Tagged Questions

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

learn more… | top users | synonyms

4
votes
1answer
24 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 ...
0
votes
0answers
10 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 ...
0
votes
0answers
36 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 ...
0
votes
0answers
14 views

Convergence in MGF's [on hold]

I am working on something and ran into a problem. Can anyone offer some assistance? Let X1, X2, ... be iid Bernoulli RV's, Xi~Bern(p) Let Sn = X1 + ... + Xn, Xbar = Sn/n Tn = sqrt(n)(Xbar - ...
2
votes
0answers
22 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
votes
1answer
91 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
votes
1answer
52 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 $$ ...
1
vote
1answer
32 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 ...
1
vote
0answers
8 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?
0
votes
0answers
19 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 ...
1
vote
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
votes
2answers
45 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
votes
1answer
45 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
votes
0answers
32 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) ...
0
votes
0answers
15 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?
1
vote
1answer
40 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
votes
1answer
62 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 ...
0
votes
0answers
31 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?
0
votes
1answer
70 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
votes
1answer
60 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 ...
1
vote
0answers
35 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 ...
1
vote
0answers
36 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 ...
1
vote
1answer
18 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 ...
4
votes
1answer
57 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 ...
1
vote
1answer
91 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 = ...
0
votes
0answers
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 ...
0
votes
0answers
47 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 ...
2
votes
1answer
38 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 ...
0
votes
0answers
15 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 ...
0
votes
1answer
82 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 ...
2
votes
1answer
51 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 ...
3
votes
1answer
99 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) ...
1
vote
1answer
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 ...
3
votes
2answers
27 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 ...
5
votes
2answers
81 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 ...
4
votes
2answers
376 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 ...
0
votes
0answers
15 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 ...
5
votes
1answer
47 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 ...
6
votes
1answer
244 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) = ...
1
vote
0answers
74 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 ...
5
votes
1answer
81 views

Simulating Convergence in Probability to a constant

Asymptotic results cannot be proven by computer simulation, because they are statements involving the concept of infinity. But we should be able to obtain a sense that things do indeed march the way ...
1
vote
0answers
43 views

Logistic Regression doesn't converge if I use a particular baseline

Apologies if the question is too broad, then please close the thread. Or maybe this belongs in StackOverflow? I observed something strange and wonder if someone more educated can shed some light on ...
0
votes
0answers
99 views

Coefficients from a Dynamic Panel Data Model of Economic Growth

I am having difficulties with the interpretation of the regression results from estimating a growth regression in a dynamic panel data set-up, estimated using Stata. (I'm using difference GMM and ...
2
votes
0answers
23 views

Convergence of a sequence of random variables [duplicate]

Suppose $P(X=1)=P(X=-1)=1/2$ and define $$X_n=\begin{cases} X\ \text{with probability}\ 1-\frac{1}{n} \\ e^n\ \text{with probability}\ \frac{1}{n} \end{cases}$$ I then need to prove or disprove ...
3
votes
2answers
137 views

Limiting distribution of the first order statistic of a general distribution

Let $Z_i,Z_2,\ldots$ be IID Random Variables with density $f$. Suppose that $P(Z_i>0)=1$ and that $\lambda=\lim_{x \to 0+} f(x)>0$. How can I show that $X_n=n \times \min\{Z_i\}$ has a limiting ...
3
votes
1answer
47 views

How to report results from analyses that did not converge

I am an analyst on a paper and, in writing up methods and results, noted that one of the proposed (logistic regression) models did not converge due to separation. I noted this in the results section ...
4
votes
2answers
96 views

Convergence in probability, $X_i$ IID with finite second moment

Let $\{X_i\}_{i\geq 1}$ be IID with finite second moment, and $$ Y_n = \frac{2}{n(n+1)}\sum_{i=1}^n \,i\cdot X_i \, , \qquad n\geq 1 \, . $$ Could you please tell me how can I show that $Y_n$ ...
1
vote
0answers
21 views

Uniform convergence of Monte Carlo approximation

Usually Monte Carlo method is used to compute integration. For example, let $g(x,\theta)$ be a continuous function about $x$ and $\theta$, $f(x \mid \theta)$ is a continuous pdf with parameter ...
2
votes
0answers
31 views

Difference between sample and sequence in Law of Large Numbers

I'm comparing the Chebychev (Weak) Law of Large Numbers (LLN) to the Kolmogorov (Strong) LLN in an econometric textbook and both definitions start off differently. The Chebychev LLN begins with If ...
0
votes
0answers
34 views

Checking convergence in MCMC with single chain

I have reed the Gelman-Rubin method for check the convergence in MCMC on $m\geq 2$ chain, but when I work with only one chain, what can i do to check the convergence? There is some method that work ...