Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression function, the shape-restricted regression splines are robust to knot choices. Monotone regression splines were introduced by Ramsay [Statist. Sci. 3 (1998) 425--461], but were limited to quadratic and lower order. In this paper an algorithm for the cubic monotone case is proposed, and the method is extended to convex constraints and variants such as increasing-concave. The restricted versions have smaller squared error loss than the unrestricted splines, although they have the same convergence rates. The relatively small degrees of freedom of the model and the insensitivity of the fits to the knot choices allow for practical inference methods; the computational efficiency allows for back-fitting of additive models. Tests of constant versus increasing and linear versus convex regression function, when implemented with shape-restricted regression splines, have higher power than the standard version using ordinary shape-restricted regression.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS167 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Few studies have compared the quantification of mRNA by DNA microarray to the results obtained by reverse transcription PCR (RT-PCR). In this study, mRNA was collected from the healing femoral fracture callus of adult and juvenile rats at various times after fracture. Ten samples were measured by both methods for 26 genes. For RT-PCR, mRNA was reverse transcribed, amplified, electrophoresed, blotted, and probed with 32P-labeled internal oligonucleotides, which were quantified. For DNA microarray, the mRNA was processed to biotin-labeled cRNA, hybridized to 10 Affymetrix Rat U34A microarrays, and quantified. Correlation coefficients (r) for each gene for the agreement between RT-PCR and microarray ranged from -0.48 to +0.93. This variation made the interpretation gene-specific. Genes with moderate expression levels gave the highest r values. Increased numbers of absent calls by the microarray software and increased separation between the location of the PCR primers and the microarray probes both led to reduced agreement. Microarray analysis suggested a floor effect in expression levels measured by RT-PCR for two genes. In conclusion, moderate mRNA expression levels with overlap in the location of PCR primers and microarray probes can yield good agreement between these two methods.

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In this paper, we study the drivers of customer satisfaction for financial services. We discuss a full Bayesian analysis based on data collected from customers of a leading financial services company. Our approach allows us to explicitly accommodate missing data and enables quantitative assessment of the impact of the drivers of satisfaction across the customer population. We find that satisfaction with product offerings is a primary driver of overall customer satisfaction. The quality of customer service with respect to financial statements and services provided through different channels of delivery, such as information technology enabled call centers and traditional branch offices, are also important in determining overall satisfaction. However, our analysis indicates that the impact of these service delivery factors may differ substantially across customer segments. In order to facilitate managerial action, we discuss how specific operational quality attributes for designing and delivering financial services can be leveraged to enhance satisfaction with product offerings and service delivery. Our approach and findings have significant implications for managing customer satisfaction in the financial services industry.financial services, customer satisfaction, Bayesian analysis, information technology