac{1}{n-1} \sum_{i=1}^n{X_i^2} } $$ Given ...
2
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1answer
539 views

glm.fit: algorithm did not converge -Tweedie

I'm trying to estimate $p$ in tweedie regression, but I got the following message: glm.fit: algorithm did not converge I'm using public data from "GLMs for insurance data" book by Piet de ...
4
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1answer
79 views

estimating the upper bound on a uniform distribution from max order statistic

I have a question. Suppose that $X_1,\ldots,X_n$ are iid $U(0,\lambda)$ and let $X(n)$ denote the nth order statistic. Suppose $\lambda$ is unknown and should be estimated from the sample. Take ...
5
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1answer
73 views

Do these random variables satisfy Lindeberg's condition?

I have the followig sequences: $Pr(X_n=n)=Pr(X_n=-n)=0.5$ $Pr(X_n=2^{n/2})=Pr(X_n=-2^{n/2})=0.5$ I have to show whether they satisfy Lindeberg's condition or not, but this condition is a bit ...
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1answer
51 views

Vowpal wabbit and SGD divergence

I have the following vowpal wabbit log. To me it looks quite counter-intuitive: the objective function (l1-regularized hinge loss) seems to go down then suddenly spiking up. I am aware that gradient ...
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52 views

Rate of convergence of the coverage probability of bootstrap confidence intervals

I was wondering if someone knows good books or references that deal with this subject : "The rate of convergence of the coverage probability of bootstrap confidence intervals" Many thanks for your ...
2
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0answers
36 views

Refining “good” mixing time estimate

Fix a Markov chain $\{ X_{t} \}_{t \in \mathbb{N}}$ with mixing time $\tau_{\mathrm{mix}}$. Assume that I know some finite bound on the mixing time $\tau_{\mathrm{mix}} < \tau < \infty$, and ...
2
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1answer
104 views

Convergence of $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$ if $X_1, \dotsc , X_n \sim U(0,1)$

$X_1,X_2,\dotsc ,X_n$ are independent, uniformly distributed random variables on the interval $[0,1]$ The question is the convergence of the sequence: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
2
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1answer
71 views

Slutsky's theorem

If I have a set of $N$ i.i.d. random variables $X$ with sample mean $\bar{X}=\frac{1}{N}\sum_i^N X_i$, does Slutsky's theorem http://en.wikipedia.org/wiki/Slutsky%27s_theorem imply that $$ ...
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1answer
81 views

How to deal with bootstrap replicates that fail to converge?

I'm using a wild bootstrap to explore the confidence intervals of a nonlinear regression mixed-effects model (specifically one that was solved using nlmer). The ...
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0answers
10 views

How can parameter expansion be applied to cox proportional hazard models with random effects?

Parameter expansion is used in various GLMMs to accelerate e.g. EM or Gibbs convergence. Is anybody aware of a paper/work which implements PX for CPH?
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28 views

Create a damping function for discrete time series data such that values converge to constant value

I have an agent-based model where an agent predicts output and then compares that value to the actual output. How can I create a damping function of sorts that will cause the delta between expected ...
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0answers
20 views

Learning the distribution of a phenomenon's occurrence with partial observation

I recently came across this problem: There is a phenomenon, which occurs exactly on one of a set of M (finite) places at every time step t= 1,2,... At each time step t, the place of occurrence is ...
2
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2answers
60 views

Does convergence in mean imply convergence almost surely if the limit is zero and the sequence is nonnegative?

Say $X_k$ is a non-negative sequence and it is known that it convergences in mean to zero. It feels like it should also convergence almost surely due to the fact that the only value a non-negative ...
0
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1answer
54 views

Is the assumption of linearity necessary for the convergence of the least squares method to the MSE solution

More formally, say there are input vectors $\bf x$ and scalar outputs $Y$ being generated i.i.d. from a joint distribution $p$ and we are interested in estimating $\mu({\bf x}) = {\mathbb ...
0
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0answers
107 views

Convergence warnings in glmer

I am running a Generalized Linear Mixed Model in R 3.0.2 using lme4 1.1-7 for a dichotomous outcome variable (success, 0 = no, 1 = yes) ...
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0answers
19 views

Convergence of Random Variables meaning

What is the intuitive explanation of convergence of random variables? what is meant by saying that a sequence of random variables CONVERGE?
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1answer
63 views

Asymptotic consistency with non-zero asymptotic variance -what does it represent?

The issue has come up before, but I want to ask a specific question that will attempt to elicit an answer that will clarify (and classify) it: In Poor Man's Asymptotics, one keeps a clear distinction ...
2
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1answer
88 views

Almost sure convergence and limiting variance goes to zero

Say an estimator converges with probability one and at the same time its variance goes to zero in the limit. How is it different than an estimator that converges with probability one but its variance ...
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42 views

Convergence of an estimator with infinite variance

Is it true that an estimator with infinite variance can converge both in probability and with probability one?
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1answer
73 views

Convergence of Random Sequence

I have a two statements. One says: $$-\frac{1}{T} \sum_{t=1}^T X_t \rightarrow a $$ in probability as $T \rightarrow \infty$. The other: $$-\frac{1}{g(T)} \sum_{t=1}^{g(T)} X_t \rightarrow a $$ in ...
2
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1answer
70 views

Understanding $O_p$

One thing I feel like I have never mastered is the concept of $O_p$ convergence and how to use it. I understand the basic idea and what bounded in probability means, but I always have a hard time ...
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0answers
48 views

Certainty estimate for prediction of largest of several converging variables

Problem I want to have an estimate for the certainty which of several (3-4) variables is the variable with the largest value, given some sample values which should eventually converge to different ...
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0answers
44 views

Can a perceptron be modified so as to converge with non-linearly separable data?

Normally, a perceptron will converge provided data are linearly separable. Now if we select a small number of examples at random and flip their labels to make the dataset non-separable. How can we ...