All Questions
Tagged with estimation mean
77 questions
3
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1
answer
70
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Sample mean or James-Stein estimator?
I have a simple practical question, which I posted in Quant Finance SE (posting here as well, as I am not getting an answer(s) for it).
Suppose we have $n\geq3$ financial time series (correlated or ...
- 557
0
votes
0
answers
40
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Can I compare two estimates by their sample variance?
For example, to estimate the population mean $\mu$, I am given two sample mean $\bar{x}_1$ and $\bar{x}_2$ from two (independent) data sets of $N_1$ and $N_2$ observations respectively.
Without access ...
- 51
1
vote
0
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50
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Does the confidence interval for Poisson rate contain the sample mean?
Let $X_1, X_2, \dots, X_N$ be iid random variables from $Poisson(\lambda)$. The confidence interval for $\lambda$ with confidence level $1-\alpha$ is
$$ \frac{1}{2N} \chi^2 \left(\alpha/2; 2 \sum_{i=...
- 141
1
vote
1
answer
99
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Estimating the mean of a Poisson process from data
My data shows the daily number of logins per person over the last three months.
I am modelling the number of events per person per day as a Poisson process. I am interested in estimating the ...
- 569
1
vote
0
answers
68
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Combining Averages to Improve Estimates?
I am an MBA student taking courses in statistics.
Recently, I posted a question (Can "Pooled Averages" be considered as "Better" compared to "Individual Averages"?) in ...
0
votes
1
answer
150
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Properties of Estimators Using Dice Rolls?
I am an MBA student taking courses in statistics.
Today, some of the students from the actual statistics faculty presented a seminar on estimation and probability - it was really interesting! In our ...
1
vote
0
answers
27
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Estimation of mean, variance, proportion for cakes baking in 30 ± 2 minutes, or estimation of parameters of a law for a distribution: is it the same? [closed]
I'm a beginner in statistics and I'm trying to figure things to ensure that I can consider parameters the same manner in two cases :
I believe that if we have enlighten a distribution with the ...
- 243
2
votes
0
answers
45
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Probability that interval arithmetic estimate of mean covers the true mean of a normal variable?
Background
Suppose there exists a normal variable $X \sim \mathcal{N}(\mu, \sigma)$ where $\mu, \sigma$ are known. Also suppose that you only observe rounded instances $Y = \operatorname{round}(X, d)$ ...
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3
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3
answers
375
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We're estimating mean, variance, proportion or compare samples with them. I understand for mean and variance. But why is it required for proportions?
I have learned how to estimate a mean, variance or proportion from a sample.
and also, how to compare those for samples.
I'm understanding well why we might need to estimate or compare means or ...
- 243
2
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0
answers
150
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Symmetric distribution with defined mean: is the median always unbiased for the mean?
Let $X_1,\cdots,X_n\overset{iid}{\sim} F_X(x)$ be a random sample from a symmetric distribution with a defined mean. If need be, assume that $n$ is odd and that $F_X(x)$ is continuous.
Is it always ...
- 67.1k
3
votes
1
answer
3k
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Different Ways to Calculate the Pooled Means
I have the following question about the properties of individual means vs. pooled means. To illustrate my example, I will use the R programming language.
Suppose we have measurements from two ...
2
votes
0
answers
177
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covariance estimate for the means of two unpaired dependent samples
I have two dependent samples $\mathbf{X}$ and $\mathbf{Y}$ of $s$ and $t$ observations, respectively, that is $$
\mathbf{X} = \{X_1, \dots, X_s\} \;, \\
\mathbf{Y} = \{Y_1, \dots, Y_t\} \;.
$$
For ...
1
vote
1
answer
812
views
Can you take the Expected Value of a Kernel Density Estimates?
I was looking at the formula for the Kernel Density Estimator:
I have always considered the main purpose of the Kernel Density Estimator to provide an estimate of the density at some point "x&...
29
votes
8
answers
5k
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Why are hypothesis tests still used when we have the bootstrap and central limit theorem?
Why are hypothesis tests still used when we have the bootstrap and central limit theorem?
To give context to my question, I briefly go over the central limit theorem and illustrate a simulation ...
8
votes
2
answers
6k
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Estimating the Population Mean with the Sample Mean
I am trying to better understand how the sample mean can be used to estimate the population mean. Using the R language, suppose I have the following population:
...
1
vote
1
answer
612
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How does Michaud Resampling improve Mean-Variance Optimization?
Michaud Resampling claims to reduce estimation error through the following process:
Step 1. Sample a mean vector and covariance matrix of returns from distribution of both
centered at the original (...
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0
votes
0
answers
20
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Estimation of coefficients of variables x when the sum of the x is equal to y
I'm a new beginner in learning statistics, and I have an issue with the estimation of coefficients.
To begin with, let's suppose I have 3 observations and 4 explanatory variables:
First observation: y=...
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1
vote
0
answers
69
views
number of samples required to estimate mean
I have a dataset consisting of number of times an individual pauses when speaking during a particular recording. I have several recordings per individual (around 10). I ultimately want a measure of ...
- 11
0
votes
1
answer
93
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Estimate a sum using proportional sampling
I have some set of items. Each item has a weight and I can sample the items from the population with probabilities proportional to their weights. I know the size of the population. I want to estimate ...
- 145
11
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3
answers
1k
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Randomly Sample M samples from N numbers with replacement, how to estimate N?
Can you estimate $N$ with MLE or method of moment or whatever strategy?
$N$ numbered balls are in a bag. $N$ is unknown.
Pick a ball uniformly at random, record its number, replace it, shuffle.
After ...
- 211
2
votes
1
answer
49
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Combining Estimates with Actual Values
I am exploring stature (living height), calculated from arm and leg bones, from an archaeological sample. Unfortunately, there are very few complete bones that can be measured and entered into the ...
- 141
2
votes
1
answer
135
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Why do the mean and proportion measurements take the spotlight in estimation?
Based on information I have read and from this website, sampling distributions do exist for statistic variants of measurements other than the mean. Sample ranges, maxima, minima, variance and ...
- 231
0
votes
0
answers
25
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Combination of different estimates of the same quantities?
Suppose we have $n$ number of estimates for a parameter, each derived independently. How will one combine these estimates to get a single estimate which has lower variance than each individual ...
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5
votes
2
answers
94
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What estimation method establishes sample mean and sample variance as estimators of mean and variance?
Sample mean and sample variance can be derived as MLE estimators for the mean and variance of a normal distribution.
For a distribution in general, what kind of estimation method leads to sample ...
- 19.8k
1
vote
2
answers
58
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More robust measure than Mean
I am currently dealing with data with many outliers and I shall not to eliminate them from the data for analytical purposes. What measure shall I use to describe central tendency of the data yet with ...
R_10
1
vote
0
answers
159
views
Estimating the mean from interval censored data
Say you had a sample of ages from a population, but the ages are in buckets...Such as <1, 1-4, 5-14, 15-24, ..., 55-64, 65+...And you want to get an estimate for the average of the age distribution ...
1
vote
0
answers
652
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Finding Average Wait Time From Number of People Waiting
Problem:
We are trying to estimate the average wait time for a process. Only data we have is how many people are in the system at a given time, how many have entered this period, how many exited this ...
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1
vote
1
answer
85
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Standard error of the $n^n$ bootstrap means
I need to show that the standard error of the $n^n$ bootstrap means is $SE^*(\bar{Y^*}) = \frac{S\sqrt{n-1}}{n}$, where $\bar{Y^*}$ is the sample mean of a randomly drawn bootstrap sample, and $S^2 = \...
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1
vote
1
answer
50
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How to modify the mean?
I have data collected in consecutive time periods using two sensors (i.e. sensor1 and sensor2) as follows.
...
- 602
1
vote
1
answer
109
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Estimate mean of a population with multiple samples when the individual sample mean is biased
I am working with datasets of grades going ~15 years back for different classes. I am trying to determine if there is a difference in the average grade for odd years compared to even years. There is a ...
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8
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3
answers
110
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Name of mean- or median-like values?
Consider the data points $x_i \in \mathbb R$ for $i=1,\ldots,n$ as well as following definition:
$$\hat x_c := \underset{{r\in \mathbb R}}{\operatorname{argmin}}\sum_i \vert r - x_i \vert^c $$
This ...
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0
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0
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64
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Mean and variance of the median estimator [duplicate]
We are given an i.i.d sample of size n, $X_{1},...,X_{2}$.
We also know that for all i, $EX_{i}=\mu,Var{X_{i}}=\sigma^{2}$.
Let us define $\hat{X}_{median}$ as the median of these samples:
$\hat{X}...
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2
votes
1
answer
79
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Finding a UMVU estimator for the mean
I am struggling with the following problem.
We are given an i.i.d sample of size $n,$ with the form $X_{i}=\mu+n_{i}$, where $\mu$ is a deterministic unknown constant, and $n_{i}$ is a noise with a ...
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0
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0
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21
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Comparing population averages while accounting for changes in composition
I have two populations (i.e., men / women) with different average measurements (let's say height). I observe the combined average of their height decreases. I also observe the proportion of women ...
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3
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1
answer
215
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Finding mode using mean and skewness (and higher moments)?
I have a pdf that doesn't yield trivial derivatives, so I cannot differentiate it and find the root to determine where its max exactly occurs.
However, I have a general formula to express all its ...
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4
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1
answer
1k
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Estimation of mean of AR(1) process
It is well known that for the basic AR(1) model $X_k=\phi X_{k-1}+\varepsilon_k$ where $\vert\phi\vert<1$ and $\varepsilon\propto\mathrm{WN}(0,\sigma^2)$ the sample mean $\bar{X}_n$ (after being ...
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1
vote
0
answers
43
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sampling: question about variance estimation
I'm new in this field, I'm studying montecarlo methods for sampling; I understand that,with a basic approach, we have an estimation for the mean
$$\hat{\mu}=\frac{1}{n}\sum f(x)$$
and for variance
$$\...
- 747
3
votes
1
answer
1k
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Estimating with the geometric mean
I heard about an interesting technique for making ballpark guesses:
If you need a variable that you have no idea about (like the average number of pianos per household), you can try to come up with ...
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0
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1
answer
28
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Estimating the mean when a few points in either tail are grouped into <a or >b?
I have a data set with approximately 150 observations. The data is measured to the nearest tenth. However, a few points on the left are measured as <50 and one on the right as >650. What is the ...
2
votes
4
answers
14k
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Is the mean of a specific sample of the population an unbiased estimator of the mean of the overall population?
I'm just at the beginning of learning this stuff. I learnt that we can obtain what is called the 'expected mean' of the sample, which is basically the mean that we'd expect to get if we sampled the ...
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1
vote
1
answer
323
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Average of noisy samples
I am not a statistician so I hope my question is not trivial. I have a set of $n$ samples affected by Gaussian noise with mean 0. I need to estimate the average of the samples, without the noise. Is ...
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1
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2
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755
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Stein's identity with Normal random variable
I'm having trouble to understand the Stein's identity in Theory of point estimation
Let $X$ a random variable with density in canonical form given by
$$p(x|\eta)=\exp\Big(\sum \eta_iT_i(x)-A(\...
user72621
9
votes
2
answers
4k
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Choosing the number of bootstrap resamples
Say we have the following sample and we are trying to estimate the variance of the sample mean of the population.
X = [0, -1, 2, 10, -3]
If I take an increasing ...
- 4,598
0
votes
1
answer
385
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Mean of Sum vs Sum of Means with Maximum Likelihood estimation
The sum of the means of two normally distributed random variables is the same as taking the mean of the sum of the two signals.
Does this hold true for maximum likelihood estimation?
Is summing the ...
- 101
1
vote
1
answer
95
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Estimating percent change on average
Suppose I want to estimate the percent change of something over a fixed amount of time. I have some values of before and after, so I can either choose to get the average of the "before" values and ...
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1
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0
answers
89
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Estimating subgroup standard deviation from mean but unknown cases
I have a set of unknown values, say 100 cases, with a mean of 10 and a standard deviation of 5. I know that a subgroup of 20 of the cases has a mean of 8 and a SD of 6.
How can I find the SD of the ...
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9
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3
answers
3k
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Estimate of parameter of exponential distribution with binned data
I have the following data, which can be modeled by exponential distribution
...
- 1,452
6
votes
1
answer
5k
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Is the sample mean a better point estimate of the population median than the sample median?
A beginner's question to check I've understood correctly. A basic stats textbook says:
"The variance of the sampling distribution of the median is greater than that of the sampling distribution of ...
- 1,975
0
votes
1
answer
575
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Method For Calculating Performance from Average Scores
In a simplification of my problem, let's assume we have players who can get an integer value score $s$ considering $\{ s \in \mathbb{N} : 0 \leq s \leq 3 \}$.
Same sample data for scores:
Player A: ...
- 103
1
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0
answers
3k
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Proof of why sample mean is best estimator for population mean
I am learning about the idea of estimators in statistics and understand that the role of an estimator is to estimate a parameter of the population distribution. In my book it says that the estimation ...
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