diff --git a/Project.toml b/Project.toml
index 2cf97f9..29ffccc 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,18 +4,20 @@ keywords = ["multivariate statistics", "dimensionality reduction"]
 license = "MIT"
 desc = "A Julia package for multivariate statistics and data analysis"
 repository = "https://github.com/JuliaStats/MultivariateStats.jl.git"
-version = "0.9.0"
+version = "0.9.1"
 
 [deps]
 Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+StatsAPI = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
 Arpack = "0.3, 0.4, 0.5"
-StatsBase = "0.29, 0.30, 0.31, 0.32, 0.33"
+StatsBase = "~0.33"
+StatsAPI = "~1.2"
 julia = "1.1"
 
 [extras]
diff --git a/src/MultivariateStats.jl b/src/MultivariateStats.jl
index 3bc91fa..1f058d4 100644
--- a/src/MultivariateStats.jl
+++ b/src/MultivariateStats.jl
@@ -1,12 +1,15 @@
 module MultivariateStats
+
     using LinearAlgebra
-    using StatsBase: SimpleCovariance, CovarianceEstimator, RegressionModel,
-                     AbstractDataTransform, pairwise!
+    using SparseArrays
+    using Statistics: middle
+    using StatsAPI: RegressionModel
+    using StatsBase: SimpleCovariance, CovarianceEstimator, AbstractDataTransform,
+                     ConvergenceException, pairwise, CoefTable
+
     import Statistics: mean, var, cov, covm, cor
-    import Base: length, size, show, dump
-    import StatsBase: fit, predict, predict!, ConvergenceException, coef, weights,
-                      dof, pairwise, r2, CoefTable
-    import SparseArrays
+    import Base: length, size, show
+    import StatsAPI: fit, predict, coef, weights, dof, r2
     import LinearAlgebra: eigvals, eigvecs
 
     export
@@ -118,17 +121,17 @@ module MultivariateStats
     include("fa.jl")
 
     ## deprecations
-    @deprecate indim(f) size(f)[1]
-    @deprecate outdim(f) size(f)[2]
-    @deprecate transform(f, x) predict(f, x) #ex=false
+    @deprecate indim(f) size(f,1)
+    @deprecate outdim(f) size(f,2)
+    @deprecate transform(f, x) predict(f, x)
     @deprecate indim(f::Whitening) length(f::Whitening)
     @deprecate outdim(f::Whitening) length(f::Whitening)
     @deprecate tvar(f::PCA) var(f::PCA)
     @deprecate classical_mds(D::AbstractMatrix, p::Int) predict(fit(MDS, D, maxoutdim=p, distances=true))
     @deprecate transform(f::MDS) predict(f::MDS)
-    @deprecate xindim(M::CCA) size(M)[1]
-    @deprecate yindim(M::CCA) size(M)[2]
-    @deprecate outdim(M::CCA) size(M)[3]
+    @deprecate xindim(M::CCA) size(M,1)
+    @deprecate yindim(M::CCA) size(M,2)
+    @deprecate outdim(M::CCA) size(M,3)
     @deprecate correlations(M::CCA) cor(M)
     @deprecate xmean(M::CCA) mean(M, :x)
     @deprecate ymean(M::CCA) mean(M, :y)
diff --git a/src/cmds.jl b/src/cmds.jl
index 6d6f21f..0c2f82a 100644
--- a/src/cmds.jl
+++ b/src/cmds.jl
@@ -175,7 +175,7 @@ function predict(M::MDS, x::AbstractVector{T}; distances=false) where {T<:Real}
         else
             size(x, 1) != size(M.X, 1) && throw(
                 DimensionMismatch("Points and original data must have same dimensionality."))
-            pairwise((x,y)->norm(x-y), M.X, x)
+            pairwise((x,y)->norm(x-y), eachcol(M.X), eachcol(x))
         end
     end
 
diff --git a/src/common.jl b/src/common.jl
index 51becac..b6d23f2 100644
--- a/src/common.jl
+++ b/src/common.jl
@@ -120,6 +120,3 @@ function calcscattermat(Z::DenseMatrix)
     return calcscattermat(SimpleCovariance(), Z)
 end
 
-# calculate pairwise kernel
-pairwise(kernel::Function, X::AbstractMatrix, x::AbstractVector; kwargs...) =
-    [kernel(x,y) for y in eachcol(X)]
diff --git a/src/pca.jl b/src/pca.jl
index b7d78f4..a1f8495 100644
--- a/src/pca.jl
+++ b/src/pca.jl
@@ -134,7 +134,9 @@ gives the principal components for an observation, and \$\\mathbf{P}\$ is the pr
 """
 reconstruct(M::PCA, y::AbstractVecOrMat{T}) where {T<:Real} = decentralize(M.proj * y, M.mean)
 
-## show & dump
+
+## show
+
 function show(io::IO, M::PCA)
     idim, odim = size(M)
     print(io, "PCA(indim = $idim, outdim = $odim, principalratio = $(r2(M)))")
@@ -240,7 +242,7 @@ function pcasvd(Z::AbstractMatrix{T}, mean::AbstractVector{T}, n::Real;
     v = Svd.S::Vector{T}
     U = Svd.U::Matrix{T}
     for i = 1:length(v)
-        @inbounds v[i] = abs2(v[i]) / n
+        @inbounds v[i] = abs2(v[i]) / (n-1)
     end
     ord = sortperm(v; rev=true)
     vsum = sum(v)
diff --git a/src/types.jl b/src/types.jl
index 6ff1372..dbaecb1 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -1,5 +1,17 @@
 abstract type AbstractDimensionalityReduction <: RegressionModel end
 
+"""
+    size(model::AbstractDimensionalityReduction, d::Int)
+
+Returns the dimension of the input data if `d == 1`, the dimension of the output data
+if `d == 2`, otherwise throws error.
+"""
+function size(model::AbstractDimensionalityReduction, d::Integer)
+    dims = size(model)
+    @assert length(dims) >= d "Cannot access dimensional information"
+    return dims[d]
+end
+
 """
     projection(model::AbstractDimensionalityReduction)
 
diff --git a/test/cmds.jl b/test/cmds.jl
index dd22ce0..cdc3127 100644
--- a/test/cmds.jl
+++ b/test/cmds.jl
@@ -52,7 +52,7 @@ using Test
 
     @test_throws AssertionError predict(M, X0[:, 1])
     @test_throws DimensionMismatch predict(M, rand(d+1); distances = true)
-    d = MultivariateStats.pairwise((x,y)->norm(x-y), X0, X0[:,2]) #|> vec
+    d = MultivariateStats.pairwise((x,y)->norm(x-y), eachcol(X0), eachcol(X0[:,2])) |> vec
     y = predict(M, d, distances=true)
     @test X[:, 2] ≈ y
 
diff --git a/test/kpca.jl b/test/kpca.jl
index edf03e5..1142706 100644
--- a/test/kpca.jl
+++ b/test/kpca.jl
@@ -36,8 +36,7 @@ import Statistics: mean, cov
     # kernel calculations
     ker  = (x,y)->norm(x-y)
 
-    K = similar(X, n, n)
-    MultivariateStats.pairwise!(ker, K, eachcol(X))
+    K = MultivariateStats.pairwise(ker, eachcol(X), symmetric=true)
     @test size(K) == (n, n)
     @test K[1,1] == 0
     @test K[2,1] == norm(X[:,2] - X[:,1])
@@ -46,7 +45,7 @@ import Statistics: mean, cov
     Iₙ = ones(n,n)/n
     @test MultivariateStats.transform!(KC, copy(K)) ≈ K - Iₙ*K - K*Iₙ + Iₙ*K*Iₙ
 
-    K = MultivariateStats.pairwise(ker, X, X[:,1])[:,1:1]
+    K = MultivariateStats.pairwise(ker, eachcol(X), eachcol(X[:,1]))[:,1:1]
     @test size(K) == (n, 1)
     @test K[1,1] == 0
     @test K[2,1] == norm(X[:,2] - X[:,1])
diff --git a/test/pca.jl b/test/pca.jl
index db5de3d..5fb1559 100644
--- a/test/pca.jl
+++ b/test/pca.jl
@@ -24,6 +24,9 @@ import SparseArrays
     M = PCA(Float64[], P, pvars, 15.0)
 
     @test size(M) == (5, 3)
+    @test size(M,1) == 5
+    @test size(M,2) == 3
+    @test_throws AssertionError size(M, 3)
     @test mean(M) == zeros(5)
     @test projection(M) == P
     @test principalvars(M) == pvars