Sucharita Ghosh, PhD, is a statistician at the Swiss Federal Research Institute WSL, Switzerland. She also teaches graduate level Statistics in the Department of Mathematics, Swiss Federal Institute of Technology in Zurich. She obtained her doctorate in Statistics from the University of Toronto, Masters from the Indian Statistical Institute and B.Sc. from Presidency College, University of Calcutta, India. She was a Statistics faculty member at Cornell University and has held various short-term and long-term visiting faculty positions at universities such as the University of North Carolina at Chapel Hill and University of York, UK. She has also taught Statistics to undergraduate and graduate students at a number of universities, namely in Canada (Toronto), USA (Cornell, UNC Chapel Hill), UK (York), Germany (Konstanz) and Switzerland (ETH Zurich). Her research interests include smoothing, integral transforms, time series and spatial data analysis, having applications in a number of areas including the natural sciences, finance and medicine among others.

• Preface ixDensity Estimation 11.1 Introduction 11.1.1 Orthogonal polynomials 21.2 Histograms 81.2.1 Properties of the histogram 91.2.2 Frequency polygons 141.2.3 Histogram bin widths 151.2.4 Average shifted histogram 191.3 Kernel density estimation 191.3.1 Naive density estimator 211.3.2 Parzen–Rosenblatt kernel density estimator 251.3.3 Bandwidth selection 431.4 Multivariate density estimation 53Nonparametric Regression 592.1 Introduction 592.1.1 Method of least squares 602.1.2 Influential observations 702.1.3 Nonparametric regression estimators 712.2 Priestley–Chao regression estimator 732.2.1 Weak consistency 772.3 Local polynomials 802.3.1 Equivalent kernels 842.4 Nadaraya–Watson regression estimator 872.5 Bandwidth selection 932.6 Further remarks 992.6.1 Gasser–M¨uller estimator 992.6.2 Smoothing splines 1002.6.3 Kernel efficiency 103Trend Estimation 1053.1 Time series replicates 1053.1.1 Model 1113.1.2 Estimation of common trend function 1143.1.3 Asymptotic properties 1143.2 Irregularly spaced observations 1203.2.1 Model 1223.2.2 Derivatives, distribution function, and quantiles 1253.2.3 Asymptotic properties 1293.2.4 Bandwidth selection 1373.3 Rapid change points 1413.3.1 Model and definition of rapid change 1443.3.2 Estimation and asymptotics 1453.4 Nonparametric M-estimation of a trend function 1493.4.1 Kernel-based M-estimation 1493.4.2 Local polynomial M-estimation 154Semiparametric Regression 1574.1 Partial linear models with constant slope 1574.2 Partial linear models with time-varying slope 1604.2.1 Estimation 1654.2.2 Assumptions 1664.2.3 Asymptotics 171Surface Estimation 1815.1 Introduction 1815.2 Gaussian subordination 1935.3 Spatial correlations 1955.4 Estimation of the mean and consistency 1975.4.1 Asymptotics 1975.5 Variance estimation 2035.6 Distribution function and spatial Gini index 2065.6.1 Asymptotics 213References 217Author Index 243Subject Index 251

Sucharita Ghosh, PhD, is a statistician at the Swiss Federal Research Institute WSL, Switzerland. She also teaches graduate level Statistics in the Department of Mathematics, Swiss Federal Institute of Technology in Zurich. She obtained her doctorate in Statistics from the University of Toronto, Masters from the Indian Statistical Institute and B.Sc. from Presidency College, University of Calcutta, India. She was a Statistics faculty member at Cornell University and has held various short-term and long-term visiting faculty positions at universities such as the University of North Carolina at Chapel Hill and University of York, UK. She has also taught Statistics to undergraduate and graduate students at a number of universities, namely in Canada (Toronto), USA (Cornell, UNC Chapel Hill), UK (York), Germany (Konstanz) and Switzerland (ETH Zurich). Her research interests include smoothing, integral transforms, time series and spatial data analysis, having applications in a number of areas including the natural sciences, finance and medicine among others.

• Preface ixDensity Estimation 11.1 Introduction 11.1.1 Orthogonal polynomials 21.2 Histograms 81.2.1 Properties of the histogram 91.2.2 Frequency polygons 141.2.3 Histogram bin widths 151.2.4 Average shifted histogram 191.3 Kernel density estimation 191.3.1 Naive density estimator 211.3.2 Parzen–Rosenblatt kernel density estimator 251.3.3 Bandwidth selection 431.4 Multivariate density estimation 53Nonparametric Regression 592.1 Introduction 592.1.1 Method of least squares 602.1.2 Influential observations 702.1.3 Nonparametric regression estimators 712.2 Priestley–Chao regression estimator 732.2.1 Weak consistency 772.3 Local polynomials 802.3.1 Equivalent kernels 842.4 Nadaraya–Watson regression estimator 872.5 Bandwidth selection 932.6 Further remarks 992.6.1 Gasser–M¨uller estimator 992.6.2 Smoothing splines 1002.6.3 Kernel efficiency 103Trend Estimation 1053.1 Time series replicates 1053.1.1 Model 1113.1.2 Estimation of common trend function 1143.1.3 Asymptotic properties 1143.2 Irregularly spaced observations 1203.2.1 Model 1223.2.2 Derivatives, distribution function, and quantiles 1253.2.3 Asymptotic properties 1293.2.4 Bandwidth selection 1373.3 Rapid change points 1413.3.1 Model and definition of rapid change 1443.3.2 Estimation and asymptotics 1453.4 Nonparametric M-estimation of a trend function 1493.4.1 Kernel-based M-estimation 1493.4.2 Local polynomial M-estimation 154Semiparametric Regression 1574.1 Partial linear models with constant slope 1574.2 Partial linear models with time-varying slope 1604.2.1 Estimation 1654.2.2 Assumptions 1664.2.3 Asymptotics 171Surface Estimation 1815.1 Introduction 1815.2 Gaussian subordination 1935.3 Spatial correlations 1955.4 Estimation of the mean and consistency 1975.4.1 Asymptotics 1975.5 Variance estimation 2035.6 Distribution function and spatial Gini index 2065.6.1 Asymptotics 213References 217Author Index 243Subject Index 251

Sucharita Ghosh, PhD, is a statistician at the Swiss Federal Research Institute WSL, Switzerland. She also teaches graduate level Statistics in the Department of Mathematics, Swiss Federal Institute of Technology in Zurich. She obtained her doctorate in Statistics from the University of Toronto, Masters from the Indian Statistical Institute and B.Sc. from Presidency College, University of Calcutta, India. She was a Statistics faculty member at Cornell University and has held various short-term and long-term visiting faculty positions at universities such as the University of North Carolina at Chapel Hill and University of York, UK. She has also taught Statistics to undergraduate and graduate students at a number of universities, namely in Canada (Toronto), USA (Cornell, UNC Chapel Hill), UK (York), Germany (Konstanz) and Switzerland (ETH Zurich). Her research interests include smoothing, integral transforms, time series and spatial data analysis, having applications in a number of areas including the natural sciences, finance and medicine among others.

• Preface ixDensity Estimation 11.1 Introduction 11.1.1 Orthogonal polynomials 21.2 Histograms 81.2.1 Properties of the histogram 91.2.2 Frequency polygons 141.2.3 Histogram bin widths 151.2.4 Average shifted histogram 191.3 Kernel density estimation 191.3.1 Naive density estimator 211.3.2 Parzen–Rosenblatt kernel density estimator 251.3.3 Bandwidth selection 431.4 Multivariate density estimation 53Nonparametric Regression 592.1 Introduction 592.1.1 Method of least squares 602.1.2 Influential observations 702.1.3 Nonparametric regression estimators 712.2 Priestley–Chao regression estimator 732.2.1 Weak consistency 772.3 Local polynomials 802.3.1 Equivalent kernels 842.4 Nadaraya–Watson regression estimator 872.5 Bandwidth selection 932.6 Further remarks 992.6.1 Gasser–M¨uller estimator 992.6.2 Smoothing splines 1002.6.3 Kernel efficiency 103Trend Estimation 1053.1 Time series replicates 1053.1.1 Model 1113.1.2 Estimation of common trend function 1143.1.3 Asymptotic properties 1143.2 Irregularly spaced observations 1203.2.1 Model 1223.2.2 Derivatives, distribution function, and quantiles 1253.2.3 Asymptotic properties 1293.2.4 Bandwidth selection 1373.3 Rapid change points 1413.3.1 Model and definition of rapid change 1443.3.2 Estimation and asymptotics 1453.4 Nonparametric M-estimation of a trend function 1493.4.1 Kernel-based M-estimation 1493.4.2 Local polynomial M-estimation 154Semiparametric Regression 1574.1 Partial linear models with constant slope 1574.2 Partial linear models with time-varying slope 1604.2.1 Estimation 1654.2.2 Assumptions 1664.2.3 Asymptotics 171Surface Estimation 1815.1 Introduction 1815.2 Gaussian subordination 1935.3 Spatial correlations 1955.4 Estimation of the mean and consistency 1975.4.1 Asymptotics 1975.5 Variance estimation 2035.6 Distribution function and spatial Gini index 2065.6.1 Asymptotics 213References 217Author Index 243Subject Index 251