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Show local asymptotic distribution of the Maximum Likelihood estimator

from a problem set I have the following exercise: Let $X_1, \ldots, X_n$ be iid with $X_1 \sim N(\theta, 1)$, where $\theta \geq 0$. The ML estimator of $\theta$ is $\hat{\theta}_n = \max (\bar{X}_n, ...
The Anon Learner's user avatar
1 vote
1 answer

fast distance metric between a new data entry and available clusters of data

Assume we divide a large data set D into m different partitions of data in a distributed learning case, using ...
Ham82's user avatar
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2 votes
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Implementation of time-varying coefficients model for Cox regression

I would like to implement the time-varying coefficients model (cf. Fan and Zhang, 1999) for a Cox proportional hazards model, as proposed by Cai and Sun (2003), and studied by Tian, Zucker and Wei (...
user36302's user avatar
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1 vote
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Validity of local auto-correlation in the presence of global auto-correlation

I'm just wondering if someone could clarify something for me regarding spatial auto-correlation. I've been reading up on Moran's I (global and local) and Gi* statistics, and saw that at the end of ...
KaanKaant's user avatar
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7 votes
1 answer

When do we use local alternatives?

I am trying to get a better grasp of the local asymptotic framework, i.e. for parameter sequences of the form: $$\theta_n = \theta_0 + \frac{h}{\sqrt{n}} $$ Where $n$ denotes sample size and $\...
Matthias Schmidtblaicher's user avatar
13 votes
2 answers

Difference between local regression and moving average for smoothing

Typically, local regression (loess / lowess) is used to create smooth plots. Assuming the points are equidistant along the X axis, what's the advantage of using local regression compared to a simple ...
max's user avatar
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2 votes
0 answers

What is the standard results from density estimation?

Below comes from "Ruppert and Wand, Multivariate Locally weighted least squares regression, 1994, p.7 or p.1352 in the Journal" This is about using Kernel function. But I don't know what 'the ...
kurtkim's user avatar
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4 votes
1 answer

Moving window PCA vs local PCA vs kernel PCA vs rolling PCA

All all these terms mean the same thing? Are there other terms for MWPCA? Are there any decent online references to theory and applications? Which term is most popular (if they are equivalent)? I'm ...
Oleg Melnikov's user avatar
1 vote
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Partitioning Spatial Dependence?

So, I have a group of nations that exhibit global spatial dependence. I want to partition the nations into groups so that, at an intuitive level at least, the "sum of the spatial dependence within ...
LJB's user avatar
  • 211
1 vote
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Local linear regression: number of grid points?

Local linear regression is a popular tool. How can one choose the number of grid points for which to estimate the unknown function on?
Kian's user avatar
  • 477
4 votes
2 answers

Combining many small regressions to answer question "what was most related?"

I have an interesting data set for which I want to answer the question: Question How do I rank consumption of a key resource from my data set. I am not interested in predicting, rather measuring ...
zlooop's user avatar
  • 41
4 votes
3 answers

Two significant covariates in coxph analysis: exploring whether the two covariates interact significantly

I am using R 2.15.2 GUI1.53 64-bit on MacOSX 10.5.8 to perform these analyses. I am a molecular biologist by training, not a statistician, so all this analysis represents my own bootstrapped learning ...
user21068's user avatar
3 votes
0 answers

Detecting outstanding events [duplicate]

Possible Duplicate: Simple algorithm for online outlier detection of a generic time series Observing the time series data I noticed there are some outstanding peaks (the picture below). I would ...
niko's user avatar
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