Variance components estimation in the presence of drift Kim, Jaehee; Ogden, Todd;
Variance components should be estimated based on mean change when the mean of the observations drift gradually over time. Consistent estimators for the variance components are studied for a particular modeling situation with some underlying functions or drift. We propose a new variance estimator with Fourier estimation of variations. The consistency of the proposed estimator is proved asymptotically. The proposed procedures are studied and compared empirically with the variance estimators removing trends. The result shows that our variance estimator has a smaller mean square error and depends on drift patterns. We estimate and apply the variance to Nile River flow data and resting state fMRI data.
Achard S, Raymond S, Whitcher B, Suckling J, and Bullmore E (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs, Journal of Neuroscience, 26, 63-72.
Brown LD and Levine M (2007). Variance estimation in nonparametric regression via the difference sequence method, Annals of Statistics, 35, 2219-2232.
Buckley MJ, Eagleson GK, and Silverman BW (1988). The estimation of residual variance in non-parametric regression, Biometrika, 75, 189-199.
Chaudhuri A (1992). A note on estimating the variance of the regression estimator, Biometrika, 79, 217-218.
Dette H, Munk A, andWagner T (1998). Estimating the variance in nonparametric regression-what is a reasonable choice?, Journal of Royal Statistical Society B, 60, 751-764.
Eddington, A. S. and Plakidis, S. (1929). Irregularities of period of long-period variable stars, Monthly Notices of the Royal Astronomical Society, 90, 65-71.
Gasser T, Sroka L, and Jennen-Steinmetz C (1986). Residual variance and residual pattern in nonlinear regression, Biometrika, 73, 625-633.
Hall P, Kay JW, and Titterington DM (1990). On variance estimation in nonparametric regression, Biometrika, 77, 515-419.
Hastie T and Tibshirani R (1990). Generalized Additive Models, Chapman and Hall, London.
Kim J and Hart J (2011). A change-point estimator using local Fourier series, Journal of Nonpara-metric Statistics, 23, 83-98.
Kott PS (1990). Estimating the conditional variance of a design consistent regression estimator, Journal of Statistical Planning and Inference, 24, 287-296.
Lindquist MA, Waugh C, and Wager TD (2007). Modeling state-related fMRI activity using change-point theory, NeuroImage, 35, 1125-1141.
Lindquist MA, Xu Y, Nebel MB, and Caffo BS (2014). Evaluating dynamic bivariate correlations in resting-state fMRI: A comparison study and a new approach, NeuroImage, 101, 531-546.
Logothetis NK, Pauls J, Augath M, Trinath T, and Oeltermann A (2001). Neurophysiological investi-gation of the basis of the fMRI signal, Nature, 412, 150-157.
Muller UU, Schick A, and Wefelmeyer W (2003). Estimating the error variance in nonparametric regression by a covariate-matched U-statistic, Statistics, 37, 179-188.
Ogden RT and Collier GL (2002). Inference on variance components of autocorrelated sequences in the presence of drift, Journal of Nonparametric Statistics, 14, 409-420.
Reinsch C (1967). Smoothing by spline functions, Numerical Mathematics, 24, 375-382.
Rice JA (1984). Bandwidth choice for nonparametric regression, Annals of Statistics, 12, 1215-1230.
Sarndal CE, Swensson B, and Wretman JH (1989). The weighted residual technique for estimating the variance of the general regression estimator, Biometrika, 76, 527-537.
Tong T and Wang Y (2005). Estimating residual variance in nonparametric regression using least squares, Biometrika, 92, 821-830.
Wahba G (1990). Spline models for observational data, CBMS-NSF Regional Conference Series in Applied Mathematics, 59, PA:SIAM.