All Questions
Tagged with computational-statistics estimation
16 questions
2
votes
0
answers
46
views
An estimation method/algorithm for estimating the value of a specific parameter in a convex function
I am looking for an estimation/iteration process to estimate the value of a specific unobserved parameter of a convex function that fits the observed data of the other variables closely. Specifically, ...
- 21
3
votes
2
answers
227
views
Orthonormalization to use closed form Lasso solution
Given the Lasso problem
$$
min_\beta (Y-X\beta)^\top(Y-X\beta) \quad s.t. \|\beta\|_1\leq\lambda,
$$
and assuming that X is orthonormal such that $X^\top X=I$, we know that the closed form solution ...
0
votes
0
answers
66
views
complexity of empirical estimator
Assume we have i.i.d. data $x_{1}, \dots, x_{n}$ from discrete distribution.
Then, let's us consider empirical estimator:
$$
\hat{p}_{i} = \frac{ \sum_{j=1}^{n}1(x_{j}=i)}{n}
$$
What is the ...
- 668
4
votes
0
answers
199
views
Dynamic panel data model with AR(2) process in the errors
I set up the following dynamic panel data model:
$$y_{it}=\alpha y_{it-1}+x_{it}^T\beta+v_{it}$$
Additionally, I have the process in the errors:
$$v_{it}=\rho_1u_{it-1}+\rho_2u_{it-2}+\epsilon_{it}$$
...
- 141
2
votes
0
answers
95
views
Tuning density in Gelfand-Dey estimator (Reciprocal Importance Sampling) of Marginal Likelihood
If y denotes the data and (t,L) denotes set of parameters, then the marginal likelihood is
Here, is a proper prior, f(y|t,L) denotes the (conditional) likelihood, m(y) is used to denote the marginal ...
- 63
4
votes
1
answer
2k
views
What are the general methods for parameter estimation in statistics?
I have a task to estimate the probability of evolution selection of a given node.
The only parameter estimation method I can think of is using the law of large numbers, i.e., use the proportion to ...
- 489
2
votes
0
answers
74
views
Is there any alternative to the EM algorithm? [duplicate]
I am working on biomedical signal analysis and the most used method for parameters estimation is the EM algorithm.
My question is : what are the most powerful alternatives to this algorithm?
- 141
0
votes
1
answer
75
views
A Simple Regression Model for Our Experiment? [closed]
We know, In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a ...
0
votes
1
answer
115
views
uniform distribution with density function? [closed]
If $0.3,0.2,0.8,0.3,0.4$ are found from one random instance with uniform distribution with following density function, We need to find $\theta $ estimate with Method of moments. how should we do this?...
- 11
7
votes
2
answers
2k
views
Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-built estimator when software runs out of memory
Is there a way to speed up $Z(Z'Z)^{-1}Z'$ type matrices? I am implementing the expression below directly using a matrix language and my program frequently crashes while if I run OLS on them using a ...
- 1,007
6
votes
1
answer
193
views
Estimate mean & standard deviation of set S if I know stats of an inner set and outer set
Suppose I have sets $S_1\subset S_2\subset S_3$. I know exactly the size, mean, and standard deviation of both $S_1$ and $S_3$ and want to estimate the mean and standard deviation of $S_2$, where I ...
- 71
3
votes
0
answers
297
views
Tricks for a very fast implementation of Random Forest
I am implementing my own Random (regression) Forest algorithm and am looking for tricks to speed up the estimation of forests on large datasets.
So far I have implemented three main tricks:
1) Use a ...
- 2,286
8
votes
1
answer
5k
views
How to split nodes in regression trees
I am looking for a comparison of different regression tree node splitting approaches within the random forest framework. I am looking at the trade-off between ensemble accuracy/reliability (holding ...
- 2,286
2
votes
2
answers
2k
views
EM algorithms - confidence interval estimation
Does anybody know how to find the confidence intervals for estimated parameters of a mixture of Gaussians by using EM algorithm?
- 21
2
votes
1
answer
130
views
Is there a qualitatively useful statistic or approach to an ill-behaving sample average?
I was running some timing simulations on a computer. As is often done with low latency things like this, I was running the relevant block in a loop $k$ times and then recording the total time over $k$ ...
- 1,003
5
votes
1
answer
247
views
Bayesian analysis of data
I have a big dataset in the form: $X_1, X_2, X_3, X_4, Y$. All the $X_i, i \in {1,...,4}$ come from different unknown distributions and $Y$ follows a bernoulli distribution, so it can take only values ...
- 405