RECORD
Hypothesis Testing of One-Sample Mean Vector in Distributed Frameworks
Methodology · Submitted 6 Oct 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Comparing the power of centralized test statistics and the distributed ones, it is observed that there is a fundamental tradeoff between communication costs and the powers of the tests.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Distributed frameworks are widely used to handle massive data, where sample size $n$ is very large, and data are often stored in $k$ different machines. For a random vector $X\in \mathbb{R}^p$ with expectation $\mu$, testing the mean vector $H_0: \mu=\mu_0$ vs $H_1: \mu\ne \mu_0$ for a given vector $\mu_0$ is a basic problem in statistics. The centralized test statistics require heavy communication costs, which can be a burden when $p$ or $k$ is large. To reduce the communication cost, distributed test statistics are proposed in this paper for this problem based on the divide and conquer technique, a commonly used approach for distributed statistical inference. Specifically, we extend two commonly used centralized test statistics to the distributed ones, that apply to low and high dimensional cases, respectively. Comparing the power of centralized test statistics and the distributed ones, it is observed that there is a fundamental tradeoff between communication costs and the powers of the tests. This is quite different from the application of the divide and conquer technique in many other problems such as estimation, where the associated distributed statistics can be as good as the centralized ones. Numerical results confirm the theoretical findings.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Distributed frameworks are widely used to handle massive data, where sample size $n$ is very large, and data are often stored in $k$ different machines. | background 1.00 | 0.06 | 0.02 | asserted 0.99 |
| s1 | For a random vector $X\in \mathbb{R}^p$ with expectation $\mu$, testing the mean vector $H_0: \mu=\mu_0$ vs $H_1: \mu\ne \mu_0$ for a given vector $\mu_0$ is a basic problem in statistics. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | The centralized test statistics require heavy communication costs, which can be a burden when $p$ or $k$ is large. | background 0.72 | 0.14 | 0.03 | asserted 0.87 |
| s3 | To reduce the communication cost, distributed test statistics are proposed in this paper for this problem based on the divide and conquer technique, a commonly used approach for distributed statistical inference. | contribution 0.78 | 0.85 | 0.07 | asserted 1.00 |
| s4 | Specifically, we extend two commonly used centralized test statistics to the distributed ones, that apply to low and high dimensional cases, respectively. | method 0.65 | 0.87 | 0.05 | asserted 1.00 |
| s5 | Comparing the power of centralized test statistics and the distributed ones, it is observed that there is a fundamental tradeoff between communication costs and the powers of the tests. | result 0.85 | 0.86 | 0.65 | asserted 0.96 |
| s6 | This is quite different from the application of the divide and conquer technique in many other problems such as estimation, where the associated distributed statistics can be as good as the centralized ones. | interpretation 0.85 | 0.46 | 0.37 | asserted 0.99 |
| s7 | Numerical results confirm the theoretical findings. | result 0.99 | 0.90 | 0.08 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Distributed frameworks are widely used to handle massive data, where sample size $n$ is very large, and data are often stored in $k$ different machines. For a random vector $X\in \mathbb{R}^p$ with expectation $\mu$, testing the mean vector $H_0: \mu=\mu_0$ vs $H_1: \mu\ne \mu_0$ for a given vector $\mu_0$ is a basic problem in statistics. The centralized test statistics require heavy communication costs, which can be a burden when $p$ or $k$ is large. To reduce the communication cost, distributed test statistics are proposed in this paper for this problem based on the divide and conquer technique, a commonly used approach for distributed statistical inference. Specifically, we extend two commonly used centralized test statistics to the distributed ones, that apply to low and high dimensional cases, respectively. Comparing the power of centralized test statistics and the distributed ones, it is observed that there is a fundamental tradeoff between communication costs and the powers of the tests. This is quite different from the application of the divide and conquer technique in many other problems such as estimation, where the associated distributed statistics can be as good as the centralized ones. Numerical results confirm the theoretical findings.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 2 sentences without a confident label
Cites as background 1 paper
-
The divide and conquer technique has been applied successfully in many problems, including regression and classification, hypothesis testing, confidence intervals, principal eigenspaces analysis, linear discriminant analysis, and many others [ref] .
Distributed Statistical Inference for Massive Data · Introduction · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.