# Tagged Questions

Point estimation is the application of an estimator to the data in order to learn about a certain population parameter.

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### Rao-Blackwellization of Gibbs Sampler

I am currently estimating a stochastic volatility model with Markov Chain Monte Carlo methods. Thereby, I am implementing Gibbs and Metropolis sampling methods.Assuming I take the mean of the ...
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### Are there examples of non exponential family distributions with sufficient statistics?

In Casella Berger's Statistical Inference, they observe that it is rare to find 'a sufficient statistic with dimension smaller than the sample' (section 6.2.1). Although rare, are there examples of ...
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### How best to summarize a predictive discrete distribution in a single number?

I have generated a predictive distribution for a future discrete observable outcome, and would like to generate a single value $p$ which we would most likely encounter when we perform the experiment ...
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### How to define a study area for RIpley's L analysis?

I have a spatial point pattern which spans across multiple districts in the country. Now I want to examine its pattern using Ripley's L function. I know that Ripley's L function is used for ...
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### Find point estimate, bias and variance

I am kind of new to Statistics and I stuck at this question. Lets say in a consumer survey, 250 people out of a representative sample of 450 people say that they prefer product A to product B. Let p ...
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### Does Cramer-Rao Inequality needs the parameter space to be an open subset of the real line?

I came across a lecture on Cramer-Rao lower bounds for an unbiased estimator and the visiting professor remarked that for CR inequality to be valid one of the regularity conditions we need is that the ...
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### What is λ in the context of Spatial Point Statistics?

What is a small lambda λ in the context of spatial point statistics and how do I calculate it for a given set of point? Specifically I am trying to calculate it for different sets of observations of ...
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### Practical situation in which the posterior mean is prefered to the MAP

Sometimes experts for which we design models are interested in having a point estimate and in practical situations, they always say me "give us the most probable parameter value". And whether the ...
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### Estimating accurately the mean of an autocorrelated bounded integer time series

I have a bounded integer time series $X_{1:\infty}$ ($1\leq X_k\leq M$), and I want to estimate the mean $$s = \lim_{L\to\infty} \frac{1}{L}\sum_{k=1}^L X_k.$$ I'm assuming it exists and that $X_k$ ...
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### Cramér-Rao Lower Bound for Exponential Families

I am having a problem with applying the Cramér-Rao inequality to identify the lower bound for the variance of an unbiased estimator and hoped that you guys could help me. The problem is the following: ...
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### Point configuration given distribution of distances

Does anybody know if there is a method/algorithm to find coordinates for $N$ points, given a probability density function from which the $N(N-1)/2$ different pairwise distances between them can be ...
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### Limits of integration of Pitman Estimator for Laplace (Double exponential) distribution

I am struggling, in general and specifically, with trying to determine the limits of integration for the Pitman Estimator to find a Minimum Risk Equivariant (MRE) estimator of a location parameter ...
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### Is p-value a point estimate?

Since one can calculate confidence intervals for p-values and since the opposite of interval estimation is point estimation: Is p-value a point estimate?
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### Shrunken $r$ vs unbiased $r$: estimators of $\rho$

There has been some confusion in my head about two types of estimators of the population value of Pearson correlation coefficient. A. Fisher (1915) showed that for bivariate normal population ...
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### Cramer-Rao bound for $\chi^2$ distribution parameter estimates

I've struck an unpleasant problem with the noncentral $\chi^2$ distribution. I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ ...
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### Biased but consistent estimator for the mean of Gaussian distribution?

$(X_1,X_2,\ldots,X_n)$ is a random sample from $\mathrm{N}(θ, 1)$. We know sample mean is a unbiased estimator that is consistent. What would be a biased but consistent estimator for θ? Would it be ...
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### Comparing two estimators for accuracy using empirical bootstrap

I am trying to figure out the proper way to compare the quality of two estimators of a parameter based on data. The basic approach I've taken is to compute the MSE of the empirical bootstrap ...
Suppose I want to make inference on a parameter vector $\theta$=$(\theta_{1},\theta_{2},\theta_{3})$ and I have some missing data $Y_{mis}$. I would like to use the EM algorithm to find the mode of ...
### Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$
The more detailed question. I'm kinda having some trouble starting out with answering this question. My initial approach would be to $g(x)= x^2$ since that is a convex function and find the ...