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関連する概念動画

Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

7.4K
To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
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Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
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Obtaining 3D Chemical Maps by Energy Filtered Transmission Electron Microscopy Tomography
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指数式傾斜混合モデルを用いた半監督評価について

Ye Tian1, Xinwei Zhang2, Zhiqiang Tan1

  • 1Department of Statistics, Rutgers University, Piscataway, NJ 08854, United States of America.

Journal of statistical planning and inference
|August 21, 2025
PubMed
まとめ
この要約は機械生成です。

この研究では,推定効率を向上させるため,半監督のロジスティック回帰のための指数関数傾き混合 (ETM) モデルを導入します. このアプローチは,ラベル付けされたデータとラベル付けされていないデータのクラス比率が異なる場合に統計モデリングを強化します.

キーワード:
アシンプトティック効率エクスポネンショナル・ティルト混合モデルロジスティック回帰最大確率の推定半監督学習

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科学分野:

  • 統計について
  • 機械学習
  • バイオ統計学

背景:

  • 半監督学習はラベル付きデータとラベルなしデータの両方を活用します
  • 論理回帰は バイナリ結果の基本的統計モデルです
  • クラス比率が異なる場合,既存の方法は,ラベルを付けていないデータを完全に利用できない場合があります.

研究 の 目的:

  • 半監督のロジスティック回帰のための指数関数傾き混合 (ETM) モデルを開発および分析する.
  • 監督方法と比較してETMベースの推定の効率を調査する.
  • ラベル付けされたデータセットとラベル付けされていないデータセットの間の異なるクラス比の影響を調査する.

主な方法:

  • エクスポネンショナル・ティルト・ミックス (ETM) のモデルを使用した.
  • 最大非パラメトリック確率の推定を用いた.
  • 提案された推定値のアシンプトティックな性質を導いた.
  • 数値検証のためのシミュレーション研究を実施した.

主要な成果:

  • 監督された物流回帰と比較して,ETMベースの推定の効率が改善されたことが実証されています.
  • ランダムと結果分層のサンプリングセットアップの両方で有効性を示しました.
  • 特定の条件下で既存の半パラメトリック効率理論と調和した効率の向上.

結論:

  • ETMモデルは,半監視のロジスティック回帰のための統計的に堅実なアプローチを提供します.
  • この方法は,特にクラス比率が異なる場合,効率の向上をもたらします.
  • 理論的発見はシミュレーションの証拠によって裏付けられ,実用性を強調しています.