# Questions tagged [estimation]

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828 views

### Estimation of ARMA: state space vs. alternatives

I am interested in estimation of ARMA models. I understand that a popular approach is to write the model down in the state space form and then maximize the likelihood of the model using some ...
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315 views

### Validity of confidence interval for $\rho$ when $X\sim N_3(0,\Sigma)$ with $\Sigma_{ij}=\rho^{|i-j|}$

Suppose $X\sim N_3(0,\Sigma)$, where $\Sigma=\begin{pmatrix}1&\rho&\rho^2\\\rho&1&\rho\\\rho^2&\rho&1\end{pmatrix}$. On the basis of one observation $x=(x_1,x_2,x_3)'$, I have ...
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103 views

### Rationale behind Good–Turing frequency estimation?

Good–Turing frequency estimation is a smoothing estimator for estimating a multinomial distribution. It seems very convoluted. From mathematical statistics point of view, what is the rationale ...
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241 views

### asymptotic unbiasedness of weibull mle

It's known that the MLEs of the two-parameter Weibull distribution scale and shape parameters are not available in a closed form. It is, however, known that they do exist, are unique, and moreover, ...
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866 views

### Gauss-Newton method for MA parameter estimation

Please check my solution below for estimating Moving Average parameter using the Gauss-Newton (Linearization) method. I consider MA(1). MA(1) model: $$z_t=a_t-\theta_1a_{t-1}.$$ Solution: The ...
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1k views

### Sampling distribution of average of some covariance matrices

I have $K$ datasets, each with $N$ variables and $M$ samples (they are in fact EEG time series, but I discard time and treat them as $K$ iid multivariate samples) and assume they are coming from the ...
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913 views

### Why would I use ratio estimation instead of regression estimation to estimate means?

I am taking a graduate course on survey data analysis. I was recently introduced to ratio estimation and regression estimation. I understand that using ratio estimator may be easier if we are ...
0answers
1k views

### Methods of Proving that a UMVUE does not exist?

Are there efficient methods of showing when a UMVUE does not exist? I can think of the trivial case when no unbiased estimators exist at all. But that's not really interesting. I feel like this ...
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180 views

### bias of an estimator when using stopping rules

Consider the setting where $X_1,X_2,...$ are i.i.d. real-valued random variables with $\mathbb{E}[X_i] = \theta$ and let the random variable $\tau$ be an associated stopping time. I'm wondering what ...
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172 views

### Estimating population size, minimum variance estimators

I am trying to understand what can be proved about minimum variance estimators. I am a little confused by Cramér–Rao and how to apply it even to really simple examples or if it's even the right tool ...
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181 views

### Time series modeling the number of users of a mobile app

I want to model the number of users of an mobile app. This app has two kinds of users: free and paid. I thought of this autoregressive model: $x_t = Ax_{t-1}$ with $x_t$ being a 4-dimensional vector,...
1answer
331 views

### Expression for the median of a sum of half-Cauchy random variables

This is a technical problem I encountered in research. Sorry if it reads simple for professional statisticians. Let $X_1, \cdots, X_n$ be iid standard Cauchy random variables. What estimate or exact ...
1answer
640 views

### Error in estimation with continuous data

Is there a way to correlate error in a fit (MSD - mean squared displacement) to the error of the a calculation performed with the parameters associated with the fit? My specific problem is dealing ...
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196 views

### Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$

Question: Let $X_1,X_2,\dots,X_n$ be random sample from Poisson($\theta$). Find MVUE of $e^{-2\theta}$ My attempt has been by modifying the answer from this question: The Poisson distribution is a one-...
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384 views

### Probability with an unbalanced coin where consecutive flips are not independent

Thanks in advance for the help. Suppose someone has an unbalanced coin that they flip 100,000 or so times in a row. This person then gives you the results. You do not know the probability of ...
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664 views

### Implementing ARMA Log Likelihood with the Kalman Filter Algorithm

A popular algorithm to determine the (complex) log likelihood function of an ARMA(p,q) process involves generating it through the use of a state-space model and the Kalman Filter. I started reading ...
1answer
277 views

### Are there better estimators of misclassification error than the fraction of misclassified test points?

Assume we train a binary classification model using the training set. Also assume that the model returns an estimate of the probability of success $\hat f(x)$ for every feature vector $x$ and was ...
1answer
316 views

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2k views

### Why would concatenating feature vectors lead to better estimates?

I wish to estimate the state of a system from two separate and disparate observations. A simple approach that I have seen in some literature is to combine the feature vectors (observations) by simply ...
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59 views

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367 views

### Why are the prediction error estimate and the true prediction error negatively correlated?

Section 12.2 of Computer Age Statistical Inference reports simulation results that indicate that the cross-validated estimate of the prediction error for a given prediction rule is negatively ...
1answer
41 views

### What is Generative Training?

I know that the difference between generative and discriminative classifiers is that the generative ones directly model the distribution of the observed data while the discriminative ones do not. ...
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90 views

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221 views

### Comparing the performance of two classifiers using cross-validation

Consider the following excerpt (paraphrased, see sec. 4.6.3 for original wording) from Introduction to Data Mining (free chapter) by Pang-Ning Tan, Michael Steinbach, and Vipin Kumar. Suppose we ...
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512 views

### Delta Method vs. Lognormal

I have a single parameter $\theta > 0$ of a probability model I estimate with MLE on i.i.d. data. To get rid of the positivity constraint I instead estimate $\log \theta$ for which MLE gives me an ...
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164 views

### Estimation of sample mean for hypergeometric distribution under a constraint

Assume that we have a dataset $D$ that contains the age of N people: $X_1, \dots , X_N$. We draw a sample $S$ of size $n$ using sampling without replacement ($Y_1, ... , Y_n$). In order to estimate ...
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289 views

### Unbiased Estimator of the truncation points in a truncated normal distribution?

Consider the variables $x_i \text{~} \mathcal{N}(\mu, \sigma^2,a,b)$ iid with truncation points $a$ and $b$, i.e. $a < x_i < b$. Suppose all 4 parameters, namely $\mu, \sigma, a, b$ are all ...
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444 views

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### Calculating a Constrained Mean

Assume that I have ten measurements of a physical quantity that must be non-negative (e.g., mass). Because of measurement error, some of the results are nevertheless negative. Can someone suggest a ...