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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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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37 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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28 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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17 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 ...
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2answers
133 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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15 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 ...
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119 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
15 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 ...
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1answer
40 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 ...
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1answer
114 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 ...
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1answer
49 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 ...
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58 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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16 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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43 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 ...
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33 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 ...
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1answer
95 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: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
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1answer
55 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
43 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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9 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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20 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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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 ...
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2answers
48 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 ...
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1answer
48 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 ...
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52 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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16 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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47 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 ...
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1answer
68 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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34 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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71 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 ...
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1answer
65 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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40 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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40 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 ...
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26 views

Weight Decay in Neural Neural Networks Weight Update and Convergence

I have a neural network (That I created using java) for a class assignment that is working when I do not use any weight decay value, but when I use a value greater than or equal to .001, my accuracy ...
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58 views

Glivenko-Cantelli Theorem

The Glivenko-Cantelli Theorem (http://en.wikipedia.org/wiki/Glivenko%E2%80%93Cantelli_theorem) states that if $F$ is a distribution function, $X_1,\dots,X_n \sim F$, and $\hat{F}_n$ is the empirical ...
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1answer
93 views

Maximum convergence rate of empirical probability

Given a sequence of events $$(a_1, a_2, \dots, a_n),$$ then the sequence of empirical probabilities of some event $\alpha$ is $$\left(p_1 = \frac{\sum_{i = 1}^1 [a_i = \alpha]}{1}, p_2 = ...
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15 views

Value Iteration exact convergence

I'm running Gauss Seidel value iteration on a weapon-target assignment problem (I can explain this more later if necessary, but i don't think it is). My VI is converging exactly in 2 iterations. I'm ...
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50 views

Multiple imputation to part of a dataset

I am working with a survey dataset which contains hundreds of variables. The item-missing data rate ranges from 0.2% to 10%. In order to retain study units with missing values and to maintain a ...
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1answer
39 views

How to measure if a mean is stable

Background I am a physics major, however I am currently interning at a psychiatry/neuro-imaging laboratory. The primary area of research in my lab is diffusion tensor imaging (DTI). A lot of the ...
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18 views

How to intuitively understand the relationship between difference convergences?

Given a series of random variables $X_1, X_2, \cdots, X_n, \cdots$ convergence in quadratic mean ⟹ convergence in probability ⟹ convergence in probability distribution How to intuitively understand ...
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1answer
103 views

Consistency of unbiased estimator of error term variance in Multiple regression

Let $Y=X\beta+\epsilon$. We know that $\frac{e'e}{n-k}$ is an unbiased estimator of $Var(\epsilon)$, where $e$ is the vector of residuals, and $\epsilon$ is multivariate normal distributed in this ...
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1answer
54 views

Convergence Issues for Bootstrap Distributions

the following is part of a proof from van der Vaarts book on asymptotic statistics: I want to show that if for a continuous distribution function F ...
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1answer
103 views

Use only the last sample as the posterior in MCMC

I am new to statistics. After an MCMC sampler warmed up, the posterior is better estimated as the mean of several samples. (e.g. related question: http://stats.stackexchange.com//questions/56077) ...
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28 views

Convergence of Gini index

Let $\theta(F)=2\int^1_0(t-q_F(t))dt$, where $\displaystyle q_F(t)=\frac{\int_0^tF^{-1}(s)ds}{\int_0^1F^{-1}(s)ds}$. For discrete distributions I'm assuming that $F^{-1}(s)=\inf\{x:F(x)=s\}$ (the ...
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2answers
29 views

X vs x Notation in law of large numbers

This may be a silly question, but I can't find a concise answer. I've been studying Convergence of Random Variables in Wasserman's All of Statistics, which starts out by explaining: $X_n$ is a ...
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2answers
83 views

Convergence in distribution of sum implies marginal convergence?

Let $X_n, X, Y$ be random variables such that $X_n + cY \stackrel{d}{\rightarrow} X + cY $ for every positive constant $c$. Prove that $X_n \stackrel{d}{\rightarrow} X$. I know if only we have joint ...
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2answers
513 views

Distribution function of maximum of n iid standard uniform random variables where n is poisson distributed

I am studying probability theory on my own and am trying to work the following problem in the book - Let $X_1, X_2, . . .$ be independent, $U(0, 1)$-distributed random variables, and let $Nm \in ...
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16 views

Let $f(x)$ be the density of $X$. What is $\lim_{n\rightarrow \infty}\mathrm{E}_X[nf(X+n)]$?

The expectation can be written as $\mathrm{E}_X[nf(X+n)] = \int_{-\infty}^\infty nf(x+n)f(x)\,\mathrm{d}x$. The expectation relies on the speed of tail $f(x+n)$ goes to $0$. I posted a related ...
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1answer
49 views

Reference request: local limit theorem for log-concave densities

The following is easy to prove and can't possibly be new. But I can't find it printed anywhere despite some effort. Can anyone tell me where it is published? Let $X_1,X_2,\ldots$ be a sequence of ...
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271 views

Extreme Value Theory - Show: Normal to Gumbel

The Maximum of $X_1,\dots,X_n. \sim$ i.i.d. Standardnormals converges to the Standard Gumbel Distribution according to Extreme Value Theory. How can we show that? We have $$P(\max X_i \leq x) = ...
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85 views

What to Do When a Log-binomial Model's Convergence Fails

There are times when one might want to estimate a prevalence ratio or relative risk, in preference to an odds ratio, for data with binary outcomes - say, if the outcome in question isn't rare, so the ...