Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.

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7 views

How much weight should be given to sample mean as an estimate of the population mean?

This R code creates a population of size 10,000 with a population mean of 3 and a population standard deviation of 2: population <- rnorm(10000, 3, 2) We can ...
3
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1answer
38 views

Is my work correct (easy problem, confidence intervals)

The r.v. $X$ represents the time taken by a computer in company $1$ in order to perform a certain job, and $Y$ represents the same thing but for company $2$. A sample of $n_X = 12$ computers are taken ...
2
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2answers
51 views

The role of validation in estimation and hypothesis testing

Validation, with or without statistical/machine learning procedures, is used often, if not universally, in prediction. In estimation or hypothesis testing that does not seem to be the case, yet I ...
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0answers
9 views

How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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4 views

Minimum Covariance Determinant (MCD) vs DCC GARCH

I've been reading about various covariance estimation techniques in an attempt to understand which one has performed the best. In this paper, the authors conclude that DCC GARCH outperforms most ...
2
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1answer
25 views

Meaning of large values of parameter b (|b| >>) 4 in IRT theory

I'm working with a set of data from a 100 itens, 5 alternatives, medicine test and analyzing them by means of IRT (. The IRT - 3 parameter model yielded some values of b that are very large (...
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0answers
16 views

Improving estimates of linear system regression when parameters are unevenly weighted

I have a system with a linear model $ax + by = c$. I can adjust $a,b$, measure $c$ (with some error in the measurement) and then use linear regression to estimate $x,y$. The problem I'm running into ...
2
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2answers
66 views

Why is MCMC needed when estimating a parameter using MAP

Given the formula for MAP estimation of a parameter Why is a MCMC (or similar) approach needed, couldn't I just take the derivative, set it to zero and then solve for the parameter?
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22 views

How to estimate parameter k in hyperbolic discounting equation using maximum likelihood?

I've been learning and trying to estimate parameters using maximum likelihood, and I'm trying to understand the hyperbolic discounting equation. Here's the equation for hyperbolic discounting: $$y = ...
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0answers
9 views

Autocovariance Estimation and Stationary Processes

I am going to work on a project involving time series and therefore I am trying to understand some basic definitions. I am currently trying to grasp the autocovariance estimation procedure. When we ...
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1answer
16 views

Estimating Poisson-distributed rate using sampling

You have been hired by the border patrol agency of a nation to estimate the number of people who enter into the country by circumventing the fence during their busiest season. You have reason to ...
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19 views

Finite population correction, where does the square root come from?

The correction factor for finite populations is $\sqrt{1-\frac{n}{N}}$ (for known variance) where $n$ is the sample size and $N$ is the population size. I wonder where the square root comes from. ...
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1answer
21 views

dangers of averaging between model approaches

I am working with some ridership data that is broken down by route, year and month. I have built and tested a whole bunch of models ranging from GLM, GEE, GENLIM, and Panel and ARIMA data models. I ...
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2answers
42 views

How can I estimate the sliding window standard deviation of a stream?

I am processing a stream of database records. At current levels, about 250 million records are added per week, but this will increase. I wish to compute the 90-day sliding window standard deviation of ...
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0answers
28 views

How to estimate parameters for each observation using MLE

Given a sample of variables $x_i$, which are each a function of the known variables $y_i,b_i$ and an unknown parameter $\alpha_i$ $$x_i=y_ib_i-y_i^{\alpha_i}$$ I thought I might solve for the ...
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7 views

Estimate parameters of transformed AR1 process

I have a process, $W_t$, which follows an AR1 process, where the error $\epsilon_t\sim N(0,\sigma)$: $W_t = \rho W_{t-1} + (1-\rho) \bar{W} + \epsilon_t$ However, I don't have $W_t$, whereas I do ...
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48 views

How to estimate mean and variance of censored normal?

Supposing I have data which I know is normally distributed, but because the recording process is right censored, how do I estimate the parameters of the distribution?
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22 views

Find a scaling transform of a function

Let us consider some function $f(x)$ (that is similar to sum of many separate gaussian peaks) and a function $F(x)=Cf(s(x)) + b(x)$. We know the values of $f(x)$ at points ${x_i}, (i=1,...,N)$ and ...
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0answers
39 views

Identifiability in Parameter Estimation Problem

I have a question regarding the identifiability of parameters. I know that if $f(y;\theta)=f(y;\theta')$ then $\theta = \theta'$, otherwise it would be impossible to estimate $\theta$. However, ...
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4 views

Weighting Factor Calculation - what is the best approach?

I have a set of figures that I need to apply a multiplicative weighting factor to. I have 2 tables, I need to apply the weighting factor to the final table 3. Table 1: E.G "CT1 buys 5 shoes" ...
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0answers
23 views

ARIMA-GARCH Parameter Estimation

I fitted an ARIMA Model on a time series and then did an ARCH-LM Test which shows heteroscedasticity. So i want to get an ARIMA-GARCH Model. My question: Do i need to reestimate the parameters of ...
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58 views

Estimating model's parameters from repeated measurement of a process, concept and application in R

I've asked a similar question here. A process is observed on various days, where each observation is a time series. for example the above figure shows 5 of these observations. My goal is to perform ...
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1answer
47 views

Interpretation Maximum Likelihood Plot

When using the likelihood method, plotting the relative likelihood or evidence against the range of possible values for the parameter ($\theta$) being estimated results in a curve. The maximum value ...
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0answers
15 views

What is the fixed design parameter estimated by $R^2$?

A previous question asks which is the paramater estimated by $R^2$ in the random design. What would be the equivalent for a fixed design? I.e.- what is the population quantity estimated by $R^2$ in a ...
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0answers
35 views

95% confidence interval for an estimate average

I have a single dataset - from that dataset I have used four methods ($i=1, 2, 3, 4$) to estimate a parameter ($u_i$) and to generate a 95% confidence interval. In other words, I know $V[u_i]$ but not ...
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1answer
49 views

What is estimated by $R^2$? [duplicate]

The coefficient of determination, $R^2$, is an empirical quantity. What population quantity does it estimate and are there other estimators for this quantity? I am particularly interested in the fixed ...
2
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1answer
61 views

Why are coefficients estimates more accurate when using a hierarchical model?

I am reading a paper and I do not understand a bit: "We use a hierarchical model such that all slopes are calculated within the same model and the intercepts and slope components are normally ...
3
votes
1answer
94 views

What's the maximum expectation of a conditional variance, $E[Var(X+Z_1 \mid X+Z_2)]$?

Let $X,Z_1,Z_2$ be 3 mutually independent RV's, with $Z_1, Z_2$ assuming $N(0,1)$ distribution. $X$ is constrained to have unit 2nd moment, i.e. $E[X^2] =1$, but may take arbitrary distribution. The ...
2
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0answers
115 views

Estimation on evolving distribution with small updates

I have a set $X$ of $10^6$ elements and a time series of probability distributions $\mu_1,\mu_2,\ldots$ on $X$. I want to estimate the expected value of a function $f$ over each $\mu_t$. It is easy to ...
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0answers
45 views

How can one estimate the number of illegal aliens in the US?

My question, I guess, is really two-fold: #1: What kind of data would a statistician look at, and #2: From that data, how would they extract an estimate of the number of illegal aliens? Estimates of ...
3
votes
1answer
54 views

Shrinkage of the Sample Covariance matrix

Assume we have N independent and identically distributed random vectors $X_1, X_2, ..., X_N$ where each of them is of size p $\times$ 1. The sample covariance matrix, denoted here by $S$, is computed ...
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1answer
45 views

On estimating ARIMA models on artificially made time series data

For each day, I observe my variable, y(t), for a period of 12 hours. In order to understand the data and make predictions, I want to put together these data and ...
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0answers
11 views

Covariance matrix of estimated parameters of SVAR

How to get covariance matrix of estimated parameters of structural VAR? Any reference, if possible. Thank you in advance.
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0answers
36 views

Why no MAX models?

I'm diving into the field of system identification, black box modeling and forecasting. A lot still has to become clear to me, but one question that came to my mind (and to which the answer might ...
0
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0answers
10 views

why are these uplift estimates different?

I recently stumbled upon an ODSC presentation: Machine Learning Based Personalization Using Uplift Analytics: Examples and Applications Uplift wherein two methods for "uplift" estimation are provided: ...
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1answer
42 views

Estimating population variance through simulation in R

I want to estimate the variance of the exponential distribution with a rate of $\lambda=0.2$. I'm drawing a sample of 5 exponentials 1000 times, and know that the theoretical variance of my ...
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2answers
42 views

How can maximum likelihood be used to estimate parameters for a Weibull distribution? [duplicate]

Consider the following survival data (cumulative): Month 0 - 100% Month 1 - 50% Month 2 - 33% Month 3 - 25% Month 4 - 20% (meaning 20% of all initial units have survived by the end of Month 4) ...
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1answer
47 views

Maximum likelihood estimation for Cauchy noise

What is the maximum likelihood estimator of the covariance matrix for a given vector in the presence of Cauchy noise? How can we calculate it given that the Cauchy distribution has infinite variance? ...
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0answers
27 views

Estimation of variance: How to bring Bessel's correction together with degrees of freedom?

I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given: ...
0
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1answer
43 views

Variance of the $\hat{\sigma^2}$ of a Maximum Likelihood estimator

Given some normally distributed observations $x_1,x_2,...,x_n$ $\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$ the ML estimator decides that the variance that maximizes the likelihood function is ...
2
votes
2answers
63 views

How to predict property value using lat/lon?

I have lat/lon and property values for households in a particular region. Format: Lat Lon value 32.2 -98.22 120000 .... Now I have new data of the ...
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1answer
22 views

Covariance Estimation for cauchy noise

Apart from Ledoit wolf shrinkage technique which can be better shrinkage covariance estimators for data with cauchy distribution? How to calculate optimum shrinkage intensity for data containing ...
5
votes
2answers
243 views

Just “take the average” they say. It's not that straightforward, right?

I have an acquaintance who does not study statistics and doesn't understand that summing data and dividing by the number of data is a summary statistic, i.e. that information is lost. For example, ...
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0answers
10 views

Finding a joint distribution of a large dimension

This is a rather soft question. I have data samples that are definitely pairwise correlated, and possibly correlated in higher order. It is of dimension $50$, and I am looking to describe it via some ...
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0answers
23 views

ARIMA Fitting: CSS vs CSS log likelihood

Can someone explain to me: in estimating the parameters for an ARIMA model, what is the advantage of optimizing the CSS log likelihood(pg 2), versus optimizing CSS (pg 3)? Are there any ...
6
votes
1answer
164 views

Fastest way to solve Bayes estimator problem

The below problem is from an old PhD qualifying exam in our department. My own solution below is time-consuming and quite possibly wrong. It also relies on recognizing a less common distribution, so I ...
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0answers
10 views

Correct formula for unbiased estimate of population covariance [duplicate]

Is this formula a correct way to estimate population covariance from a sample? $$s_{xy} = \frac{1}{n-1}\sum\limits_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})$$
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0answers
14 views

multiple, related, time-series applied to Statistical Process Control

I tried looking online (google), searching in stack-overflow and cross-validated, and just looking through "R" documentation for the answer, but either I am not seeing it, or I don't know how to tell ...
3
votes
1answer
40 views

How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper

I'm reading through Fan and Li's paper "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties". In Page 2 near bottom right corner, they proposed three properties that a ...
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20 views

Capture recapture model validation

In the absence of an actual population to test on, what are the best practices for validating capture recapture models?