.- help for ^warpdenm^ [STB-38: snp13] .- WARPing density estimation -------------------------- ^warpdenm^ varname [^if^ exp] [^in^ range], ^b^width^(^#^)^ ^m^val^(^#^)^ ^k^ercode^(^#^)^ [^st^tep ^numo^des ^mo^des ^np^oints ^g^en^(^denvar midvar^)^ ^nog^raph graph_options] Description ----------- This program estimates univariate density estimator by means of the ASH-WARPing procedure (Scott, 1985, 1992; Haerdle, 1991), draws the result and provide modality information. Options ------- ^b^width^(^#^)^ is the smoother parameter h (binwidth for histograms, frequency polygons and averaged shifted histograms or FP-ASH; bandwidth for kernel density estimators). ^m^val^(^#^)^ is the number of averaged shifted histograms used to calculate the required density estimations. ^k^ercode^(^#^)^ specifies the weight function (kernel) to calculate the univariate densities according to the following numerical codes: 1 = Uniform 2 = Triangle 3 = Epanechnikov 4 = Quartic (Biweight) 5 = Triweight 6 = Gaussian ^st^ep is included to draw the step (histogram like) version. The default is the linear interpolated (polygon) version. ^numo^des display the number of modes in the density estimation. ^mo^des lists the estimated values for each modes. The ^numo^des option must be included first. ^np^oints gives the number of points used for estimation. ^g^en^(^denvar midvar^)^ permits to create two variables containing respectively the estimated density and the corresponding midpoints used for calculation. ^nog^raph suppresses the graph drawing. graph_options are any of the options allowed with ^graph, twoway^. Remarks ------- ^b^width, ^m^val, and ^k^ercode, are not optional. If the user does not provide them, the program halts and displays an error message on screen. This program is an all Stata command. In contrast with ^warpden^ it does not require any external executable file. The user is warned that this implementation is not as fast as warpden, specially with a high value for M (a value of 10 is suggested but not obligatory). The "smoothness" of the resulting estimate can be regulated by changing the bandwidth: wide intervals produce smooth results; narrow intervals give noiser results. Except for the Gaussian all the weight functions are supported on [-1,1]. As ^m^val increases, the approximation is closer to the true kernel estimation, but the quantity of calculation increases too. A good compromise is to use an ^m^val around 10 (Haerdle, 1991). This procedure can be regarded as a descriptive smoother of histograms besides a nonparametric density estimator. Examples -------- . ^warpdenm snow, bwidth(10) mval(1) kercode(2) step^ Will display a histogram for ^snow^ using a bindwidth of 10. . ^warpdenm snow, b(10) m(1) k(2)^ Will display a frequency polygon for ^snow^. . ^warpdenm snow, b(10) m(5) k(2) step^ Will display the estimate from averaging five histograms with the triangle weight function. . ^warpdenm bodlen, b(10) m(15) k(4) gen(denq10 mid10) nog^ Will calculate the WARPing approximation for the Quartic kernel, and will generate two variables with the resulting density estimation and the corresponding midpoints, without any graphical display. . ^warpdenm snow, b(3) m(10) k(6) numo mo np nog^ Will display the number of modes and their corresponding estimates; besides reports the number of points used to estimate density. References ---------- Haerdle, W. (1991) Smoothing Techniques with Implementation in S. Springer-Verlag Chapter 2: 43-84; Chapters 1-2: 1-84. Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1993) snp6: Exploring the shape of univariate data using kernel density estimators. Stata Technical Bulletin 16: 8-19. Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1995) snp6.1: ASH, WARPing, and kernel density estimation for univariate data. Stata Technical Bulletin 26: 23-31. Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (199x) snp6.2: Practical Rules for bandwidth selection in univariate density estimation. Stata Technical Bulletin 27: 5-19. Salgado-Ugarte, I.H., M. Shimizu, and T. Taniuchi (1997) snp6.4: Nonparametric assessment of multimodality for univariate data. Stata Technical Bulletin XX: XX-XX. Scott, D.W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. John Wiley Chapter 6: 125-143; Chapters 3-6: 47-193. Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall. Authors ------- Isaias H. Salgado-Ugarte(*), Makoto Shimizu, and Toru Taniuchi (*)Universidad Nacional Autonoma de Mexico Facultad de Estudios Superiores Zaragoza Biologia, Guelatao 66 Col. Ejercito de Oriente Iztapalapa 09230, Mexico D.F., Mexico (Fax 52-5-773-0151) e-mail: fes01@@tzetzal.dcaa.unam.mx; isalgado@@servidor.unam.mx Also see -------- STB: snp6 (STB-16); snp6.1 (STB-26); snp6.2 (STB-27); snp13 (STB-38) On-line: ^help^ for @warpdens@, @kerneld@, @bandw@, @l2cvwarp@, @bcvwarp@, @kernreg@, @numode@