# 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.

1,055 questions
Filter by
Sorted by
Tagged with
22 views

### Slutsky's theorem and joint convergence

Consider $Z_i$ a random variable that converges in distribution to $Z$ where $Z$ is a standard exponential random variable and $R_i$ a continuous random variable that converges in probability to $0$. ...
• 73
1 vote
60 views
+100

### When the sample mean converges to the population mean, does the probability that the sample mean is equal to the population mean tend to 0?

Let $y_1, y_2, \ldots , y_N$ be arbitrary real numbers and suppose a process of simple random sampling without replacement that selects $n$ out of $N$ elements. Then suppose that these $N$ elements ...
428 views

### Simulated data for logistic regression

I used the code below to create the random variable x1 and binary variable y, and fit the regression with y and x1. My questions are: Why regression coefficient estimates are not close to 2 and 10 (...
• 113
47 views

### Does a misspecified model always have lower likelihood value than the correct model?

Suppose the true dgp is $$x_i \sim d_1(\theta_1), \quad i=1,\ldots,N$$ where $d_1$ is some probability distribution with parameter(s) $\theta_1$, but I wrongly assume $$x_i \sim d_2(\theta_2).$$ ...
• 812
1 vote
71 views

### How to show that $X_n + Y_n \to X + Y$ holds in the $L^1$ norm?

Let $X_n$ and $Y_n$ be sequences of random variables. Show that $X_n + Y_n \to X + Y$ (1) $X_nY_n \to XY$ (2) If $\mathbb{P}(X=0) = 0, \; \frac{Y_n}{X_n} \to \frac{Y}{X}$ (3) are true for convergence ...
1 vote
26 views

### Show the ergodicity of a random sum of ergodic processes

We say that a mean stationary stochastic process $(X_t)_{t \in \mathbb N}$ - i.e. $E[X_t]= \mu_X$ for all $t$ - is ergodic mean if \begin{equation}\tag{I} \frac 1 T \sum_{t=1}^T X_t \overset {pr} \...
• 1,007
40 views

### But what if the 2-th absolute moments converge in probability?

I'm trying to understand a kind of convergence. I had posted another question, but I think it got too polluted and I decided to delete it and simplify it a bit. We know that $X_n \to X$ in mean square ...
• 1,007
1 vote
31 views

### The results from 2 programs are conflicting on convergence issues in my multivariate logistic regression, how do I deal with this?

Currently I am analyzing a dataset using logistic regression, I ran it in R using the glm function to run a multivariate logistic regression with 12 predictors. Some of these are quite collinear as ...
1 vote
10 views

### Minimisation of KL divergence vs minimisation of empirical processes indexed by a metric space in MLE

I am trying to relate the interpretations of MLE as (1)minimisation of KL-divergence and (2)minimisation of empirical processes indexed by a metric space. Questions: Is it always true that maximum ...
• 121
20 views

• 1,863
27 views

### Limiting distribution of $G_n(X_n)$

Consider two sequences of random variables. At each point in the sequence $X_n \sim F_n$ and $Y_n \sim G_n$, and let $F_n(t)$ and $G_n(t)$ denote their respect CDFs. The distributions $(F_n, G_n)$ are ...
• 670
36 views

### Why does my mixed effects model fail to converge when fixed effects are added? How do I solve this problem?

I'm running a study in which participants rate the politeness of two different types of smiles (two levels: rewarding and affiliative) presented in three different situational contexts (three levels: ...
• 21
1 vote
12 views

### Comparing forecast models for signs of conversion

I am trying to analyze two external forecast models for weather data that each generate hourly forecasts twice a day for one week ahead. Thereby I get a panel-like dataset, in which I am interested in ...
• 11
1 vote
39 views

### The convergence of random variables to standard normal distribution

Let $V_s$ be $n\times s$ real matrix and consisting i.i.d $\mathcal{N}(0,1)$ random variables [*]. Suppose that $O_s^1$ is the orthogonal matrix, its first column being the normalization of the first ...
1 vote
35 views

• 769
48 views

### Normal density's rate of convergence to 0 as mean goes to infinity while x and standard deviation are fixed

Consider the density of the Normal distribution given by $$f(x; \mu, \sigma) = \dfrac{1}{\sigma\sqrt{2\pi}}\exp\left(-\dfrac{1}{2}\left(\dfrac{x - \mu}{\sigma}\right)^2\right)$$ It is obvious that, ...
26 views

### Procedures to show that a process is not ergodic

I'm trying to show that a certain process is not ergodic, but as I don't have much experience, I would first like to learn how to show simple cases. We know that if a discrete stochastic process is i....
• 1,007
34 views

105 views

### Convergence Rate of $t$ Test Statistic (Regression)

Consider a simple regression model, $y=\beta^Tx+\epsilon$, say using the cars dataset. We get the following summary: ...
• 2,391
21 views

• 542
16 views

### Reporting summary statistics for stochastic optimization algorithms

In employing stochastic optimization for applied problems, one typically runs algorithms like simulated annealing and genetic algorithms multiple times to get a sense of overall variability. Based on ...
• 1,169
33 views

### Correctly specifying nested random effects and fixed effects with the same variable: how do I specify without running in convergence issues in lmer?

This question is a follow-up question on nested random effects and fixed effects in lmer from the following answer. https://stats.stackexchange.com/a/228814/257284 ...
• 15
27 views

### Gamma multilevel mixed-effects generalized linear model with random intercept and random slope does not converge

I would be super thankful your help with an issue I have with a multilevel mixed-effects generalized linear model that I'm trying to fit to my ecological momentary assessment data using Stata. I am ...
24 views

### Linear Mixed-effect Model Could Not Converge (an issue participants' coding?)

I ran a linear mixed-effect model with 'participants" and "PV" (phrasal words) as a random effect, and the context as the main effect. I found that the model could not converge after I ...
• 13
1 vote
Assume we have a sequence $\mathsf{X}_1,\mathsf{X}_2,\mathsf{X}_3,...$ of iid random variables. Then the Fisher-Tippet-Gnedenko theorem shows that  \mathbb{P}\left(\frac{\max\{\mathsf{X}_1,\mathsf{X}...