PACE 2.9 (released May 24, 2009) is written in Matlab and can be downloaded from PACE 2.9.

The core program of this package is functional principal component analysis, a key technique for functional data analysis, for sparsely or densely sampled random trajectories and time courses, via the Principal Analysis by Conditional Estimation (PACE) algorithm. PACE does not use pre-smoothing of trajectories which is problematic if functional data are sparsely sampled or measurements are corrupted with noise. The development of PACE has been supported by various NSF grants.

PACE version 2.9 provides the following core options: (1) Fitting of both sparsely and densely sampled random functions and their derivatives. Spaghetti plots to view the sample of functions. (2) Functional linear regression, fitting functional linear regression models for both sparsely or densely sampled random trajectories, for cases where the predictor is a random function and the response is a scalar or a random function. (3) Diagnostics and bootstrap inference for functional linear regression. (4) Assessing functional dependence through functional singular value decomposition. (5) Generalized functional linear regression (GFLM), where the response is a scalar generalized variable such as binary or Poisson, can also be used for classification of functional data via binary regression. Also includes a variant where the response is a series of generalized (binary, Poisson etc.) responses, which are modeled by a latent Gaussian process. (6) Functional Additive Modeling (FAM), an additive generalization of functional linear regression, for the case of functional predictors and both functional and scalar responses (6) Time-synchronization based on pairwise warping (alignment, registration) for sparsely and densely sampled functions. (7) Generalized functional distance for sparse data, which can be used for functional clustering and other applications. A requirement for all methods is that the pooled measurement times are dense on the domain and their pooled pairs are dense on the domain squared (design plot can be used as a check). If you use the program, refer to the articles below which contain some of the core methodology.

References:

Yao, F., Müller, H.G., Clifford, A.J., Dueker, S.R., Follett, J. Lin, Y., Buchholz, B. A., Vogel, J.S. (2003). Shrinkage estimation for functional component scores with application to the population kinetics of plasma folate. Biometrics 59 676-685. (pdf)

Yao, F., Müller, H.G., Wang, J.L. (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association 100 577-590. (pdf)

Yao, F., Müller, H.G., Wang, J.L. (2005). Functional linear regression analysis for longitudinal data. Annals of Statistics 33 2873-2903. (pdf)

Müller, H.G., Stadtmüller, U. (2005). Generalized functional linear models. Annals of Statistics 33, 774-805. (pdf)

Chiou, J.M., Müller, H.G. (2007). Diagnostics for functional regression via residual processes. Computational Statistics and Data Analysis 51 4849-4863. (pdf)

Müller, H.G., Chiou, J.M., Leng, X. (2008). Inferring gene expression dynamics via functional regression analysis. BMC Bioinformatics 9:60 (pdf)

Peng, J., Müller, H.G. (2008). Distance-based clustering of sparsely observed stochastic processes, with applications to online auctions. Annals of Applied Statistics 2, 1056-1077. (pdf)

Tang, R., Müller, H.G. (2008). Pairwise curve synchronization for high-dimensional data. Biometrika 95, 875-889. (pdf)

Müller, H.G., Yao, F. (2008). Functional additive models. Journal of the American Statistical Association 103, 426-437. (pdf)

Liu, B., Müller, H.G. (2009). Estimating derivatives for samples of sparsely observed functions, with application to on-line auction dynamics. Journal of the American Statistical Association 104, 704-717. (pdf)

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HADES 1.0 is written in Matlab and can be downloaded from HADES. This program implements nonparametric hazard and density estimation from aggregated (binned) or censored data. Input formats include lifetables. The algorithm for hazard function estimation combines smoothing with local linear least squares with a transformation approach to reduce discretization bias. Options include centralized mortality rates q_c (method =1) or the transformation psi(x) = log(4/(2-x*Delta)-1) (method = 2, default). Density estimation is implemented via histogram smoothing by local linear least squares. A related program for continuously observed non-aggregated survival data is the R routine muhaz . The development of HADES has been supported by various NSF grants.

References:

Müller, H.G., Wang, J.L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics 50, 61-76.

Müller, H.G., Wang, J.L., Capra, W.B. (1997). From lifetables to hazard rates: The transformation approach. Biometrika 84, 881-892.

Wang, J.L., Müller, H.G., Capra, W.B. (1998). Analysis of oldest-old mortality: Lifetables revisited. Annals of Statistics 26, 126-163.

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SPQR 1.0 is written in Matlab and can be downloaded from SPQR. The program is implements generalized linear regression, where the response variable should be a scalar and the predictor could be a vector. The main feature of this program is that the link function and the variance function can be left unspecified (smoothness assumption is necessary), whereupon the estimating equations include parametric and nonparametric components and this model becomes a semiparametric quasi-likelihood regression (SPQR). The user can also specify the link function or the variance function or both, selecting from a menu of common choices, which is a special case in which the algorithm performs similar tasks as the existing Matlab function glmfit. The algorithm uses the iterated weighted least squares (IWLS) approach to maximize a semiparametric quasi-likelihood and applies kernel smoothing for the case where the link function and the variance function are unknown. In addition, inference for the coefficients of the parametric part is included. Note: If the predictors are functional trajectories rather than vectors and contain noise, preprocessing steps are needed for covariance smoothing and eigen-decomposition which can be executed with PACE (see above), which includes a suitably adapted version of the SPQR algorithm for the case of functional predictors. The development of SPQR has been supported by various NSF grants.

References:

Müller, H.G., Stadtmüller, U. (2005). Generalized functional linear models. Annals of Statistics 33, 774-805. (pdf)

Chiou, J.M., Müller, H.G. (2004). Quasi-likelihood regression with multiple indices and smooth link and variance functions. Scandinavian J. Statistics 31, 367-386. (pdf)

Chiou, J.M., Müller, H.G. (1999). Nonparametric quasi-likelihood. Annals of Statistics 27, 36-64.

Chiou, J.M., Müller, H.G. (1998). Quasi-likelihood regression with unknown link and variance functions. J. American Statistical Association 93, 1376-1387.