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src/library/stats/man/ARMAacf.Rd

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% File src/library/stats/man/ARMAacf.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2015 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{ARMAacf}
@@ -23,7 +23,7 @@ ARMAacf(ar = numeric(), ma = numeric(), lag.max = r, pacf = FALSE)
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}
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\details{
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The methods used follow
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\bibcite{Brockwell & Davis (1991, section 3.3)}. Their
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\bibcitet{|R:Brockwell+Davis:1991|section 3.3}. Their
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equations (3.3.8) are solved for the autocovariances at lags
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\eqn{0, \dots, \max(p, q+1)}{0, \dots, max(p, q+1)},
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and the remaining autocorrelations are given by a recursive filter.
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}
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\references{
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Brockwell, P. J. and Davis, R. A. (1991) \emph{Time Series: Theory and
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Methods}, Second Edition. Springer.
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\bibshow{*}
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}
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\seealso{\code{\link{arima}}, \code{\link{ARMAtoMA}},
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\code{\link{acf2AR}} for inverting part of \code{ARMAacf}; further

src/library/stats/man/Beta.Rd

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% File src/library/stats/man/Beta.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2023 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{Beta}
@@ -51,7 +51,7 @@ rbeta(n, shape1, shape2, ncp = 0)
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\code{[dpqr]beta()} functions are defined correspondingly.
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\code{pbeta} is closely related to the incomplete beta function. As
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defined by \bibcite{Abramowitz and Stegun 6.6.1}
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defined by \bibcitet{|R:Abramowitz+Stegun:1972|section 6.6.1}
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\deqn{B_x(a,b) = \int_0^x t^{a-1} (1-t)^{b-1} dt,}{
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B_x(a,b) = integral_0^x t^(a-1) (1-t)^(b-1) dt,}
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and 6.6.2 \eqn{I_x(a,b) = B_x(a,b) / B(a,b)} where
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}
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}
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\references{
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Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
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\emph{The New S Language}.
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Wadsworth & Brooks/Cole.
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Abramowitz, M. and Stegun, I. A. (1972)
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\emph{Handbook of Mathematical Functions.} New York: Dover.
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Chapter 6: Gamma and Related Functions.
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\bibinfo{R:Abramowitz+Stegun:1972}{footer}{Chapter 6: Gamma and
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Related Functions.}
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\bibshow{*, R:Becker+Chambers+Wilks:1988}
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Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
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\emph{Continuous Univariate Distributions}, volume 2, especially

src/library/stats/man/Fdist.Rd

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% File src/library/stats/man/Fdist.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2022 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{FDist}
@@ -62,7 +62,8 @@ rf(n, df1, df2, ncp)
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for \eqn{x > 0}.
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The F distribution's cumulative distribution function (\abbr{cdf}),
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\eqn{F_{\nu_1,\nu_2}}{F_{n1,n2}} fulfills (\bibcite{Abramowitz & Stegun 26.6.2, p.946})
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\eqn{F_{\nu_1,\nu_2}}{F_{n1,n2}} fulfills
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\bibcitep{|R:Abramowitz+Stegun:1972|section 26.6.2\\\\\\, page 946}
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\eqn{F_{\nu_1,\nu_2}(qF) = 1 - I_x(\nu_2/2, \nu_1/2) = I_{1-x}(\nu_1/2, \nu_2/2),}{%
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F_{n1,n2}(qF) = 1 - I_x(n2/2, n1/2) = I_{1-x}(n1/2, n2/2),} where
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\eqn{x := \frac{\nu_2}{\nu_2 + \nu_1*qF}}{x := n2/(n2 + n1*qF)}, and
@@ -95,9 +96,7 @@ rf(n, df1, df2, ncp)
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else \emph{via} \code{\link{qbeta}}.
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}
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\references{
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Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
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\emph{The New S Language}.
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Wadsworth & Brooks/Cole.
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\bibshow{*, R:Becker+Chambers+Wilks:1988}
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102101
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
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\emph{Continuous Univariate Distributions}, volume 2, chapters 27 and 30.

src/library/stats/man/KalmanLike.Rd

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% File src/library/stats/man/KalmanLike.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2018 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{KalmanLike}
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It computes the covariance matrix of
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\eqn{(X_{t-1},...,X_{t-p},Z_t,...,Z_{t-q})}
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by the method of difference equations
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(page 93 of \bibcite{Brockwell and Davis (1991)}),
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(page 93 of \bibcitet{R:Brockwell+Davis:1991}),
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apparently suggested by a referee of Gardner \abbr{et al.}\sspace(see p.314 of
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their paper).
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}
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}
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\references{
125-
Brockwell, P. J. and Davis, R. A. (1991).
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\emph{Time Series: Theory and Methods}, second edition.
127-
Springer.
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\bibshow{*,
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R:Gardner+Harvey+Phillips:1980}
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129128
Durbin, J. and Koopman, S. J. (2001).
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\emph{Time Series Analysis by State Space Methods}.
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Oxford University Press.
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Gardner, G, Harvey, A. C. and Phillips, G. D. A. (1980).
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Algorithm AS 154: An algorithm for exact maximum likelihood estimation
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of autoregressive-moving average models by means of Kalman filtering.
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\emph{Applied Statistics}, \bold{29}, 311--322.
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\doi{10.2307/2346910}.
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R bug report PR#14682 (2011-2013)
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\url{https://bugs.r-project.org/show_bug.cgi?id=14682}.
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}

src/library/stats/man/StructTS.Rd

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% File src/library/stats/man/StructTS.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2009 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{StructTS}
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initial state of the filter, \code{model} its final state.}
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\item{xtsp}{the \code{tsp} attributes of \code{x}.}
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}
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\note{
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Optimization of structural models is a lot harder than many of the
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references admit. For example, the \code{\link{AirPassengers}} data
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are considered in \bibcitet{R:Brockwell+Davis:1996}: their solution appears to
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be a local maximum, but nowhere near as good a fit as that produced by
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\code{StructTS}. It is quite common to find fits with one or more
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variances zero, and this can include \eqn{\sigma^2_\epsilon}{sigma^2_eps}.
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}
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\references{
102-
Brockwell, P. J. & Davis, R. A. (1996).
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\emph{Introduction to Time Series and Forecasting}.
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Springer, New York.
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Sections 8.2 and 8.5.
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\bibinfo{R:Brockwell+Davis:1996}{footer}{Sections 8.2 and 8.5.}
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\bibshow{*}
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Durbin, J. and Koopman, S. J. (2001) \emph{Time Series Analysis by
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State Space Methods.} Oxford University Press.
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Harvey, A. C. (1993) \emph{Time Series Models}.
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2nd Edition, Harvester Wheatsheaf.
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}
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\note{
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Optimization of structural models is a lot harder than many of the
119-
references admit. For example, the \code{\link{AirPassengers}} data
120-
are considered in \bibcite{Brockwell & Davis (1996)}: their solution appears to
121-
be a local maximum, but nowhere near as good a fit as that produced by
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\code{StructTS}. It is quite common to find fits with one or more
123-
variances zero, and this can include \eqn{\sigma^2_\epsilon}{sigma^2_eps}.
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}
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\seealso{
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\code{\link{KalmanLike}}, \code{\link{tsSmooth}};

src/library/stats/man/ansari.test.Rd

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% File src/library/stats/man/ansari.test.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2018 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{ansari.test}
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approximations.
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Note that mid-ranks are used in the case of ties rather than average
73-
scores as employed in \bibcite{Hollander & Wolfe (1973)}.
74-
See, e.g., \bibcite{Hajek, Sidak and Sen (1999), pages 131ff}, for
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scores as employed in \bibcitet{R:Hollander+Wolfe:1973}.
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See, e.g., \bibcitet{|R:Hajek+Sidak+Sen:1999|pages 131ff}, for
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more information.
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}
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\value{
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for \eqn{s^2} in the F test.
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}
100100
\references{
101-
David F. Bauer (1972).
102-
Constructing confidence sets using rank statistics.
103-
\emph{Journal of the American Statistical Association},
104-
\bold{67}, 687--690.
105-
\doi{10.1080/01621459.1972.10481279}.
106-
107-
Jaroslav Hajek, Zbynek Sidak and Pranab K. Sen (1999).
108-
\emph{Theory of Rank Tests}.
109-
San Diego, London: Academic Press.
110-
111-
Myles Hollander and Douglas A. Wolfe (1973).
112-
\emph{Nonparametric Statistical Methods}.
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New York: John Wiley & Sons.
114-
Pages 83--92.
101+
\bibinfo{R:Hollander+Wolfe:1973}{footer}{Pages 83--92.}
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\bibshow{*, R:Bauer:1972}
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}
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\seealso{
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\code{\link{fligner.test}} for a rank-based (nonparametric)

src/library/stats/man/ar.Rd

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% File src/library/stats/man/ar.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2024 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{ar}
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\code{ar.burg} allows two methods to estimate the innovations
109109
variance and hence AIC. Method 1 is to use the update given by
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the \I{Levinson}-\I{Durbin} recursion
111-
(\bibcite{Brockwell and Davis, 1991, (8.2.6) on page 242}),
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\bibcitep{|R:Brockwell+Davis:1991|(8.2.6) on page 242},
112112
and follows S-PLUS. Method 2 is the mean of the sum
113113
of squares of the forward and backward prediction errors
114-
(as in \bibcite{Brockwell and Davis, 1996, page 145}).
115-
\bibcite{Percival and Walden (1998)} discuss both.
114+
(as in \bibcitet{|R:Brockwell+Davis:1996|page 145}).
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\bibcitet{R:Percival+Walden:1998} discuss both.
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In the multivariate case the estimated
117117
coefficients will depend (slightly) on the variance estimation method.
118118

@@ -178,25 +178,9 @@ ar.mle(x, aic = TRUE, order.max = NULL, na.action = na.fail,
178178
}
179179

180180
\references{
181-
Brockwell, P. J. and Davis, R. A. (1991).
182-
\emph{Time Series and Forecasting Methods}, second edition.
183-
Springer, New York.
184-
Section 11.4.
185-
186-
Brockwell, P. J. and Davis, R. A. (1996).
187-
\emph{Introduction to Time Series and Forecasting}.
188-
Springer, New York.
189-
Sections 5.1 and 7.6.
190-
191-
Percival, D. P. and Walden, A. T. (1998).
192-
\emph{Spectral Analysis for Physical Applications}.
193-
Cambridge University Press.
194-
195-
Whittle, P. (1963).
196-
On the fitting of multivariate autoregressions and the approximate
197-
canonical factorization of a spectral density matrix.
198-
\emph{Biometrika}, \bold{40}, 129--134.
199-
\doi{10.2307/2333753}.
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\bibinfo{R:Brockwell+Davis:1991}{footer}{Section 11.4.}
182+
\bibinfo{R:Brockwell+Davis:1996}{footer}{Sections 5.1 and 7.6.}
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\bibshow{*, R:Whittle:1963}
200184
}
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202186
\examples{

src/library/stats/man/bandwidth.Rd

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% File src/library/stats/man/bandwidth.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2018 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{bandwidth}
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It defaults to 0.9 times the
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minimum of the standard deviation and the interquartile range divided by
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1.34 times the sample size to the negative one-fifth power
52-
(= \I{Silverman}'s \sQuote{rule of thumb}, \bibcite{Silverman (1986, page 48, \abbr{eqn} (3.31))})
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(= \I{Silverman}'s \sQuote{rule of thumb},
53+
\bibcitet{|R:Silverman:1986|page 48\\\\\\, \\\\\\abbr{eqn} (3.31)})
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\emph{unless} the quartiles coincide when a positive result
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will be guaranteed.
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\code{bw.ucv} and \code{bw.bcv} implement unbiased and
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biased cross-validation respectively.
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\code{bw.SJ} implements the methods of \bibcite{Sheather & Jones (1991)}
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\code{bw.SJ} implements the methods of \bibcitet{R:Sheather+Jones:1991}
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to select the bandwidth using pilot estimation of derivatives.\cr
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The algorithm for method \code{"ste"} solves an equation (via
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\code{\link{uniroot}}) and because of that, enlarges the interval
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of \code{density} and so give answers four times as large.
9394
}
9495
\references{
96+
\bibshow{*, R:Venables+Ripley:2002}
97+
9598
Scott, D. W. (1992)
9699
\emph{Multivariate Density Estimation: Theory, Practice, and
97100
Visualization.}
98101
New York: Wiley.
99-
100-
Sheather, S. J. and Jones, M. C. (1991).
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A reliable data-based bandwidth selection method for kernel density
102-
estimation.
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\emph{Journal of the Royal Statistical Society Series B},
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\bold{53}, 683--690.
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\doi{10.1111/j.2517-6161.1991.tb01857.x}.
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%% \url{https://www.jstor.org/stable/2345597}.
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108-
Silverman, B. W. (1986).
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\emph{Density Estimation}.
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London: Chapman and Hall.
111-
112-
Venables, W. N. and Ripley, B. D. (2002).
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\emph{Modern Applied Statistics with S}.
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Springer.
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}
116103
\examples{
117104
require(graphics)

src/library/stats/man/binom.test.Rd

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% File src/library/stats/man/binom.test.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2018 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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\name{binom.test}
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2828
}
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\details{
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Confidence intervals are obtained by a procedure first given in
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\bibcite{Clopper and Pearson (1934)}.
31+
\bibcitet{R:Clopper+Pearson:1934}.
3232
This guarantees that the confidence level
3333
is at least \code{conf.level}, but in general does not give the
3434
shortest-length confidence intervals.
@@ -48,21 +48,13 @@ binom.test(x, n, p = 0.5,
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\item{data.name}{a character string giving the names of the data.}
4949
}
5050
\references{
51-
Clopper, C. J. & Pearson, E. S. (1934).
52-
The use of confidence or fiducial limits illustrated in the case of
53-
the binomial.
54-
\emph{Biometrika}, \bold{26}, 404--413.
55-
\doi{10.2307/2331986}.
51+
\bibinfo{R:Hollander+Wolfe:1973}{footer}{Pages 15--22.}
52+
\bibshow{*, R:Hollander+Wolfe:1973}
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5754
William J. Conover (1971),
5855
\emph{Practical nonparametric statistics}.
5956
New York: John Wiley & Sons.
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Pages 97--104.
61-
62-
Myles Hollander & Douglas A. Wolfe (1973),
63-
\emph{Nonparametric Statistical Methods.}
64-
New York: John Wiley & Sons.
65-
Pages 15--22.
6658
}
6759
\seealso{
6860
\code{\link{prop.test}} for a general (approximate) test for equal or

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