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Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing Abstract: In this paper, we study some relationships between the detection and estimation theories for a binary composite hypothesis test H 0 against H 1 and a related estimation problem. We start with a one-dimensional 1D space for the unknown parameter space and one-sided hypothesis problems and then extend out results into more general cases.
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In statistical significance testing the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. That is, a p-value might be found from an appropriately defined cdf , rather than a pdf.
Let's now consider - assuming we have a sample from the right cdf - whether a kernel density estimate computed on that sample is appropriate for computing p-values. The CDF estimate will therefore also have bias. If you want an good smooth estimate of a CDF, you may be better directing effort to optimizing desirable properties of that. In aummary: Yes, it's legitimate in the sense that - done correctly - it might provide reasonable estimates of p-values.
It will be biased tend to give too high a p-value in the tails and correspondingly too low in the middle. You should take care to try to optimize your smoothing to the purpose you are putting it to.
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Learn more. Is it legitimate to use a conditional PDF derived using kernel density estimation for hypothesis testing? Ask Question. Asked 7 years, 11 months ago.
Active 5 years, 10 months ago. Viewed times. Improve this question. Danica Add a comment. Active Oldest Votes. Wikipedia has it right: In statistical significance testing the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. There are a number of relevant points I can make: i the estimate of the CDF obtained from a kernel density estimate is smoother than the original ECDF; indeed smoothness of the PDF estimate is the point of kernel density estimates ii the kernel density estimate has larger variance than the thing it estimates; it's not an unbiased estimate of the PDF.
Improve this answer. Do you still think that kernel density estimation could give me an "appropriately defined cdf" to use in this way? Note that the point about 'appropriately defined' relates to your particular null and alternative hypothesis and the choice of test statistic. The points that I'm interested in evaluating tend to fall towards the extremes where I have relatively few actual samples in my empirical distribution.
In any case, I'm somewhat reassured that my estimated CDF ought to tend to overestimate p-values in the tails, since this will just make my hypothesis test overly conservative and I care more about type I errors. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. State of the Stack Q1 Blog Post. Stack Overflow for Teams is now free for up to 50 users, forever.
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Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution. Confidence intervals use data from a sample to estimate a population parameter. Hypothesis testing requires that we have a hypothesized parameter. One primary difference is a bootstrap distribution is centered on the observed sample statistic while a randomization distribution is centered on the value in the null hypothesis. All of the confidence intervals we constructed in this course were two-tailed. These two-tailed confidence intervals go hand-in-hand with the two-tailed hypothesis tests we learned in Lesson 5. The conclusion drawn from a two-tailed confidence interval is usually the same as the conclusion drawn from a two-tailed hypothesis test.
This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA Analysis of Variance and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations. Introduction to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables. Advanced graduate students interested in applying cutting-edge methods for analyzing data. Preface, 1. Introduction; 2.
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Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. In statistical significance testing the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.
Sign in. Statistical inference is the process of making reasonable guesses about the population's distributio n and parameters given the observed data. Conducting hypothesis testing and constructing confidence interval are two examples of statistical inference.
The analysis of a number of independent first-order autoregressive time series is considered in a normal theory context. A model is studied which allows for nonstation-ary and nonidentical distribution of the series caused by both fixed effect and random effect components. Most users should sign in with their email address. If you originally registered with a username please use that to sign in. To purchase short term access, please sign in to your Oxford Academic account above. Don't already have an Oxford Academic account?
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