Scale space consistency of piecewise constant least squares estimators -- another look at the regressogram

We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in $L^2([0,1])$, the space of c\`{a}dl\`{a}g functions equipped with the Skorokhod metric or $C([0,1])$ equipped with the supremum metric. Moreover, we consider the family of estimates under a varying smoothing parameter, also called scale space. We prove convergence of the empirical scale space towards its deterministic target.Comment: Published at http://dx.doi.org/10.1214/074921707000000274 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

A robust measure of correlation between two genes on a microarray

<p>Abstract</p> <p>Background</p> <p>The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing with microarray data (well known to be typically quite noisy.)</p> <p>Results</p> <p>We propose a resistant similarity metric based on Tukey's biweight estimate of multivariate scale and location. The resistant metric is simply the correlation obtained from a resistant covariance matrix of scale. We give results which demonstrate that our correlation metric is much more resistant than the Pearson correlation while being more efficient than other nonparametric measures of correlation (e.g., Spearman correlation.) Additionally, our method gives a systematic gene flagging procedure which is useful when dealing with large amounts of noisy data.</p> <p>Conclusion</p> <p>When dealing with microarray data, which are known to be quite noisy, robust methods should be used. Specifically, robust distances, including the biweight correlation, should be used in clustering and gene network analysis.</p

Similar levels of nitric oxide in exhaled air in non-asthmatic rhinitis and asthma after bronchial allergen challenge

Background: Nitric oxide in exhaled air (eNO) is elevated in allergic asthma compared with healthy subjects and has been proposed as a marker of bronchial inflammation. However, eNO is elevated to a lesser extent in allergic non-asthmatic rhinitis as well. Considering the distinctive clinical appearances of both allergic diseases, differences in eNO are expected to persist after allergen exposure. The aim of the study was to compare allergen-induced changes in eNO in house dust mite sensitized patients with asthma and patients with perennial rhinitis without asthma symptoms. Methods: Bronchial allergen challenge was performed in 52 patients sensitized to house dust mite (Dermatophagoides pteronyssinus ), of whom 26 had non-asthmatic rhinitis and 26 had asthma. Levels of eNO were measured before and 1 h, 1 day and 1 week after challenge. Results: At baseline eNO was significantly lower in non-asthmatic rhinitis compared with asthma (geometric mean eNO (SEM): 121 (1.1) in non-asthmatic rhinitis vs 197 (1.1) nl/min in asthma, P <0.006). However, the increase in eNO after bronchial allergen challenge in non-asthmatic rhinitis, in particular in those patients with a dual asthmatic response, significantly exceeded the increase in asthma resulting in similar levels of eNO after challenge (geometric mean eNO (SEM) at 24 h postchallenge 204 (1.1) in non-asthmatic rhinitis vs 244 (1.1)nl/min in asthma, P = 0.3). Conclusion: The difference in eNO between non-asthmatic rhinitis and asthma at baseline is abolished after allergen exposure due to a significantly greater increase in eNO in non-asthmatic rhiniti

Asymptotics: Particles, Processes and Inverse Problems. Festschrift for Piet Groeneboom

Electrical Engineering, Mathematics and Computer Scienc

The minimum weighted covariance determinant estimator

Robust estimation, Efficiency, Outlier detection,

Atopy, lung function, and obstructive airways disease after prenatal exposure to famine

BACKGROUND: Associations have been found between a large head size at birth and atopy, and between low birth weight and obstructive airways disease. A study was undertaken of people born around the time of the Dutch famine in 1944-5 to determine the effects of maternal malnutrition during specific periods of gestation on the prevalence of obstructive airways disease and atopy. METHODS: Nine hundred and twelve people aged about 50, born at term between November 1943 and February 1947 in Amsterdam, were asked about their medical history. Lung function was measured in 733 and serum concentrations of total IgE and specific IgE against mite, pollen and cat were measured in 726. Those exposed in late, mid, and early gestation (exposed participants) were compared with those born before or conceived after the famine (non-exposed participants). RESULTS: Exposure to famine during gestation affected neither the concentrations of total or specific IgE nor lung function values. The prevalence of obstructive airways disease was increased in people exposed to famine in mid gestation (odds ratio adjusted for sex 1.7, 95% confidence interval (CI) 1.1 to 2.6) and tended to be higher in those exposed in early gestation (odds ratio 1.5, 95% CI 0. 9 to 2.6). CONCLUSIONS: The observed increase in the prevalence of obstructive airways disease in people exposed to famine in mid and early gestation was not parallelled by effects on IgE concentrations or lung function. The link between exposure to famine in mid and early gestation and obstructive airways disease in adulthood suggests that fetal lungs can be permanently affected by nutritional challenges during periods of rapid growt

Serum surfactant protein D is elevated in allergic patients

Background There is evidence that surfactant protein (SP)-D is important in the innate, as well as in the adaptive pulmonary immune response. Serum concentrations of SP-D have been proposed as parameter of the integrity of the blood-airspace barrier in interstitial lung diseases. We hypothesized that serum SP-D concentrations are affected in allergic patients and correlate with changes in allergic airway inflammation. Objective To determine levels of serum SP-D in allergic patients compared with non-allergic controls. Furthermore, to investigate associations between serum SP-D concentrations on the one hand and changes in commonly used markers of bronchial inflammation in allergic airways disease on the other hand. Materials and methods Fifty allergic patients were studied and bronchial allergen challenge was used as a model to increase bronchial allergic inflammation in these patients. Serum SP-D concentrations. inflammatory parameters in induced sputum and bronchial hyper-responsiveness (BHR) were determined before and after allergen challenge. Twenty-five non-allergic volunteers served as controls. Results Baseline serum SP-D was significantly higher in allergic patients as compared with controls (mean serum SP-D concentration (95% confidence interval): 62.7 (55.5, 70.0) in allergic patients vs. 49.5 (36.7. 62.3)ng/mL in non-allergic controls. P = 0.006). In addition. baseline serum SP-D appeared to be an independent predictor for the magnitude of the late asthmatic response alter allergen challenge. Furthermore, serum SP-D was predictive for the sputum eosinophil cationic protein concentration after allergen challenge. Conclusion We propose that serum SP-D concentrations are associated with allergic bronchial inflammation and may give additional information, beside BHR and sputum eosinophils. about the degree of bronchial inflammation in allergic patient

An L1-type estimator of multivariate location and shape

Multivariate location and shape, Influence function, Efficiency,