Testing Theory: an introduction

By Peter Teunissen. 2009

214 citations recorded by the source corpus.

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Citations in the corpus

Detecting offsets in GPS time series: First results from the detection of offsets in GPS experiment (2013, unknown): “…there is no outlier in the FD time series, which corresponds to no offset in the raw position time series at the current epoch; the alternative hypothesis H 1 is that there is an outlier at the current epoch, indicating a potential offset (see Teunissen [2006] for more details on testing theory).”
Outlier separability analysis with a multiple alternative hypotheses test (2013, background): “The test statistic which returns the largest absolute value is the observation that is most likely to contain the outlier (Teunissen 2000, 2006).”
Multiple Outlier Detection: Hypothesis Tests versus Model Selection by Information Criteria (2016, methodology): “…exclusively of elements with values 0 and 1, whereas 1 in row 𝑖 and column 𝑘 means that the 𝑘 th gross error affects the 𝑖th observation by its full magnitude, such that it becomes an outlier; 0 implies that this gross error does not affect this observation at all (Teunissen 2000, p. 37).”
On the formulation of the alternative hypothesis for geodetic outlier detection (2013, methodology): “T g can be derived from a slippage or deterministic alternative with n2 = n−u (Teunissen 2000; Kargoll 2012).”
3σ-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment (2013, unknown): “In geodetic adjustment textbooks (e.g. Koch 1999, Teunissen 2000), one finds for the test of 𝐻0 versus 𝐻𝐴, the test statistic 𝑇𝑛,𝑖 = 𝑣𝑖 𝜎√𝑞𝑣𝑣,𝑖𝑖 and refers to this as individual normalized (or standardized) residual.”
Distributional theory for the DIA method (2017, methodology): “As t ∈ Rr and ê0 ∈ Rm are related as t = BT ê0, we have (Teunissen 2000) ||t ||2Qtt = ||ê0||2Qyy (29) and |wi | = ||Pcti t ||Qtt = |cTi Q−1yy ê0|√ cTi Q −1 yy Qê0 ê0Q −1 yy ci (30) Thus, the actual verification in which of the regionsPi the misclosure vector t lies can be done using the…”
On the nature of GPS draconitic year periodic pattern in multivariate position time series (2013, methodology): “…argument ok of the maximum power is used: Tk ¼ P okð Þ ¼ êTQ 1y Ak ATk Q 1y P⊥A Ak 1 ATk Q 1 y ê , which, under H0, has a central chi-square distribution with 2 degrees of freedom provided that Qy is known and that the original time series has multivariate normal distribution [Teunissen, 2000].”
Generalised measures of reliability for multiple outliers (2010, background): “The statistic then follows a non-central chi-squared distribution, with non-central parameter given by (Baarda 1967; Teunissen 2000, 2006), λ = z THTPQvPHz σ 20 (7) where z is the true vector of outliers, and H corresponds to the true outlier vector.”