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Questions tagged [efficiency]

A measure of the quality of a statistical estimator.

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24 views

FGLS vs OLS tradeoff

Hi, Can someone tell me what is the tradeoff between using OLS and FGLS? I know the conditions under which FGLS is more efficient than OLS. But what about robustness? It is usually said that the ...
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14 views

Does C-efficiency exist? If so, how is it defined?

When using an algorithm to construct an optimal experimental design one has a measurement of optimality to find an optimal design with this optimality-criterion. For any arbitrary chosen design a D- ...
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1answer
81 views

What may be an inefficient estimator of the population mean?

If the sample mean is an efficient estimator of the population mean, what may be an example of an inefficient such estimator?
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72 views

What is the difference between BLUE and MVUE?

What is the difference between a Best Linear Unbiased Estimator (BLUE) and a Minimum Variance Unbiased Estimator (MVUE)? I know that "best" mean efficient, but that is also what "minimum variance" ...
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26 views

Forecast efficiency: why no correlation between errors and available information?

(Applied Economic Forecasting using Time Series methods; Ghysels, Marcellino, 2018), in the chapter about forecast evaluation, relates efficiency as "the efficient use of the available information". ...
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19 views

Sterling vs Combustion Engines [closed]

This may be difficult to answer but, theoretically, if you had a car with a sterling engine that produces say approximately 300 horsepower how much of any specific heat source would need to be used if ...
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95 views

Minimum-variance unbiased estimator to estimate quantiles when the errors are normal distributed

What is the minimum-variance unbiased estimator to estimate quantiles when the errors are normal distributed? median When we wish to estimate the median, $\mu$, of a normal distributed variable then ...
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1answer
45 views

QR decomposition computational efficiency

I am struggling to find a reference for this: In terms of big Oh notation does anyone know of any expressions for the computational time taken by commonly used algorithms for QR decompositions?
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26 views

dummy variables and interaction terms: when the number of observations matters

Some authors conducted a univariate cross-section regression using 26 observations: $$Y_i = a + b \cdot X_i + e_i$$ Some others did the same regression and added another one where $X$ is split ...
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1answer
45 views

Speeding up in R [closed]

for(i in 1 : n){ y[i] <- length(X[X >= X[i]]) } This is my code in R (partially given) to obtain the number of X's greater than or equal to each Xi, where X is a vector of values. When I run ...
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56 views

Is this the only way to determine if a parameter can be estimated efficiently?

I am tasked with determining if a particular parameter can be estimated efficiently. Given that an efficient estimator is an unbiased estimator which achieves the Cramer-Rao lower-bound, is the only ...
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76 views

Using Mean Cumulative Function (Nelson-Aalen) to assess drug efficacy

I have a large medical retrospective longitudinal dataset of electronic health records. An individual is identified by an ID. A medical event or drug prescription event is identified using a code and ...
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1answer
40 views

How to control for severe medical cases using survival analysis and Cox regression?

I have a longitudinal medical record dataset. My cohort is made up of patients with a particular disease. There are no members of this cohort without this disease. Disease indications are denoted by a ...
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30 views

Proof that sequential GARCH fitting is not efficient?

I've read that authors like Tsay (as well as several other researchers) use a sequential method for fitting a ARCH-type model. This means first estimating the conditional mean model (ARMA-type) and ...
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1answer
190 views

Efficient Estimator from Insufficient Statistic

Suppose that I have a statistic $T(X)$, and I know for sure that it is not sufficient to estimate a parameter $\theta$. Is it still possible to have an estimator $\hat\theta(T(X))$ that is efficient (...
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41 views

Efficiency of Bayesian Estimator

In the Wikipedia article for Minimum Mean Square Error https://en.wikipedia.org/wiki/Minimum_mean_square_error the Bayesian estimator is referred as Asymptotically Efficient using the similar ...
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127 views

Is an inadmissible estimator necessarily dominated by some admissible estimator

Basic example: $X$ has a $p$-variate iid standard Normal distribution; the sample mean is not admissible if $p>2$ and is dominated by the Stein shrinkage estimator. However, the Stein shrinkage ...
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45 views

Proving First Difference is more efficient than OLS

I am trying to prove that the First Difference method is asymptotically more efficient than OLS when the error term follows a random walk. Assume the following model $$\begin{align}y_i&= \mathbf{...
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42 views

Compare efficiency of several linear combinations of random variables

I have the following linear combinations of (non-independent) random variables: $Y1=X1+X2$ and $Y2=X1+X2+X3$ With the following general formula, I can calculate the variance for combinations $Var(Y)=...
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1answer
303 views

Why does asymptotic efficiency require normality?

Greene (Econometric Analysis), states the defintiion of Asymptotic Efficiency. My question is, why does this definition contain a reference to normal distribution? We already know by the central ...
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1answer
127 views

Using parallel tempering, is it possible to swap too often?

In parallel tempering I have replicas of the Markov chain I'm studying evolving at different temperatures, and intermittently I swap the replicas on a nearest-neighbouring temperatures basis. Between ...
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1answer
126 views

Efficiency of the command pmvnorm in R

Let $X_1,\,X_2,\ldots,\,X_n$ be $n$ independent random variables, where $X_i\sim\text{N}(\mu_i,\,\sigma_i^2)$, for all $i\in\{1,\ldots,\,n\}$. Consider the $n$-dimensional random vector $$\boldsymbol{...
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1answer
125 views

Efficient estimator in OLS and statistical power in t-test

Could please anybody help me to understand the difference between those two concepts? I know that statistical power refers to $1-\beta$, the type II error and that efficiency of estimator is related ...
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4answers
5k views

How to speed up training of a Neural Network?

I'm writing a thesis where I developed a script that generates NN and precalculates weights and biases to reduce a required number of epochs when I train a network. In my work, using examples I ...
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154 views

Is it valid to calculate relative efficiency of the mean and median on data sampled from an asymmetric distribution?

Let the relative efficiency between two estimators $T_1$ and $T_2$ of a parameter $\theta$ be defined as: $$e(T_1,T_2) = \frac{E[(T_2-\theta)^2]}{E[(T_1 - \theta)^2]}$$ This definition indicates ...
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1answer
526 views

efficiency of variance / standard deviation

Is there any literature on the efficiency/asymptotic efficiency of the variance estimators like sample variance? I can find enough analysis about efficiency of mean estimators but nothing on that of ...
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335 views

How general is the backfitting algorithm?

Hastie \& Tibshirani's original approach to fitting generalized additive models was the backfitting algorithm. For a model of the form $$ y = \alpha + \displaystyle\sum_k f_k(x_k) + \epsilon $$ ...
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62 views

Maximum Likelihood Efficiency

It is a well-known fact that ML estimates are not efficient in the class of consistent, asymptotically normal estimates due to the existence of superefficient estimates. The right way to put it is ...
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236 views

Is multiple imputation worth doing at all for data missing completely at random?

If data are missing completely at random (MCAR), then obviously multiple imputation (MI) won't serve its lauded function of lessening bias in your findings, since there's no bias to lessen. However, ...
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1answer
168 views

Multinomial logit model with alternative-independent coefficients

Having a multinomial logit model $U_{ij}=x'_{i}\theta_{j} + \epsilon_{ij}$ for 3 alternatives, I checked the efficiency of the estimators of this model through 1000 Monte-Carlo iterations, and ...
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197 views

Efficiency of the OLS estimator

I have this linear regression: $y_{i}=\beta_{0} + \beta_{1}x_{i} + u_{i}$ with $i=\{1..n\}$. Say $\hat{\beta}_{1}$ is the OLS estimator of $\beta_{1}$. $\hat{\beta}_{1}$ is BLUE since the Gauss ...
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0answers
49 views

Critera for “horse-racing” normally-distributed estimators?

I am seeking to compare how two estimators perform on a test set. These estimators are approximately normal -- they produce both point estimates and $\alpha$ intervals. One would like the point ...
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3answers
268 views

How to improve the efficiency of an estimator when the estimates significantly vary among subgroups?

In a clinical trial, patients enter the hospital (hence, the study) at different time points. We have observed that patients who respond to the primary therapy early survive longer than those who ...
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464 views

Mincer-Zarnowitz for model combination, how to construct?

Lets say we have two competing models to forecast something. We can test with the Mincer-Zarnowitz regression if model 1 is unbiased and encompessing all the information of model 2: $y_i = \beta_0 + ...
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1answer
315 views

Efficient estimator for the mean of a Gamma distribution

Let $X_1$,$X_2$,...,$X_n$ be i.i.d. according to Gamma($\alpha$,$\beta$). Denote the mean by $\mu := E[X_i] = \alpha/\beta$. Can you find an unbiased and efficient estimator for $\mu$? MLE gives ...
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91 views

Extra variable in regression model increases variance of parameter

Suppose my true Model is: $$y = Xb + u \tag 1$$ But I am estimating: $$y = Xb + Zd + u \tag 2$$ I can get the estimate of $b$ from $(2)$ by using $Mz$ operator as: $$\hat{b} = (X'MzX)^{-1}(...
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1answer
49 views

Mean estimation under known variance heterogeneity

We observe $X_1,\ldots,X_N$ and consider following model: $$ X_i = \theta + w_i\epsilon,\quad \epsilon \sim N(0, 1). $$ Based on above model, we want to estimate $\theta$ given $X_1,\ldots,X_N$ and $...
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1answer
860 views

D-efficiency in choice-based conjoint analysis

How to calculate the D-efficiency of experimental designs in conjoint analysis? Specifically, how do you specify the $X$ and the number of $nBetas$ in this formula: $$ D_e=\frac{|X'X|^{1/nBetas}}{...
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19 views

Test for informational efficiency

I need to compare one benchmark models regarding their "informational efficiency" against three other models. From my search I can now say, that this usually refers to the question how well a model is ...
4
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1answer
995 views

Restricted OLS have less variance than OLS?

According to Gauss-Markov Theorem, ordinary least squares (OLS) is the best linear unbiased estimator (BLUE). How then can restricted OLS have less variance? Please tell me the reason.
4
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1answer
387 views

Efficiency of GLS over OLS when regressors are not fixed

Suppose we have a regression model $$ y=X\beta+u,\quad E(u)=0,\quad E(uu')=\Sigma. $$ Let $\hat\beta$ and $\bar\beta$ respectively denote the OLS and GLS estimator. Then, when $X$ is fixed (or when $X$...
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1answer
402 views

Does the Hodges-Lehmann estimator perform better than trimmed/winsorized means?

I've been reading about the HL estimator, and a question came to mind. I could fairly easily create a mean-estimator where I trim or clip 29% of the data on either side and have a statistic with a ...
2
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1answer
379 views

Why the Covariance between efficient and inefficient estimator is equal to variance of the efficient one in Hausman test?

I tried to prove Hausman test for two estimators efficient and inefficient one. Then I encountered with the statement for variance of two estimators saying that: Covariance between the efficient ...
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0answers
327 views

Creating separate model for each level of a factor using caret in R

I have a large data frame in R with 51 variables/predictors one of which is a factor variable that represents the user (6 in my data) that those observations belong to and I want to predict type. <...
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1answer
638 views

Relative efficiency: mean deviation vs standard deviation

I have difficulties following a seemingly elementary claim from Tukey (1960): It is well known that, in large samples, the relative efficiency as a measure of scale of the mean deviation compared ...
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0answers
20 views

How does CoDi compares to the deep network?

I like the idea of CoDi model which uses a von Neumann neighborhood method which has four types of cells. How this models compares to the deep network in terms of efficiency? Are there any scenarios ...
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2k views

Estimator's Efficiency vs. Consistency

I know the definition of both (I think), but they seem so equal at the same time. Any clarification? I know that as the sample size goes to infinity; the estimator converges to the population ...
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1answer
3k views

OLS Regression : Efficiency of the estimator of the variance of the residuals under the assumption of normality

My question is probably already answered somewhere but I did not find it. In the standard linear regression model under the assumption that residuals are normally distributed, we have a result ...
3
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0answers
283 views

alternative to IQR [duplicate]

I am currently making a short literature study of robust and efficient estimators. Some very well known are the median absolute deviation (MAD) and the interquartile range (IQR). However they both ...
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3answers
823 views

The concept of efficiency

I have some problems in understanding the concept of efficiency as related to an estimator. My sources (Mukhopadhyay, 2000 and Casella, Berger, 2002) do not treat this argument as I expected since ...