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Related Concept Videos

Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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Introduction to Test of Independence01:21

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In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
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Hypothesis Test for Test of Independence01:16

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The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
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Significance testing is a set of statistical methods used to test whether a claim about a parameter is valid. In analytical chemistry, significance testing is used primarily to determine whether the difference between two values comes from determinate or random errors. The effect of a particular change in the measurement protocol, analyst, or sample itself can cause a deviation from the expected result. In the case of a suspected deviation/outlier, we need to be able to confirm mathematically...
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Cointegration and Unit Root Tests: A Fully Bayesian Approach.

Marcio A Diniz1, Carlos A B Pereira2, Julio M Stern2

  • 1Departamento de Estatística, Universidade Federal de S. Carlos, Rod. Washington Luis, km 235, S. Carlos 13565-905, Brazil.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study addresses statistical inference for time series, focusing on unit root and cointegration tests. The Full Bayesian Significance Test (FBST) offers a superior alternative to traditional methods for detecting trends and relationships.

Keywords:
Bayesian inferencecointegrationhypothesis testingtime seriesunit root

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Area of Science:

  • Econometrics
  • Statistical Inference
  • Time Series Analysis

Background:

  • Assessing deterministic vs. stochastic trends is crucial for time series statistical inference.
  • Unit root tests (univariate) and cointegration tests (multivariate) are standard methods.
  • Existing Bayesian approaches have limitations in testing precise hypotheses.

Purpose of the Study:

  • To review the limitations of Bayesian unit root and cointegration tests.
  • To introduce the Full Bayesian Significance Test (FBST) as a solution.
  • To compare FBST with frequentist methods like Augmented Dickey-Fuller and maximum eigenvalue tests.

Main Methods:

  • Review of Bayesian statistical inference for time series.
  • Application of the Full Bayesian Significance Test (FBST).
  • Comparative analysis with frequentist unit root and cointegration tests.

Main Results:

  • The Full Bayesian Significance Test (FBST) effectively overcomes limitations of traditional Bayesian tests.
  • FBST provides a robust procedure for testing sharp hypotheses in time series analysis.
  • Performance comparison highlights FBST's advantages over frequentist alternatives.

Conclusions:

  • The Full Bayesian Significance Test (FBST) is a powerful tool for statistical inference in time series.
  • FBST offers a more reliable approach for unit root and cointegration analysis.
  • This study advocates for the adoption of FBST in time series econometrics.