SUMMARY We present a new method for data‐based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has superior theoretical performance; second, it also has a computational advantage; third, the new method has reliably good performance for smooth densities in simulations, performance that is second to none in the existing literature. These methods are based on choosing the bandwidth to (approximately) minimize good quality estimates of the mean integrated squared error. The key to the success of the current procedure is the reintroduction of a non‐stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance.

SynopsisVisual Analogue Scales (VAS) provide a simple technique for measuring subjective experience. They have been established as valid and reliable in a range of clinical and research applications, although there is also evidence of increased error and decreased sensitivity when used some subject groups. Decisions concerned with the choice of scoring interval, experimental design, and statistical analysis for VAS have in some instances been based on convention, assumption and convenience, highlighting the need for more comprehensive assessment of individual scales if this versatile and sensitive measurement technique is to be used to full advantage.

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A Modern Approach to Regression with R is aimed, according to its preface, at first-year graduate students and senior undergraduates. This book fills an important niche in the regression textbook by providing a data-centered approach strong on graphics. Modern Approach is very much in the spirit of Cook and Weisberg (1999) and Weisberg (2005).I have taught an undergraduate applied regression course for several years, and found few textbooks that are appropriate for modern students. To reveal my prejudices up front, what I want in an applied regression text are data, graphics, and computation. Data, because an applied regression course should give students an approach for understanding the world as it is revealed through data; the regression model is an end to a means but should not be treated as the end itself. Graphics, because not only are they important to modern regression, but they can help students develop a conceptual understanding of regression models. Computation, because data analysis via graphical and numerical regression is not possible without statistical software. The choice of software not only determines the sort of diagnostics and visualizations available to one's students, but also influences how students understand regression itself.Sheather defines regression as "a method for investigating the functional relationship among variables". This definition puts the emphasis in exactly the right place and signals that the book is teaching a way of examining data, and is not a study of the linear model itself. An emphasis on real-world problems is carried throughout the book. A great strength of this book is the numerous case studies, which make for interesting reading and always include a clearly stated goal. Four primary case studies are introduced in great detail in the first chapter, and later chapters expand on these studies and introduce new problems, too. The examples are diverse: NFL kickers, wine critics, newspaper circulation, restaurant menus.Modern Approach differs from some other books in that it provides a complete examination of simple regression (including weighted least squares) before beginning multiple regression. Chapters 2-4 cover all aspects of simple regression, and these chapters mirror the development of the multiple regression in the rest of the book. When teaching undergraduates, as I do, this means a substantial part of the ten-week term is spent on simple linear regression. This

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In most patients with hypertensive nephropathy and low glomerular filtration rate (GFR), the kidney function progressively declines despite the adequate control of the hypertension with angiotensin-converting enzyme inhibition. Previously we found that 2 years of oral sodium citrate slowed GFR decline in patients whose estimated GFR (eGFR) was very low (mean 33 ml/min). This treatment also slowed GFR decline in an animal model of surgically reduced nephron mass. Here, we tested if daily oral sodium bicarbonate slowed GFR decline in patients with hypertensive nephropathy with reduced but relatively preserved eGFR (mean 75 ml/min) in a 5-year, prospective, randomized, placebo-controlled, and blinded interventional study. Patients matched for age, ethnicity, albuminuria, and eGFR received daily placebo or equimolar sodium chloride or bicarbonate while maintaining antihypertensive regimens (including angiotensin-converting enzyme inhibition) aiming for their recommended blood pressure targets. After 5 years, the rate of eGFR decline, estimated using plasma cystatin C, was slower and eGFR was higher in patients given sodium bicarbonate than in those given placebo or sodium chloride. Thus, our study shows that in hypertensive nephropathy, daily sodium bicarbonate is an effective kidney protective adjunct to blood pressure control along with angiotensin-converting enzyme inhibition.

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