Estimating the mean and its effects on Neyman smooth tests of normality for ARMA models
Bibliographic record
Abstract
Abstract Goodness‐of‐fit tests represent an important part of any model building strategy. In time series modelling, many test procedures concentrate on specifying the model structure. However it is also of interest to check distributional assumptions. In autoregressive moving‐average (ARMA) time series models, available results based on the smooth test paradigm assume that the mean of the process is known. However in practical applications, the mean is unknown and it needs to be estimated. Under general assumptions on the estimation procedures, the asymptotic distributions of the smooth test statistics based on estimation of all the parameters, including the mean, are derived. Surprisingly it is found that mean estimation has an impact on the asymptotic behaviours. This finding is in sharp contrast with portmanteau test procedures, where the degrees of freedom of the approximate distributions remain unchanged whether the mean is estimated or not. The test statistic relies on the order of the family, and a data‐driven choice of that parameter is discussed, giving a fully automatic testing procedure. Theoretical and empirical comparisons between the smooth test statistic assuming a known mean and the new test statistic are presented. Consistency is studied. In a simulation study, the effects of assuming incorrectly the mean being known are illustrated. An application using annual data on the productivity of potatoes (per acre) in Prince Edward Island for the time period 1957–2014 illustrates the procedure. The Canadian Journal of Statistics 44: 241–270; 2016 © 2016 Statistical Society of Canada
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.200 | 0.643 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".